JPH05107330A - Three-dimensional position measurement by communication satellite - Google Patents

Abstract

PURPOSE:To measure the three-dimensional position of an object which is traced to its position at a measurement precision of 1mm or less by transmitting and receiving electric waves in a given procedure among the object, a wave relay which is mounted on a satellite and a ground fixed station (thereinafter called 'three stations'). CONSTITUTION:Electric waves transmitted and received in a given procedure among three stations are stored in a memory of a computer connected to a ground fixed station. A distance among three stations is measured from a time for carrying waves transmitted and received among three stations. The measurement of the wave carrying time among three stations is carried out many times to take a correlation among elapsed time mechanisms provided in three stations by using a statistical method, based on a elapsed time mechanism provided in the ground fixed station. Because waves are refracted by the effect of atmospheric gas, calculation for correcting the length of waves passing through the atmosphere is carried out. In order to instantly measure a distance among three stations, the elevation and azimuth angles of waves transmitted and received among three stations are determined from the wave carrying time among three stations.

Description

Detailed Description of the Invention

[0001]

SUMMARY OF THE INVENTION The present invention relates to a wireless position measurement system using an artificial earth satellite, and more specifically to a method for monitoring position using one communication satellite. One satellite is sufficient to locate the position of objects on the ground and in the air by distance measurement. The position and distance are determined from the propagation delay time when a wireless signal travels at the speed of light and is transmitted and received between an object via a satellite and a fixed station on the ground. If the time position of the satellite is known, the position line of the object can be calculated from one satellite having a different time position, and the observation position is at the intersection of the three position lines. The distance measurement accuracy at the observation position is within 1 mm.

[0002]

2. Description of the Related Art Considering the use of a communication satellite for wireless measurement in which position observation is performed by using a wireless signal, often requiring two satellites is a difficulty. The present invention overcomes this difficulty by requiring only one communication satellite. Further, there is an observation position determination system which is performed by one communication satellite (and active range finder satellite), but there is a drawback that two timing signal satellites are further required to exhibit the same function. Moreover, the ranging accuracy of the observation position is 100 m to 1500 m.

[0003]

BACKGROUND OF THE INVENTION The present invention is intended to provide early position monitoring, ie, tracking of human, vehicle and aircraft positions, at fixed ground stations using current or potential satellites. Is influential in. Possible applications include length, area and height measurements, ie surveying, location monitoring of oil tankers and other dangerous cargo-laden vessels, for disaster prevention and environmental protection. Effective monitoring of foreign vessels within 200 nautical miles, offshore surveillance of aircraft for traffic control, navigation of commercial vessels from land and vessel location, and location of land mobile vehicles. .. Others include position control of intercontinental ballistic bullets, satellite orbit correction and attitude control, and tracking of missiles. This method can spread its service on a global scale, can achieve high accuracy, and is cheaper than other proposed schemes.

[0004]

[Means for solving the problem]

[Action]

1. Radio wave propagation control (1) Propagation control of radio waves radiated from the object The transmitter antenna position of the object whose position is to be determined (hereinafter referred to as the transmitter antenna position) is time T.
_{At M11} , it is at point M11. The antenna position of the radio repeater mounted on the satellite (hereinafter referred to as the radio repeater antenna position) is point P11 at time T _M11 .
It is in. The antenna position of the fixed ground station is at point W11 at time T _M11 . At time T _M11 , a radio wave is radiated from the transmitter antenna position, and the time when the radio wave reaches the radio repeater antenna position is T _P12 . During time (T _P12 -T _M11 ), the transmitter antenna position changes from point M11 to point M12, the radio repeater antenna position changes from point P11 to point P12, and the fixed ground station antenna position changes from point W11 to point W11. Move to W12. Assuming that the radio relay time of the radio repeater is Δτ, the radio wave reaching the radio repeater at time T _P12 is emitted from the radio repeater at time (T _P12 + Δτ). Time (T _P12 + Δ
τ), the transmitter antenna position moves to point M13, the radio repeater antenna position moves to point P13, and the fixed ground station antenna position moves to point W13. Time (T _P12
+ Δτ), the time when the radio wave radiated from the radio repeater antenna position reaches the fixed ground station antenna position is T
_W14 . At time T _W14 , the transmitter antenna position is at point M14, and the radio repeater antenna position is at point P1.
4, the antenna position of the fixed ground station moves to point W14. The above is summarized in Table 1. The above is illustrated in FIG. At time T _MX , when the time when the radio wave radiated from the transmitter antenna position reaches the radio repeater antenna position is (T _P12 + Δτ), when the radio repeater moves from point P12 to point P13 Since it is a radio wave that has just reached, the error in the radio wave path length due to the refractive index of atmospheric gas is ignored, and C ((T _P12 + Δ
τ) -T _MX ) is the distance between the point MX and the point P13.
(In the time column when the radio wave reaches the radio repeater antenna in Table 2, the radio wave equal to T _P12 + Δτ corresponds to this.) In order to determine the time T _MX , first, from the transmitter antenna position, Radio waves are radiated toward a radio relay station for a certain time period and at a certain time interval, and these radio waves reach a fixed ground station via the radio wave relay station. In the fixed ground station, these received radio waves are stored in the storage device of the electronic computer connected to the fixed ground station as shown in Table 2. Using Table 2,
The distance between the point MX and the point P13 is determined according to the flow chart of FIG.

(2) Propagation Control of Radio Waves Emitted from Fixed Ground Stations The time when radio waves are radiated from the fixed ground station is T _WX , and the position of the fixed ground station at this time T _WX is point WX. The time when this radio wave returns to the fixed ground station again is T
_WY , the position of the fixed ground station at this time T _WY is defined as point WY. The time when the radio wave is radiated from the transmitter antenna position is T
The radio wave of _M11 reaches the fixed ground station at time T _W14 . The position of the fixed ground station at this time is point W14.
If time T _WY is the same as time T _W14 , time T
After reaching the radio repeater, the radio wave radiated from the fixed ground station in _WX passes the same route as the radio wave radiated from the transmitter antenna position at time T _M11 . In order to determine the time _TWX , first, radio waves are radiated from the fixed ground station at a fixed time and at a fixed time interval, and these radio waves are displayed on a storage device of a computer installed in the fixed ground station. It is stored like 3. Using Table 3, the distance between the point WX and the point P12 can be calculated according to the flow chart of FIG.

(3) Radio wave propagation control in the object and the fixed ground station in the reception mode In the object and the fixed ground station, the transmission mode and the reception mode are sequentially repeated. When in the transmission mode, the incoming radio wave is not received and either the radio wave is radiated or nothing is performed. When in the receive mode, no radio waves are emitted and either incoming radio waves are received or nothing is done. (A) When the object is in the reception mode. When the radio wave arrives at the antenna, the incoming radio wave is stored in the reception data buffer via the diplexer. Next, the time when the radio wave arrives at the antenna is determined by considering the delay time from the antenna to the reception data buffer by the aging mechanism provided in the object. Then, the radio wave arrival time is added to the end of the data stored in the received data buffer. When the object is switched to transmit mode, the contents of the received data buffer are sent to the transmitter and further radiated from the antenna via the diplexer. In addition, received data
The data in the buffer is guaranteed until the object goes from receive mode to send mode and then to the next receive mode. The data stored in the received data buffer is as shown in Table 4. (B) Radio wave propagation control of the fixed ground station in the reception mode: The arrival time of the incoming radio wave is determined by the aging mechanism in the fixed ground station, and the content of the received radio wave is stored in the electronic equipment connected to the fixed ground station. Process by computer.

(4) Radio wave path using radio wave propagation control
Measuring the length L The distance between point M11 and point P12 is L₁And atmosphere
Due to the effect of the refractive index of the gas, L₁= [[-HΣ_{i = 1} ⁿtan α_1i+ {C (T_P12-T_M11  ) -HΣ_{i = 1} ⁿ(1 / cos α_1i)} Sin α₁₀]^Two + [Nh + {c (T_P12-T_M11) -HΣ_{i = 1} ⁿ(1 / cos α_1i)} Cos α₁₀]^Two]^1/2 nh is the refractive index of atmospheric gas in units of 1 km in height from point M11
The height when dividing up to a height of 1 parallel to the ground surface
The difference is usually h = 1 and n = 500. c is in vacuum
Propagation speed of radio waves in T_P12Is from point M11 to time T
_M11When the radiated radio waves reach the radio repeater
Tick, T_M11Is the time α at which the radio wave was emitted from point M11
_1i(I = 1 to n) is for each parallel plane layer of thickness h
Incident angle of radio wave, α₁₀Is above the height nhkm from point M11
It is the refraction angle of the radio wave to the parallel plane layer of the atmosphere in the sky. Snell
In the parallel plane layer (n = 1 to 12),_1Bsin α_1B= N₁₁sin α₁₁= N₁₂si
nα₁₂＝ ・ ・ ・ ・ ・ ＝ n_1isin α_1i= ...
= N₁₁₂sin α₁₁₂= N₁₀sin α₁₀  n₁₀Is a known value of the refractive index of radio waves in a vacuum. or,
n_1BIs the refractive index of atmospheric gas at point M11, and
For measuring atmospheric pressure, vapor pressure and absolute temperature of M11
Get more. n₁₁, N₁₂・ ・ ・ ・ ・ ・ ・ ・ N_1i...
..N₁₁₂Is n_1BAnd the atmosphere 1 km above the point M11
If the refraction index of the gas is known, it can be obtained from an empirical formula. Parallel sphere
In the layer (n = 12 to 500), (n₁₁₂+ 12 / a) sin α₁₁₂= (N₁₁₃+
13 / a) sin α₁₁₃＝ ・ ・ ・ ・ ・ ＝ (n_1i+ I
/ A) sin α_1i＝ ・ ・ ・ ・ ・ ＝ (n₁₅₀₀+50
0 / a) sin α₁₅₀₀= N₁₀sin α₁₀  Where a is the radius of the earth and n₁₁₂, N₁₁₃...
・ N_1i・ ・ ・ ・ ・ ・ ・ ・ N₁₅₀₀Is the atmospheric gas in the stratosphere
Refractive index, which is more stable than that of atmospheric gases in the troposphere
Yes, and ask experimentally. Also, α₁₀Is how to calculate elevation
From the law, cos α₁₀= KhΣ_{i = 1} ⁿ(1 + n_i) / {(T_P12-T_M1 1) (c ± V)}. However, V is the rotation speed of the earth, K is α₁₀To
Is the corresponding proportionality constant. From the above, L₁Is determined. Immediately
Then, the shortest distance between the point M11 and the point P12 is determined. The distance between points P13 and W14 is L_ThreeAnd atmosphere
Due to the effect of the refractive index of the gas, L_Three= [[-HΣ_{i = 1} ⁿtan α_3i+ {C (T_W14-(TP₁₂ + Δτ))-hΣ_{i = 1} ⁿ(1 / cos α_3i)} Sin α_Thirty]^Two+ [N h + {c (T_W14-(T_P12) + Δτ))-hΣ_{i = 1} ⁿ(1 / cos α_Three i)} cos α_Thirty]^Two]^1/2 nh is the refractive index of atmospheric gas at a height of 1 km from the ground surface
Altitude when dividing up to the height of 1 parallel to the ground surface
The difference is usually h = 1 and n = 500. c is in vacuum
Propagation speed of radio wave, T_P12Is from point M11 to time T
_M11When the radiated radio waves reach the radio repeater
Tick, T_M11Is the time when the radio wave was radiated from the point M11, T
_W14From point M11 to time T_M11Was radiated when
Radio waves are transmitted via the radio relay station, fixed ground station antenna position W14
The time of arrival at α_3i(I = 1 to n) is each thickness h
Refraction angle of radio wave to the plane parallel to the atmosphere, α_ThirtyIs from the ground surface
Incident of radio waves on the parallel plane layer of the atmosphere above the height nhkm
It is a horn. From Snell's law, parallel plane layers (i = 1 to 1)
In 2), n_3Bsin α_3B= N₃₁sin α₃₁= N₃₂si
nα₃₂＝ ・ ・ ・ ・ ・ ＝ n_3isin α_3i...
= N₃₁₂sin α₃₁₂= N_Thirtysin α_Thirty n_ThirtyIs a known value of the refractive index of radio waves in a vacuum. or,
n_3BIs the refractive index of atmospheric gas at W14, and W1
By measuring the atmospheric pressure, vapor pressure and absolute temperature of 4
I want it. n₃₁, N₃₂... n_3i... n
₃₁₂Is n_3BOf atmospheric gas 1km above W14 and W14
If the folding index is known, it can be obtained from an empirical formula. Parallel spherical layer (i =
12-500), (n₃₁₂+ 12 / a) sin α₃₁₂= (N₃₁₃+
13 / a) sin α₃₁₃＝ ・ ・ ・ ・ ・ ＝ (n_3i+ I
/ A) sin α_3i＝ ・ ・ ・ ・ ・ ＝ (n₃₅₀₀+50
0 / a) sin α₃₅₀₀= N_Thirtysin α_Thirty Where a is the radius of the earth and n₃₁₂, N₃₁₃...
・ N_3i... n₃₅₀₀Is the amount of atmospheric gas in the stratosphere
It is an index of refraction and is more stable than the refractive index of atmospheric gas in the troposphere.
It is experimentally obtained. Also, α_ThirtyIs the elevation angle calculation method
From cos α_Thirty= KhΣ_{i = 1} ⁿ(1 + n_i) / [{T_W14-(T_{P 12} + Δτ)} (c ± V)]. However, V is the rotation speed of the earth, K is α_ThirtyTo
Is the corresponding proportionality constant. From the above, L_ThreeIs determined. Immediately
Then, the shortest distance between the point P13 and the point W14 is determined. The distance between point WX and point W14 is L₅And L₅= V (T_W14-T_WX) V is the rotation speed of the earth. T_W14Is the transmitter antenna position M
11 to time T_M11The radio waves emitted during
When the fixed ground station antenna position W14 via the relay is reached
Ticks. T_WXHas reached the position P12 of the radio repeater antenna
Time is T_P12Fixed ground station antenna position, as in
The emission time of the radio wave emitted from WX. T_P12Is the transmitter
From antenna position M11, time T_M11Is radiated when
When the radio wave reaches the radio repeater antenna position P12
Ticks. The distance between the point P12 and the point WX is L₆And Atmosphere
Due to the influence of the refractive index of the₆= [[-HΣ_{i = 1} ⁿtan_6i+ {C (T_P12-T_WX) − HΣ_{i = 1} ⁿ(1 / cos α_6i)} Sin α₆₀]^Two+ [Nh + {c (T_{P1 Two} -(T_WX) -HΣ_{i = 1} ⁿ(1 / cos α_6i)} Cos α₆₀]^Two]^{1 / Two} nh is the refractive index of atmospheric gas at a height of 1 km from the ground surface
Altitude when dividing up to the height of 1 parallel to the ground surface
The difference is usually h = 1 and n = 500. c is in vacuum
Propagation speed of radio wave, T_P12Is from point M11 to time T
_M11When the radiated radio waves reach the radio repeater
Tick, T_WXHas reached the position P12 of the radio repeater antenna
Time is T_P12Fixed ground station antenna position, as in
The emission time of the radio wave emitted from WX. α_6i(I = 1 to 1
n) is the angle of incidence of radio waves on each parallel plane layer of thickness h,
α₆₀Is a parallel plane of the atmosphere above nhkm above the ground surface
It is the refraction angle of the radio wave to the surface layer. Parallel flat from Snell's law
In the surface layer (i = 1 to 12), n_6Bsin α_6B= N₆₁sin α₆₁= N₆₂si
nα₆₂＝ ・ ・ ・ ・ ・ ＝ n_6isin α_6i= ...
・ ＝ n₆₁₂sin α₆₁₂= N₆₀sin α₆₀  n₆₀Is a known value of the refractive index of radio waves in a vacuum. or,
n_6BIs the refractive index of atmospheric gas at point WX,
By measuring the atmospheric pressure, vapor pressure and absolute temperature of X
I want it. n₆₁, N₆₂... n_6i... n
₆₁₂Is n_6BAnd bending of atmospheric gas 1 km above the point WX
If the folding index is known, it can be obtained from an empirical formula. Parallel spherical layer (i =
12-500), (n₆₁₂+ 12 / a) sin α₆₁₂= (N₆₁₃+
13 / a) sin α₆₁₃＝ ・ ・ ・ ・ ・ ＝ (n_6i+ I
/ A) sin α_6i＝ ・ ・ ・ ・ ・ ＝ (n₆₅₀₀+50
0 / a) sin α₆₅₀₀= N₆₀sin α₆₀ Where a is the radius of the earth and n₆₁₂, N₆₁₃...
・ N_6i... n₆₅₀₀Is the amount of atmospheric gas in the stratosphere
It is a refractive index and is more stable than the refractive index of atmospheric gas in the troposphere.
It is experimentally obtained. Also, α₆₀Is the elevation angle calculation method
From cos α₆₀= KhΣ_{i = 1} ⁿ(1 + n_i) / {(T_P12-T_WX ) (C ± V)}. However, V is the rotation speed of the earth, K is α₆₀To
Is the corresponding proportionality constant. From the above, L₆Is determined. Immediately
Then, the shortest distance between the point P12 and the point WX is determined. The distance between the point P13 and the point MX is L₇And Atmosphere
Due to the influence of the refractive index of the₇= [[-HΣ_{i = 1} ⁿtan_7i+ {C ((T_P12+ Δτ) -T_MX) -HΣ_{i = 1} ⁿ(1 / cos α_7i)} Sin α₇₀]^Two+ [Nh + {c ((T_P12+ Δτ) -T_MX) -HΣ_{i = 1} ⁿ(1 / cos α_7i)} Co s α₇₀]^Two]^1/2 nh is the refractive index of atmospheric gas in units of 1 km in height from point M11
The height when dividing up to a height of 1 parallel to the ground surface
The difference is usually h = 1 and n = 500. c is in vacuum
Propagation speed of radio waves in T_P12Is from point M11 to time T
_M11When the radiated radio waves reach the radio repeater
Tick, T_MXHas reached the position P13 of the radio repeater antenna
Time is T_P12Transmitter antenna position as + Δτ
The emission time of the radio waves emitted from the MX. α_7i(I = 1
~ N) is the incidence of radio waves on each parallel plane layer of thickness h
Horn, α₇₀Is the atmospheric level above the height nhkm from point MX
It is the refraction angle of the radio wave to the row plane layer. From Snell's law,
In the parallel plane layer (i = 1 to 12), n_7Bsin α_7B= N₇₁sin α₇₁= N₇₂si
nα₇₂＝ ・ ・ ・ ・ ・ ＝ n_7isin α_7i= ...
・ ＝ n₇₁₂sin α₇₁₂= N₇₀sin α₇₀ n₇₀Is a known value of the refractive index of radio waves in a vacuum. or,
n_7BIs the refractive index of atmospheric gas at point M11, and
For measuring atmospheric pressure, vapor pressure and absolute temperature of M11
Get more. n₇₁, N₇₂・ ・ ・ ・ ・ ・ ・ ・ N_7i...
..N₇₁₂Is n_7BAnd the atmosphere 1 km above the point M11
If the refraction index of the gas is known, it can be obtained from an empirical formula. Parallel sphere
In the layer (i = 12 to 500), (n₇₁₂+ 12 / a) sin α₇₁₂= (N₇₁₃+
13 / a) sin α₇₁₃＝ ・ ・ ・ ・ ・ ＝ (n_7i+ I
/ A) sin α_7i= ... ・ = (n₇₅₀₀+500
/ A) sin α₇₅₀₀= N₇₀sin α₇₀  Where a is the radius of the earth and n₇₁₂, N₇₁₃...
・ N_7i... n₇₅₀₀Is the amount of atmospheric gas in the stratosphere
It is an index of refraction and is more stable than the refractive index of atmospheric gas in the troposphere.
It is experimentally obtained. Also, α₇₀Is the elevation angle calculation method
From cos α₇₀= KhΣ_{i = 1} ⁿ(1 + n_i) / {((T_{P 12} + Δτ) -T_WX) (C ± V)}. However, V is the rotation speed of the earth, K is α₇₀To
It is a proportional constant of the corresponding azimuth. From the above, L₇Is constant
Maru That is, the shortest distance between the point P13 and the point MX is determined.
To do. The distance between points M11 and MY is L₉, Point P12 and point
The distance between MY and L₁₀And Time T_M11Noto
The transmitter antenna position M₁₁To the radio repeater from
The emitted radio wave is at time T_P12When this radio repeater
To reach. This time T_P12When this radio repeater
From the ground to the surveyor in reception mode on the ground
Select a wave. This selected radio wave is received by the ground reception mode.
The time to reach the surveyor in Do_MYAnd Also, time
Tick T_MYPosition of the surveyor in reception mode on the ground at
Is the point MY. L₉= V (T_MY-T_M11) V is the rotation speed of the earth. T_M11Is the transmitter antenna position M
The time when the radio wave was emitted from 11 to the radio repeater. Big
L due to the influence of the refractive index of gas₁₀= [[-HΣ_{i = 1} ⁿtan_10i+ {C ((T_MY-T_{P1 Two} ) -HΣ_{i = 1} ⁿ(1 / cos α_10i)} Sin α₁₀₀]^Two+ [Nh + {c (T_MY-T_P12) -HΣ_{i = 1} ⁿ(1 / cos α_10i)} Cos α_{10 0} ]^Two]^1/2 nh is the refractive index of atmospheric gas in units of 1 km in height from point M11
The height when dividing up to a height of 1 parallel to the ground surface
The difference is usually h = 1 and n = 500. c is in vacuum
Propagation speed of radio waves in T_P12Is from point M11 to time T
_M11When the radiated radio waves reach the radio repeater
Tick, α_10i(I = 1 to n) is a parallel plane of each atmosphere with thickness h
Refraction angle of radio wave to surface layer, α₁₀₀Is the height n from the point M11
It is the angle of incidence of radio waves on the parallel plane layer of the atmosphere above hkm.
It From Snell's law to parallel plane layers (i = 1 to 12)
By the way, n_10Bsin α_10B= N₁₀₁sin α₁₀₁= N
₁₀₂sin α₁₀₂・ ・ ・ ・ ＝ n_10isin α
_10i＝ ・ ・ ・ ・ ・ ＝ n₁₀₁₂sin α₁₀₁₂= N
₁₀₀sin α₁₀₀ n₁₀₀Is a known value of the refractive index of radio waves in a vacuum.
Also, n_10BIs the refractive index of atmospheric gas at point MX
Measure the atmospheric pressure, vapor pressure and absolute temperature at point M11.
It can be obtained by things. n₁₀₁, N₁₀₂・ ・ ・ ・ ・ ・ ・ ・ N
_10i... n₁₀₁₂Is n_10BAnd point MI1
If you know the refraction index of atmospheric gas 1km above the sky,
I want it. In the parallel spherical layer (i = 12 to 500), (n₁₀₁₂+ 12 / a) sin α₁₀₁₂= (N
₁₀₁₃+ 13 / a) sin α₁₀₁₃＝ ・ ・ ・ ・ ・ ＝
(N_10i+ I / a) sinα_10i＝ ・ ・ ・ ・ ・ ＝
(N₁₀₅₀₀+ 500 / a) sin α₁₀₅₀₀= N
₁₀₀sin α₁₀₀ Where a is the radius of the earth and n₁₀₁₂, N₁₀₁₃・ ・ ・
... n_10i... n₁₀₅₀₀Is the atmosphere of the stratosphere
The refractive index of gas, which is lower than that of atmospheric gases in the troposphere.
It has been determined experimentally. Also, α₁₀₀Is elevation
From the calculation method₁₀₀= KhΣ_{i = 1} ⁿ(1 + n_i) / {(T_{M Y} -T_P12) (C ± V)}. However, V is the rotation speed of the earth, K is α₁₀₀
Is a proportional constant corresponding to. From the above, L₁₀Is fixed
It That is, the shortest distance between the point P12 and the point MY is fixed.
It The distance between the point M11 and the point P13 is L₈And Point M
The distance between 11 and the point MX is L₁₁And L₁₁= V (T_MX= T_M11) V is the rotation speed of the earth. T_MXIs a satellite-mounted radio repeater
The time when the antenna position P13 is reached is T_P12+ Δτ
Radio wave is emitted from the transmitter antenna position MX.
Time when By the second law of the cosine of the triangle, L₁₀ ^Two= L₁ ^Two+ L₉ ^Two-2L₁L₉cos∠P12 ・ M11 ・ MY ∴cos∠P12 ・ M11 ・ MY = (L₁ ^Two+ L₉ ^Two-L₁₀ ^Two) / 2L₁L₉(B-1) The distance between point P12 and point MX is L₁₂Then, L₁₂ ^Two= L₁ ^Two+ L₁₁ ^Two-2L₁L₁₁cos∠P12 · M1 1 · MY ... (B-2) Substituting equation (B-1) into equation (B-2). L₁₂ ^Two= L₁ ^Two+ L₁₁ ^Two-(2L₁L₁₁) ・ {(L₁ ^Two+ L₉ ^Two -L₁₀ ^Two) / 2L₁L₉} = L₁ ^Two+ L₁₁ ^Two-L₁₁(L₁ ^Two+ L₉ ^Two-L₁₀ ^Two) / L₉(B-3) From the formula (B-3), the distance L between the point P12 and the point MX
₁₂Is confirmed. ∠P13 ・ P12 ・ MX = γ, ∠M1
1 · P12 · MX = δ. L₇ ^Two= L_Two ^Two+ L₁₂ ^Two-2L_TwoL₁₂cosγ ∴cosγ = (L_Two ^Two+ L₁₂ ^Two-L₇ ^Two) / 2L_TwoL₁₂........... (B-4) L₁₁ ^Two= L₁ ^Two+ L₁₂ ^Two-2L₁L₁₂cos δ ∴ cos δ = (L₁ ^Two+ L₁₂ ^Two-L₁₁ ^Two) / 2L₁L₁₂········ (B-5) ∠M11 · P12 · P13 = γ + δ. L₈ ^Two= L₁ ^Two+ L_Two ^Two-2L₁L_Twocos (γ + δ) = L₁ ^Two+ L_Two ^Two-2L₁L_Two(Cos γ cos δ-sin γ sin δ) ... (B-6) sin γ = (1-cos^Twoγ)^1/2= [1-{(L_Two ^Two+ L₁₂ ^Two  -L₇ ^Two) / (2L_TwoL₁₂)}^Two]^1/2(B-7) sin δ = (1-cos^Twoδ)^1/2= [1-{(L₁ ^Two+ L₁₂ ^Two  -L₁₁ ^Two) / (2L₁L₁₂)}^Two]^1/2(B-8) Formulas (B-4), (B-5), (B-7) and (B-8)
Is substituted into equation (B-6). L₈ ^Two= L₁ ^Two+ L_Two ^Two-2L₁L_Two[{(L_Two ^Two+ L₁₂ ^Two-L₇ ^Two) / (2L_TwoL₁₂)} {(L₁ ^Two+ L₁₂ ^Two-L₁₁ ^Two) / (2L₁L₁₂)}-[1-{(L_Two ^Two+ L₁₂ ^Two-L₇ ^Two) / (2L_TwoL₁₂)}^Two]^1/2・ [1-{(L₁Two_{+ L12} ^Two-L₁₁ ^Two) / (2L₁L₁₂)}^Two]^1/2] L₈= <L₁ ^Two+ L_Two ^Two-2L₁L_Two[{(L_Two ^Two+ L₁₂ ^Two-L₇ ^Two) / (2L_TwoL₁₂)} {(L₁ ^Two+ L₁₂ ^Two-L₁₁ ^Two) / (2L₁L₁₂)}-[1-{(L_Two ^Two+ L₁₂ ^Two-L₇ ^Two) / (2L_TwoL₁₂)}^Two] 1/2 ・ [1-{(L₁ ^Two+ L₁₂ ^Two-L₁₁ ^Two) / (2L₁L₁₂)}^Two]^1/2]^1/2>^1/2 From the above, L₈Is confirmed. The distance between point WY and point W14 is L₂₁And L₂₁= V (T_W14-T_WY) V is the rotation speed of the earth. T_W14(Is the transmitter antenna position
M11 to time T_M11The radio waves emitted when
When the fixed ground station antenna position W14 via the repeater is reached
Ticks. T_WYIs time T_P12When the radio repeater antenna position
Radio waves radiated from P12 reach fixed ground station position WY
The time reached. The distance between point P12 and point WY is L₂₀And atmosphere
Due to the effect of the refractive index of the gas, L₂₀= [[-HΣ_{i = 1} ⁿtan α_20i+ {C (T_WY-T_{P1 Two} ) -HΣ_{i = 1} ⁿ(1 / cos α_20i)} Sin α₂₀₀]^Two+ [Nh + {c (T_WY-T_P12) -HΣ_{i = 1} ⁿ(1 / cos α_20i)} Cos α_{20 0} ]^Two]^1/2 nh is the refractive index of atmospheric gas at a height of 1 km from the ground surface
Altitude when dividing up to the height of 1 parallel to the ground surface
The difference is usually h = 1 and n = 500. c is in vacuum
Propagation speed of radio wave, T_P12Is from point M11 to time T
_M11When the radiated radio wave reaches the radio repeater
Tick, α_20i(I = 1 to n) is a parallel plane of each atmosphere with thickness h
Refraction angle of radio wave to surface layer, α₂₀₀Is the height nh from the point MY
It is the angle of incidence of the radio wave on the parallel plane layer of the atmosphere above km.
It From Snell's law to parallel plane layers (i = 1 to 12)
By the way, n_20Bsin α_20B= N₂₀₁sin α₂₀₁= N
₂₀₂sin α₂₀₂= ... n_20isin α
_20i= ... n₂₀₁₂sin α₂₀₁₂= N
₂₀₀sin α₂₀₀  n₂₀₀Is a known value of the refractive index of radio waves in a vacuum.
Also, n_20BIs the refractive index of atmospheric gas at point MY
To measure the atmospheric pressure, vapor pressure and absolute temperature at point MY.
Determined by n₂₀₁, N₂₀₂... n
_20i... n₂₀₁₂Is n_20BAnd above the point MY
If the refraction index of the atmospheric gas at 1 km in the sky is known, it can be obtained from the experimental formula.
Maru In the parallel spherical layer (i = 12 to 500), (n₂₀₁₂+ 12 / a) sin α₂₀₁₂= (N
₂₀₁₃+ 13 / a) sin α₂₀₁₃＝ ・ ・ ・ ・ ・ ＝
(N_20i+ I / a) sinα_20i＝ ・ ・ ・ ・ ・ ＝
(N_20,500+ 500 / a) sin α_20,500= N
₂₀₀sin α₂₀₀  Where a is the radius of the earth and n₂₀₁₂, N₂₀₁₃・ ・ ・
... n_20i・ ・ ・ ・ ・ ・ ・ ・ N_20,500Is large in the stratosphere
There is an index of refraction of air gas, which is more than that of atmospheric gas in the troposphere.
Stable and experimentally sought. Also, α₂₀₀Is upside down
From the calculation method of the angle,₂₀₀= KhΣ_{i = 1} ⁿ(1 + n_i) / {(T_{W Y} -T_P12) (C ± V)}. However, V is the rotation speed of the earth, K is α₂₀₀
Is a proportional constant corresponding to. From the above, L₂₀Is fixed
It That is, the shortest distance between the point P12 and the point WY is determined.
It (10) Set the distance between point P12 and point W14 to L_ThirteenTosu
It The coordinates of the point P12 with the origin of the point W14 are P12.
(X, Y). (X-L₅)^Two+ Y_Two ^Two= L₆ ^Two・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ (C-1) (XL₂₁)^Two+ Y^Two= L₂₀ ^Two(C-2) From the formulas (C-1) and (C-2), X = (L₆ ^Two-L₂₀ ^Two-L₅ ^Two+ L₂₁ ^Two) / 2 (L₂₁-L₅) ........... (C-3) Substituting the expression (C-3) into the expression (C-1). Y = [L₆ ^Two-{(L₆ ^Two-L₂₀ ^Two+ L₂₁ ^Two-2L₅L₂₁+ L₅ ^Two ) / 2 (L₂₁-L₅)}^Two]^1/2..... (C-4) From formulas (C-3) and (C-4), L_Thirteen ^Two= X^Two+ Y^Two= {(L₆ ^Two-L₂₀ ^Two-L₅ ^Two+ L₂₁ ^Two) / 2 (L₂₁-L₅)}^Two+ [[L₆ ^Two-{(L₆ ^Two-L₂₀ ^Two+ L₂₁ ^Two-2 L₅L₂₁+ L₅ ^Two) / 2 (L₂₁-L₅)}^Two] 1/2]^Two  ∴L_Thirteen= [{(L₆ ^Two-L₂₀ ^Two-L₅ ^Two+ L₂₁ ^Two) / 2 (L₂₁  -L₅)}^Two+ [L₆ ^Two-{(L₆ ^Two-L₂₀ ^Two+ L₂₁ ^Two-2L₅L₂₁+ L₅ ^Two ) / 2 (L₂₁-L₅)}^Two]] 1/2 [11] Time T_W14Position W14 of fixed ground station at
With the origin as time T_P12Position of the radio repeater when
Set the coordinates of P12 to P12 (X_P12, Y_P12，
Z_P12). The radio wave radiated from the point P12
The elevation angle of the radio wave when it reaches the position WY of the fixed ground station is β
_20nThen the angle β_20nIs confirmed
It X_P12 ^Two+ Y_P12 ^Two+ Z_P12 ^Two= L_Thirteen ^Two・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ (G-1) X_P12 ^Two+ (Y_P12-L₂₁)^Two+ Z_P12 ^Two= L₂₀ ^Two・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ (G-2) Z_P12= L₂₀sin β_20n..................... (G-3) From the formulas (G-1) and (G-2), Y_P12= (L_Thirteen ^Two-L₂₀ ^Two+ L₂₁ ^Two) / 2L₂₁... (G-4) From formulas (G-1), (G-3) and (G-4), X_P12[L_Thirteen ^Two-{(L_Thirteen ^Two-L₂₀ ^Two+ L₂₁ ^Two) / (2L₂₁ )}^Two-L₂₀ ^Twosin^Twoβ_20n]^1/2.. (G-5) L_Thirteen, L₂₀, L₂₁And β_20nIs confirmed
Coordinate P12 (X_P12, Y_P12, Z
_P12) Is also confirmed. (13) Set the distance between point WZ and point P13 to L₁₈Tosu
It Due to the influence of the refractive index of atmospheric gas, L₁₈= [[-HΣ_{i = 1} ⁿtan α_18i+ {C ((T_P12+ Δτ) -T_WZ) -HΣ_{i = 1} ⁿ(1 / cos α_18i)} Sin α₁₈₀]^Two+ [Nh + {c ((T_P12+ Δτ) -T_WZ) -HΣ_{i = 1} ⁿ(1 / cos α_18i )} Cos α₁₈₀]^Two]^1/2 nh is the refractive index of atmospheric gas at a height of 1 km from the ground surface
Altitude when dividing up to the height of 1 parallel to the ground surface
The difference is usually h = 1 and n = 500. c is in vacuum
Propagation speed of radio wave, T_P12Is from point M11 to time T
_M11When the radiated radio wave reaches the radio repeater
Tick, T_WZHas reached the position P13 of the radio repeater antenna
Time is T_P12Fixed ground station antenna
The emission time of the radio wave emitted from the position WZ. α
_18i(I = 1 to n) is for each atmospheric parallel plane layer of thickness h
Angle of incidence of radio waves, α₁₈₀Is nhkm above the ground
It is the refraction angle of the radio wave to the plane parallel layer in the upper atmosphere. Su
According to Nell's law, in parallel plane layers (i = 1 to 12)
Is n₁₈Bsinα₁₈B = n₁₈₁sin α₁₈₁= N
₁₈₂sin α₁₈₂・ ・ ・ ・ ・ ＝ n_18isin α
_18i＝ ・ ・ ・ ・ ・ ＝ n₁₈₁₂sin α₁₈₁₂= N
₁₈₀sin α₁₈₀  n₁₈₀Is a known value of the refractive index of radio waves in a vacuum.
Also, n_18BIs the refractive index of atmospheric gas at point W14
Measure the atmospheric pressure, vapor pressure and absolute temperature at point W14
It can be obtained by things. n₁₈₁, N₁₈₂・ ・ ・ ・ ・ ・ ・ ・ N
_18i... n_{1812 is n18B}And at point W14
If you know the refraction index of atmospheric gas 1km above the sky,
I want it. In the parallel spherical layer (i = 12 to 500), (n₁₈₁₂+ 12 / a) sin α₁₈₁₂= (N
₁₈₁₃+ 13 / a) sin α₁₈₁₃＝ ・ ・ ・ ・ ・ ＝
(N_18i+ I / a) sinα_18i＝ ・ ・ ・ ・ ・ ・ ＝
(N₁₈₅₀₀+ 500 / a) sin α₁₈₅₀₀= N
₁₈₀sin α₁₈₀  Where a is the radius of the earth and n₁₈₁₂, N₁₈₁₃・ ・ ・
..N_18i... n₁₈₅₀₀Is the atmospheric gas in the stratosphere
Refractive index, which is more stable than that of atmospheric gases in the troposphere
Yes, and ask experimentally. Also, α₁₈₀Is the elevation calculation
From the method, cos α₁₈₀= KhΣ_{i = 1} ⁿ(1 + n_i) / {((T_p12+ Δ τ) -T_WZ) (C ± V)}. However, V is the rotation speed of the earth, K is α₁₈₀
Is a proportional constant corresponding to. From the above, L₁₈Is fixed
It That is, the distance L between the point WZ and the point P13₁₈Is confirmed
To do. (14) Set the distance between point WZ and point W14 to L₂₂Tosu
It L₂₂= V (T_W14-T_WZ) V is the rotation speed of the earth. T_W14Is the transmitter antenna position M
11 to time T_M11The radio waves emitted during
The time when the antenna reaches the ground station antenna position W14 via the relay. T
_WZIs the time when it reached the radio repeater antenna position P13
T_P12Fixed ground station antenna position as + Δτ
The emission time of the radio wave emitted from WZ. ▲ 15 ▼ Time T_W14Position W14 of fixed ground station at
With the origin as time TT_P12Radio relay when + Δτ
Set the coordinates of machine position P13 to P13 (X_P13, Y_P13，
Z_P13). The radio waves emitted from point P13 are
Β is the elevation angle of the radio wave when it reaches the position W14 of the fixed ground station
_3nThen, from the term, the elevation angle β_3nIs confirmed
X_P13 ^Two+ Y_P13 ^Two+ Z_P13 ^Two= L_Three ^Two... (H-1) X_P13 ^Two+ (Y_P13-L₂₂)^Two+ Z_P13 ^Two= L₁₈ ^Two・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ (H-2) Z_P13= L_Threesin β_3n(H-3) From formulas (H-1) and (H-2), Y_P13= (L_Three ^Two-L_Thirteen ^Two+ L₂₂ ^Two) / 2L₂₂······· (H-4) From formulas (H-1), (H-3) and (H-4), X_P13= [L_Three ^Two-{(L_Three ^Two-L_Thirteen ^Two+ L₂₂ ^Two) / 2L₂₂  }^Two-L_Three ^Twosin^Twoβ_Threen]^1/2・ ・ ・ ・ ・ ・ (H-5) L_Three, L₁₈, L₂₂And β_3nHas been confirmed,
Coordinate P13 (X_P13, Y_P13，
Z_P13) Is also confirmed. (16) Set the distance between points P12 and P13 to L_TwoTosu
It L_Two= {(X_P12-X_P13)^Two+ (Y_P12-Y_P13)^Two＋ (Z_P12-Z_P13)^Two}^1/2 Since the coordinates of points P12 and P13 are fixed, L
_TwoIs also confirmed. (17) Draw a vertical line from the point P12 to the horizontal plane that passes through the point MY.
Then, the foot is designated as point Q12. Time T_M11When
It is radiated from the receiver antenna position M11 toward the radio repeater.
Radio wave at time T_P12When, reach this radio repeater
To do. This time T_P12At this time,
Select the radio wave radiated to the surveyor in the reception mode above.
Choose. This selected radio wave is in the ground reception mode.
Time to reach the surveyor_MYAnd Point P12 and point
The distance to Q12 is L_10ZThen, L_10Z= Nh + {c (T_MY-T_P12) -HΣ_{i = 1} ⁿ(1 / c os α_10i)} Cos α₁₀₀ nh is the refractive index of atmospheric gas at a height of 1 km from point MY.
Altitude when dividing up to the height of 1 parallel to the ground surface
The difference is usually h = 1 and n = 500. c is in vacuum
Propagation speed of radio wave, T_P12Is from point M11 to time T
_M11When the radiated radio waves reach the radio repeater
Tick, α_10i(I = 1 to n) is a parallel plane of each atmosphere with thickness h
Refraction angle of radio wave to surface layer, α₁₀₀Is the height from the ground surface nh
It is the angle of incidence of the radio wave on the parallel plane layer of the atmosphere above km.
It Term to L_10ZIs confirmed.

(5). Three of the objects by radio wave propagation control
Determining the dimensional position With the point W14 as the origin, the coordinates M11 (X,
Y, Z) is calculated. Point M11 has a center P12 and a radius
Is L₁Sphere and center is point P13, radius is L₈Spheres intersect
Since it is the intersection of the resulting circle and the horizontal plane passing through the point MY, (XX_P12)^Two+ (Y-Y_P12)^Two+ (Z-Z_P12)^Two= L₁ ^Two ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ (K-1) (XX_P13)^Two+ (Y-Y_P13)^Two+ (Z-Z_P13)^Two= L₈ ^Two ・ ・ ・ ・ ・ ・ ・ ・ ・ (K-2) Z = Z_P12-L_10Z・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ (K-3) From (K-1) and (K-2), 2 (X_P13-X_P12) X + 2 (Y_P13-Y_P12) Y + 2 (Z_P13 -Z_P12) Z = L₁ ^Two-L₈ ^Two-(X_P12 ^Two+ Y_P12 ^Two+ Z_P12 ^Two ) + (X_P13 ^Two+ Y_P13 ^Two+ Z_P13 ^Two) ・ ・ ・ ・ ・ (K-4) From item (11), X_P12 ^Two+ Y_P12 ^Two+ Z_P12 ^Two= L_Thirteen ^Two············ (K-5) From the section <15>, X_P13 ^Two+ Y_P13 ^Two+ Z_P13 ^Two= L_Three ^Two(K-6) (K-5), (K-6) are substituted into (K-4), and (X_P13-X_P12) X + (Y_P13-Y_P12) Y + (Z_P13  -Z_P12) Z = (L₁ ^Two-L₈ ^Two-L_Thirteen ^Two+ L_Three ^Two) / 2 ... ・ ・ ・ (K-7) X_P12, X_P13, Y_P12, Y_P13, Z_P12
And Z_P13Are the items <11>, <15> and <12>.
Since it is confirmed from the item ▼, X_P13-X_P12= A,
Y_P13-Y_P12= B and Z_P13-Z_P12= D
Then, (K-7) is aX + bY + dZ = (L₁ ^Two-L₈ ^Two-L_Thirteen ^Two+ L_Three ^Two) / 2 Y = {(L₁ ^Two-L₈ ^Two+ L_Thirteen ^Two) -2-aX-dZ} / b ... (K-8) (K-3) and from page 29 (17), Z is determined.
It Substituting (K-3) into (K-1) and (K-2), (XX)_P12)^Two+ (Y-Y_P12)^Two+ (Z_P12-L_10Z-Z_P12)^Two= L₁ ^Two・ ・ ・ ・ ・ ・ ・ ・ (K-9) (XX_P13)^Two+ (Y-Y_P13)^Two+ (Z_P12-L_10Z-Z_P13)^Two= L₈ ^Two......... (K10) From (K-9), (XX_P12)^Two+ (Y-Y_P12)^Two+ L_10Z ^Two= L₁ ^Two・ ・ ・ ・ ・ ・ ・ ・ ・ (K-11) From (K-10), (XX)_P13)^Two+ (Y-Y_P13)^Two+ (Z_P12-Z_P13)^Two -2 (Z_P12-Z_P13) L_10Z+ L_10Z ^Two= L₈ ^Two  Z_P13-Z_P12= D, from (XX_P13)^Two+ (Y-Y_P13)^Two+ D^Two+ 2dL_10Z+ L_10Z ^Two = L₈ ^Two(K-12) From (K-11)-(K-12), 2aX + 2bY = L₁ ^Two-L₈ ^Two+ 2dL_10Z+ D^Two+ A (X_{P1 Two} + X_P13) + B (Y_P12+ Y_P13) ・ ・ ・ ・ ・ (K-13) X_P12+ X_P13= E, Y_P12+ Y_P13= F
Then, (K-13) becomes 2aX + 2bY = L₁ ^Two-L₈ ^Two+ 2dL_10Z+ D^Two+ Ae + bf Y = (L₁ ^Two-L₈ ^Two+ 2dL_10Z+ D^Two+ Ae + bf-2aX) / 2b ... (K-14) Substitute (K-14) into (K-1). (XX_P12)^Two+ {(L₁ ^Two-L₈ ^Two+ 2dL_10Z+ D^Two+ Ae + b f-2aX) / 2b-Y_P12}^Two+ (Z_P12-L_10Z-Z_P12)^Two= L₁ ^Two  (1 + a^Two/ B^Two) X^Two+2 {(a / b) (L₁ ^Two-L₈ ^Two+ 2dL_10Z  + D^Two+ Ae + bf-2bY_P12-X_P12)} X + (L₁ ^Two-L₈ ^Two+ 2d L_10Z+ D^Two+ Ae + bf-2bY_P12)^Two/ 4b^Two+ X_P12 ^Two+ L_{10 Z} ^Two -L₁ ^Two= 0 X = [-(a / b) (L₁ ^Two-L₈ ^Two+ 2dL_10Z+ D^Two+ Ae + bf-2bY_P12-X_P12) ± [{(a / b) (L₁ ^Two-L₈ ^Two+ 2dL_10Z+ D^Two+ Ae + bf-2bY_P12-X_P12)}^Two-(1 + a^Two/ B^Two) {(L₁ ^Two -L₈ ^Two+ 2dL_10Z+ D^Two+ Ae + bf-2bY_P12)^Two/ 4b^Two) + X_P12 ^Two+ L_10Z ^Two-L₁ ^Two}]^1/2] / (1 + a^Two/ B^Two) ... ........ (K-15) Substitute (K-15) into (K-8). Y = (L₁ ^Two-L₈ ^Two-L_Thirteen ^Two+ L_Three ^Two) -2-a [-(a / b) (L₁ ^Two-L₈ ^Two+ 2dL_10Z+ D^Two+ Ae + bf-2bY_P12-X_P12) ± [{(a / b) (L₁ ^Two-L₈ ^Two+ 2dL_10Z+ D^Two+ Ae + bf-2bY_P12 -X_P12)}^Two-(1 + a^Two/ B^Two) {(L₁ ^Two-L₈ ^Two+ 2dL_{10 Z} + D^Two+ Ae + bf-2bY_P12)^Two/ 4b^Two) + X_P12 ^Two+ L_10Z ^Two  -L₁ ^Two}]^1/2Therefore, the position of the point M11 is determined.

2 How to synchronize the timekeeping mechanism: Fixed ground station, radio repeater mounted on satellite and position
The objects that try to find the
Have a structure. Now, let's see how to synchronize these clocks.
Explain. (1). A timekeeping mechanism and a fixed mechanism for the object whose position is to be determined.
Synchronization with the timekeeping mechanism of the fixed ground station The object whose position is to be determined (hereinafter referred to as the aforementioned object)
To do. ) And a fixed ground station (hereinafter referred to as the fixed ground station)
It ) And the radio repeater mounted on the satellite at the same time from
(Hereinafter, referred to as the above-mentioned radio repeater.)
Shoot. These two radio waves pass through the radio repeater and
It is received at the fixed ground station and the object. From the object M11
The radiated radio wave propagates and reaches the radio repeater P12.
When it reaches the fixed ground station W1Y from the radio repeater
Select the radio waves radiated toward. This selected radio wave
Radiation time T from the radio repeater of_P12, The fixed land
Arrival time T to the upper station_W1Y, Azimuth β_W1YAnd elevation α
_W1YIs a computer connected to the fixed ground station
Is recorded on the storage device. The radio wave is the radio repeater
When the radio relay time elapses after reaching
Radio waves are emitted from aircraft P13 to the fixed ground station W14.
Be done. Time T at which this radio wave is emitted from the radio repeater
_P13, Arrival time T to the fixed ground station_W14And the above
Elevation angle α at fixed ground station_W14And azimuth β_W14To
Computer storage device connected to the fixed ground station
Remember above. Radiation from the fixed ground station W11
The propagated radio wave propagates and reaches the radio repeater P22.
From the radio repeater to the fixed ground station W2Y
Select the radio wave to be radiated. In front of this selected radio wave
Radiation time T from the radio repeater_P22, The fixed ground station
Arrival time T_W2Y, Azimuth β_W2Y, And elevation α
_W2YIs a storage device of a computer connected to a fixed ground station
Recorded above. After the radio wave reaches the radio repeater,
Radiation toward the object M24 when the radio relay time has elapsed
Radiated to the fixed ground station W3Y in addition to the radio waves
There are radio waves that are generated. Radiation to this fixed ground station
Time T at which the radio wave is emitted from the radio repeater_P23, The above
Arrival time T at the fixed ground station_W3YAnd at the fixed ground station
Angle of elevation α_W3Y, Azimuth β_W3YThe fixed ground station
Stored in the storage device of the computer connected to
Ku. (See Table 4) The coordinates when the point W1Y of the point P12 is the origin is P12.
(X_P12, Y_P12, Z_P12), Point W1 of point P13
The coordinates when 4 is the origin are P13 (X_P13, Y
_P13, Z_P13), The point W2Y of the point P22 was used as the origin.
The coordinates at time P22 (X_P22, Y_P22, Z_P22)
And the coordinate when the point W3Y of the point P23 is the origin is P2.
3 (X_P23, Y_P23, Z_P23). Atmospheric gas
Neglecting the error of the radio path length due to the refractive index of
(E) The shortest apparent distance between the point P12 and the point W1Y is c (T
_W1Y-T_P12), So X_P12= C (T_W1Y-T_P12) Cos α_W1Y・ Sin β_{W1 Y YP12} = C (T_W1Y-T_P12) Cos α_W1Y・ Cos β_{W1 Y}  Z_P12= C (T_W1Y-T_P12) Sin α_{W1Y T W1Y} -T_P12= T_W3Y-T_P23, Α_W1Y= Α_W3Y (1) T_W2Y-T_P22= T_W14-T_P23, Α_W14= Α_W2Y (2) If so, the radio path M11 → P12 → P13 → W14
Wave paths W11 → P22 → P23 → M24 are equal in time
And the arrival time T of the radio wave to the object_M24And fixed land
Arrival time T of the radio wave to the upper station_W14There is a difference between
For example, when the difference is between the above-mentioned object and each time-dependent mechanism of the fixed ground station
There will be a gap between them. Therefore, the relationship of the above equations (1) and (2)
Satisfy the radio wave to the electric power connected to the fixed ground station.
Select from the storage device of the child computer, and store the object over time.
Synchronize the aging mechanism between the structure and the fixed ground station.

(2). Synchronization of a radio relay station mounted on a satellite (see FIG. 9) When the object is _TM01, a radio wave is radiated toward the radio relay station. The time when the radio wave reaches the radio repeater is T _P02 . Also, from the fixed ground station, time T
_{When W01,} a radio wave is radiated toward the radio repeater.
It is assumed that the radio wave is radiated from the fixed ground station so that the time when the radio wave reaches the radio wave repeater becomes T _P02 . Let L ₁ be the distance between the object and the radio repeater. or,
The distance between the position of the radio repeater at time T _P02 + α and the fixed ground station at time T _W04 is L ₂ . Here, α is the radio relay time of the radio repeater, and T _W04 is the time when the radio wave radiated from the object at time T _M01 reaches the fixed ground station via the radio repeater. L ₁ = c (T _P02 −T _M01 ) (4) L ₂ = c (T _P02 −T _W01 ) (5) L ₁ + L ₂ = c (T _W04 −T _M01 −α) (6) (4), From (5) and (6), T _P02 = (T _W04 + T _W01 −α) / 2 Therefore, since T _W04 , T _W01, and α are known, the true value at time T _P02 is determined. Therefore, the true value corrects the aging mechanism of the radio repeater. However, when the radio wave radiated from the object reaches the radio wave repeater and the position of the radio wave repeater, and when the radio wave relay time of the radio wave repeater elapses after the radio wave reaches the radio wave repeater. The position of the radio wave repeater of 1 is relative to the fixed ground station, and the radio wave at the same position is selected. That is, two radio waves having the same radio wave propagation time and elevation angle are selected.

3 Correction of satellite position error due to atmospheric refractive index
Fixed ground station Q in the space where positive radio waves pass_nParallel to the ground surface passing through
Divide into plane layers of thickness h. And the refraction of each parallel plane layer
Each rate is n₀, N₁... n_nAnd Guard
Let P1 be the actual position of the star and P2 be the apparent position of the satellite.
It Refraction of radio waves emitted from the actual position P1 of the satellite
Rate n₀Refractive index n from the medium₁The incident point on the medium of₀,
Refractive index n₁Refractive index n from the medium_TwoThe incident point on the medium of
₁, Refractive index n_TwoRefractive index n from the medium_ThreePoint of incidence on the medium
Q_Two, Refractive index n_ThreeRefractive index n from the medium_FourEntering the medium of
Q is the shooting point_Four・ ・ ・ Refractive index n_i-1From refractive index n_i
The incident point on the medium of_i-1・ ・ ・ Entering the ground surface
Q is the shooting point, that is, the position of the fixed ground station_nAnd Point Q₀Or
Refractive index n₁And n_TwoPut the foot of the perpendicular line on the interface of
N₁), Point Q₁From refractive index n_TwoAnd n_ThreeDown to the interface
Vertical foot N_Two, Q_TwoFrom refractive index n_ThreeAnd n_FourDown to the interface of
The dropped perpendicular line is N_Three・ ・ ・ Point Q_iFrom refractive index n
_{i + 1}And n_{i + 2}The foot of the perpendicular line that dropped on the interface of N_{i + 1}
.... Point Q_n-1The foot of the perpendicular line that has been dropped from the
_n, Q₀Set the foot of the vertical line from the ground to the ground surface as I
It Refractive index of radio wave radiated from actual satellite position P1
n₀Medium and refractive index n₁Angle of incidence on the interface of
α₀, The refraction angle is α₁, Refractive index n₁Medium and refractive index n_Twoof
The refraction angle to the interface of the medium is α_Two, Refractive index n_TwoMedium and refraction
Rate n_ThreeThe angle of refraction to the interface of the medium is α_Three.....
Folding rate n_i-1Medium and refractive index n_iRefraction to the interface of any medium
The angle is α_i, ..., refractive index n_n-1Medium and refractive index
n_nOf the refractive index of the medium of_nAnd On the contrary, the ground surface
When radiating radio waves from a satellite to a satellite, the refractive index n₁To n
_nIn the medium up to, replace the refraction angle with the incident angle
Just go. Also the refractive index n₀The angle of refraction of₀Tona
It Radio waves emitted from the satellite's actual position P1 are refracted
Rate n₀From the medium of n₁When entering the medium of
Shooting point Q₁It went straight without reaching the ground and reached the ground surface.
Assuming that, the incident point on the ground surface is J. Refractive index n₀
Number of parallel plane layers with thickness h from the interface of to the ground surface
Where n is IJ / IQ₀= Tan α₀ ∴IJ = IQ₀tan α₀= Nh · tanα₀ N₁Q₁/ N₁Q₀= Tan α₁ ∴N₁Q₁= N₁Q₀tan α₁= H · tan α₁ N_TwoQ_Two/ N_TwoQ₁= Tan α_Two ∴N_TwoQ_Two= N_TwoQ₁tan α_Two= H · tan α_Two N_ThreeQ_Three/ N_ThreeQ_Two= Tan α_Three ∴N_ThreeQ_Three= N_ThreeQ_Twotan α_Three= H · tan α_Three ・ ・ N_iQ_i/ N_iQ_i-1= Tan α_i ∴N_iQ_i= N_iQ_i-1tan α_i= H · tan α_i ・ ・ N_nQ_n/ N_nQ_n-1= Tan α_n ∴N_nQ_n= N_nQ_n-1tan α_n= H · tan α_n IQ_n= N₁Q₁+ N_TwoQ_Two+ N_ThreeQ_Three+ ... ・ + N_iQ_i+ ... N_nQ_n = H (tan α₁+ Tan α_Two+ Tan α_Three＋ ・ ・ ・ ・ ・ ＋ tan α_i  ＋ ・ ・ ・ ・ ・ ＋ tan α_n) JQ_n= IJ-IQ_n= Nh · tanα₀-H (tan α₁+ Tan α_Two + Tan α_Three＋ ・ ・ ・ ・ ・ ＋ tan α_i＋ ・ ・ ・ ・ ・ tan α_n) = H {ntan α₀-(Tan α₁+ Tan α_Two+ Tan α_Three＋ ・ ・ ・ ・ ・ ＋ tan α_i＋ ・ ・ ・ ・ ・ tan α_n)} N₁Q₀/ Q₀Q₁= Cos α₁ ∴Q₀Q₁= N₁Q₀/ Cos α₁= H / cos α₁ The radio wave is Q₀Q₁The time it takes to pass₁To
And the radio wave propagation speed is c₁= Q₀Q₁ ∴t₁= Q₀Q₁/ C = h / (cos α₁・
c) N_TwoQ₁/ Q₁Q_Two= Cos α_Two ∴Q₁Q_Two= N_TwoQ₁/ Cos α_Two= H / co
sα_Two The radio wave is Q₁Q_TwoThe time it takes to pass_TwoTo
And the radio wave propagation speed is c_Two= Q₁Q_Two ∴t_Two= N_TwoQ₁/ Cos α_Two・ C = h / (cos α_Two・ C) N_ThreeQ_Two/ Q_TwoQ_Three= Cos α_Three ∴Q_TwoQ_Three= N_ThreeQ_Two/ Cos α_Three= H / cos α_Three The radio wave is Q_TwoQ_ThreeThe time it takes to pass_ThreeTo
And the radio wave propagation speed is c_Three= Q_TwoQ_Three ∴t_Three= Q_TwoQ_Three/ C = h / (cos α_Three・
c) ・ ・ N_iQ_i-1/ Q_i-1Q_i= Cos α_i  ∴Q_i-1Q₁= N_iQ_i-1/ Cos α_i  The radio wave is Q_i-1Q_iThe time it takes to pass_iTosu
Then, assuming that the radio wave propagation speed is c, ct_i= Q_i-1Q_i ∴t₁= Q_i-1Q₁= H / (cos α_i・ C) ・ ・ N_nQ_n-1/ Q_n-1Q_n= Cos α_{n ∴Q n-1} Q_n= N_nQ_n-1/ Cos α_n= H / cos α_n The radio wave is Q_n-1Q_nThe time it takes to pass_nTosu
Then, assuming that the radio wave propagation speed is c, ct_n= Q_n-1Q_n ∴t_n= Q_n-1Q_n/ C = h / (cos α_n
・ C) Radio waves are points P1 and Q₀The time it takes to pass
_pAnd The emission time of the radio wave at the point P1 is T_p1,point
Q_nThe arrival time of the radio wave at_qnThen, T_qn-T_p1= (T₁+ T_Two+ T_Three＋ ・ ・ ・ ・ ・ ＋ t
_i＋ ・ ・ ・ ・ ・ ＋ t_n) + T_p ∴T_p= (T_qn-T_p1)-(T₁+ T_Two+
t_Three+ ... + t_i+ ... t_n) = (T_qn-T_p1)-(H / cos α₁・ C + h / c
osα_Two・ C + h / cos α_Three・ C + ・ ・ ・ + h / co
sα_i・ C + ・ ・ ・ + h / cos α_n・ C) = (T_qn-T_p1)-(H / c) (1 / cos α₁+
1 / cos α_Two+ 1 / cos α_Three+ ・ ・ ・ + 1 / cos
α_i+ ・ ・ ・ + 1 / cos α_n) Point P1 and point Q₀Between
The distance of L_p1q0Then, the refractive index of the medium is n₀(=
1), so L_p1q0= C · T_p= C (T_qn-T_p1) -H (1 / cos α₁ + 1 / cos α_Two+ 1 / cos α_Three+ ・ ・ ・ ・ + 1 / cos α_i+ ・ ・ ・ ・ +1 / cos α_n) The radio wave radiated from the point P1 is the point Q₀Go straight without refracting with
Assuming that₀And the distance between point J and point L
_JQ0Then, the radio wave is point Q₀After passing through, the ground surface
Time T to reach point J above_jq0Is the refraction of the medium
Rate is n₀Since (= 1), T_jq0= L_jq0/ C = JQ₀/ C = (1 / c) (IQ₀/ Cos α₀) = Nh / (cos α₀C) The radio wave radiated from the actual position P1 of the satellite has a refractive index n
₀The time to reach the ground surface through the medium of (= 1) is T
_iThen, (the medium is all uniform and the refractive index is n₀Tosu
It ) T_i= P1Q₀/ C + JQ₀/ C = L_p1q0/ C + L_iq0/ C = (T_qn-T_p1) + (H / c) {n / cos α₀-(1 / cos α₁+ 1 / c osα_Two+ 1 / cos α_Three+ ・ ・ ・ + 1 / cos α_i＋ ・ ・ ・ ・ ・ + 1 / cos α_n)} The radio wave radiated from the actual position P1 of the satellite has a refractive index n
₀Time and refraction required to pass through a uniform medium of (= 1)
Rate n₀, N₁, N_Two, N_Three... n_i...
・ And n_nDifference from the time required to pass through the medium
T_sThen, T_s= T_i-(T_qn-T_p1) = (H / c) {n / cos α₀-(1 / cos α₁+ 1 / cos α_Two+ 1 / cos α_Three+ ・ ・ ・ + 1 / cos α_i+ ... ・ + 1 / cos α_n) Fixed ground of radio waves radiated from the satellite's apparent position P2
The elevation angle at the station is (π / 2-α_n) Actual satellite position P1
Point Q of the radio wave emitted from₀The elevation angle at (π / 2-α₀)
Then, from Snell's law, n₀sin α₀= N_nsin α_n ∴sinα₀= (N_n/ N₀) Sin α_n ∴α₀= Sin^-1(N_n/ N₀) Sin α
_n} Therefore, the actual position of the satellite is the rear point J of the fixed ground station.
And the distance from the fixed ground station is h {n · tanα₀−
(Tanα1 + tanα2 + tanα3 + ... +
tan α_i＋ ・ ・ ・ ・ ・ ＋ tan α_n)}
Station, elevation angle is π / 2-sin^-1{(N_n/ N₀) Sin α_n} The arrival time of the radio wave is until the radio wave reaches the fixed ground station.
Compared to time, (h / c) {n / cosα₀-(1 / c
osα₁+ 1 / cos α_Two+ 1 / cos α_Three+ ... +
1 / cos α_i+ ・ ・ ・ + 1 / cos α_nJust a lot
It Fixed ground station position Q_nWith Q as the origin_n-1, Q
_n-2, ..., Q_i・ ・ ・ 、 Q_Three, Q_Two, Q
₁, Q₀, And P1 are respectively (X_{n-1, Y
n-1}), (X_n-2, Y_n-2) 、 ・ ・ ・ ・ ・ 、 (X
_i, Y_i) 、 ・ ・ ・ ・ ・ (X_Three, Y_Three), (X_Two，
Y_Two), (X₁, Y₁) (X₀, Y₀) And (X_p1，
Y_p1). X_n-1= N_nQ_n= N_nN_n-1tan α_n= H · tan α_n Y_n-1= N_nQ_n-1= H X_n-2= N_nQ_n+ N_n-1Q_n-1= H · tan α_n= H · tan α_n-1 Y_n-2= N_nQ_n-1+ N_n-1Q_n-2= 2h X_i= N_nQ_n+ N_n-1Q_n-1+ ... ・ + N_{i + 1}Q_{i + 1} = H (tan α_n+ Tan α_n-1＋ ・ ・ ・ ・ ・ ・ ＋ tan α_{i + 1}) Y_i= N_nQ_n-1+ N_n-1Q_n-2＋ ・ ・ ・ ・ ・ ＋ N_{i + 1}Q_i= (N-i) h X_Three= N_nQ_n+ N_n-1Q_n-1＋ ・ ・ ・ ・ ・ ＋ N_{i + 1}Q_{i + 1}+ ・ ・ ・ ・ ・ ・ ・ + N_FourQ_Four = H (tan α_n+ Tan α_n-1＋ ・ ・ ・ ・ ・ ＋ tan α_{i + 1}+ Tan α_Four ) Y_Three= N_nQ_n-1+ N_n-1Q_n-2＋ ・ ・ ・ ・ ・ ＋ N_{i + 1}Q_i+ ・ ・ ・ ・ ・ ・ ・ + N_FourQ_Three= (N-3) h X_Two= N_nQ_n+ N_n-1Q_n-1＋ ・ ・ ・ ・ ・ ＋ N_{i + 1}Q_{i + 1}+ ・ ・ ・ ・ ＋ N_FourQ_Four+ N_ThreeQ_Three = H (tan α_n+ Tan α_n-1＋ ・ ・ ・ ・ ・ ＋ tan α_{i + 1}＋ ・ ・ ・ ・ ・ ＋ tan α_Four+ Tan α_Three) Y_Two= N_nQ_n-1+ N_n-1Q_n-2＋ ・ ・ ・ ・ ・ ＋ N_{i + 1}Q_i+ ・ ・ ・ ・ ＋ N_FourQ_Three+ N_ThreeQ_Two= (N-2) h X₁= N_nQ_n+ N_n-1Q_n-1＋ ・ ・ ・ ・ ・ ＋ N_{i + 1}Q_{i + 1}+ ・ ・ ・ ・ ・ ・ ・ + N_FourQ_Four+ N_ThreeQ_Three+ N_TwoQ_Two = H (tan α_n+ Tan α_n-1＋ ・ ・ ・ ・ ・ ＋ tan α_{i + 1}＋ ・ ・ ・ ・ ・ ＋ tan α_Four+ Tan α_Three+ Tan α_Two) Y₁= N_nQ_n-1+ N_n-1Q_n-2＋ ・ ・ ・ ・ ・ ＋ N_{i + 1}Q_i+ ・ ・ ・ + N_FourQ_Four+ N_ThreeQ_Three+ N_TwoQ_Two+ N₁Q₁= (N-1) h X₀= N_nQ_n+ N_n-1Q_n-1＋ ・ ・ ・ ・ ・ ＋ N_{i + 1}Q_{i + 1}+ ・ ・ ・ ・ ・ ・ ・ + N_FourQ_Four+ N_ThreeQ_Three+ N_TwoQ_Two+ N₁Q₁ = H (tan α_n+ Tan α_n-1＋ ・ ・ ・ ・ ・ tan α_{i + 1}＋ ・ ・ ・ ・ ・ ＋ tan α_Four+ Tan α_Three+ Tan α_Two+ Tan α₁) Y₀= N_nQ_n-1+ N_n-1Q_n-2＋ ・ ・ ・ ・ ・ ＋ N_{i + 1}Q_i+ ・ ・ ・ ・ ＋ N_FourQ_Three+ N_ThreeQ_Two+ N_TwoQ₁+ N₁Q₀= Nh X_p1= X₀+ P1Q₀sin α₀ = HΣ_{i = 1} ⁿtan α_i+ L_p1q0sin α₀= HΣ_{i = 1} ⁿtan α_i+ {C (T_qn-T_p1) -HΣ_{i = 1} ⁿ(1 / cos α_i)} Sin α₀ Y_p1= Y₀+ P1Q₀cos α₀ = Nh + {c (T_qn-T_p1) -HΣ_{i = 1} ⁿ(1 / cos α_i)} Cos α₀ Emitted from the actual position of the satellite toward the ground station or observation point
Radio waves emitted from the ground station or observation point to the satellite.
The emitted radio wave has a refractive index n₀From refractive index n₁Or
On the other hand, the point of incidence of radio waves on the interface parallel to the ground surface is the origin.
Then, at this origin, the refractive index n₀From refractive index n₁Strange
The normal line on the interface parallel to the ground surface or vice versa
The X axis is defined as being in the plane formed by the X axis and the radio wave path.
In the XY-plane with the Y axis being a straight line orthogonal to the X axis,
Radio wave transmission from the actual position of the satellite to the ground station or observation point
Horizontal length L_XP1And the vertical distance L_YP1Ask for
And the incident angle and refraction angle reference lines are in the positive direction of the X-axis
L is a positive direction_XP1= -HΣ_{i = 1} ⁿtan (π + α_i) + {C (T_qn-T_p1) + HΣ_{i = 1} ⁿ(1 / cos (π + α_i))} Sinα₀ = -Htan α_i+ {C (T_qn-T_p1) −hΣ_{i = 1} ⁿ(1 / cos α_i)} Sin α₀ L_YP1= Nh + {c (T_qn-T_p1) + HΣ_{i = 1} ⁿ(1 / cos (π + αi))} cosα₀ = Nh + {c (T_qn-T_p1) − HΣ_{i = 1} ⁿ(1 / cosαi)} cosα₀ Therefore, the actual position P1 of the satellite and the position Q of the fixed ground station_nWhen
The shortest distance between_p1qnThen, L
_p1qn= (L_Xp1 ^Two+ L_Yp1 ^Two)^1/2 =
[[-HΣ_{i = 1} ⁿtan α_i+ {C (T_qn−
T_p1) -HΣ_{i = 1} ⁿ(1 / cos α_i)} Sin α
₀]^Two + [Nh + {c (T_qn-T_p1) -HΣ
_{i = 1} ⁿ(1 / cos α_i)} Cos α₀]^Two]^1/2

4. Determination of elevation angle The circumference of the earth is classified into three regions as shown in FIG. Ground surface
The area from the surface to the height of 12 km above the ground is the horizontal layer or the ground surface.
From the height of 12 km to 500 km in the spherical layer,
Then, the area over 500 km above the ground surface is directly
I'll call it Shinda. Geostationary satellites above the equator
Radio waves are emitted from the
Consider the path of this radio wave when reaching a ground station
To do. (See Fig. 12) The thickness of the medium through which the radio waves pass is parallel to the horizontal plane passing through the ground station.
Of parallel plane layers of size h. Point A is time T_APosition of the ground station at time point B is time T_BPosition C of the ground station at time T_CThe position of the ground station at time point P is time T_PThe position of the radio relay station mounted on the satellite at_AThen the elevation angle (π /
2-α_n) Is emitted toward the radio repeater at time T_PNoto
The radio wave dotted line PB reaching the radio wave repeater position P is the time T_PFrom the radio relay station position P to the ground station
Is emitted toward the time T_BAngle of elevation (π / 2-β_n)
The radio wave dotted line PC reaching the ground station position B at time T_PFrom the radio relay station position P to the ground station
Is emitted toward the time T_CAngle of elevation (π / 2-γ_n)
The radio wave AP reaching the ground station position C at_AGround station position A and time T_Pof
The shortest distance between the radio relay station position P and the thick line PB is the time T_BGround station position B and time T_Pof
The shortest distance from the radio relay station position P at time_CGround station position C and time T_Pof
Shortest distance L from the radio relay station position P₁Is time T_PHeight of position P of the radio repeater when_TwoIs time T_AGround station position A and time T_pWhen
Horizontal distance from the radio relay station position P_FourIs time T_BGround station position B and time T_pWhen
Horizontal distance from the radio relay station position P₆Is time T_CGround station position C and time T_pWhen
The horizontal distance δ from the radio relay station position P is_BGround station position B and time T_pWhen
The foot of the perpendicular line dropped from the position P of the radio repeater to the XY-plane.
Angle L formed by the straight line connecting Q and the positive direction of the Y-axis_ThreeIs time T_AGround station position A and time T_BWhen
Shortest distance from the ground station position B of L₅Is time T_BGround station position B and time T_CWhen
Distance from the ground station position C of (see Fig. 13)_Two ^Two= L_Three ^Two+ L_Four ^Two-2L_ThreeL_Fourcos δ (1) In ΔBCQ, from the second law of cosine, L₆ ^Two= L_Four ^Two+ L₅ ^Two-2L_FourL₅cos (π−δ) = L_Four ^Two+ L₅ ^Two + 2L_FourL₅From cos δ (2) (1), 2L_ThreeL_Fourcos δ = L_Three ^Two+ L_Four ^Two-L_Two ^Two ∴cos δ = (L_Three ^Two+ L_Four ^Two-L_Two ^Two) / 2L_ThreeL_Four (3) From (2), 2L_FourL₅cos δ = L₆ ^Two-L_Four ^Two-L₅ ^Two ∴cos δ = (L₆ ^Two-L_Four ^Two-L₅ ^Two) / 2L_FourL₅ (4) From (3) and (4), (L_Three ^Two+ L_Four ^Two-L_Two ^Two) / 2L_ThreeL_Four= (L₆ ^Two-L_Four ^Two-L₅ ^Two ) / 2L_FourL₅ L_Three ^TwoL₅+ L_Four ^TwoL₅-L_Two ^TwoL₅-L_ThreeL₆ ^Two+ L_ThreeL_Four ^Two+ L_Three L₅ ^Two= 0 (5) Radio waves radiated from the satellite position P
It is assumed that a point O on the interface YY 'with the layer is entered. At point O
At the interface YY 'between the radio wave rectilinear layer and the spherical layer
Be XX '. The traveling direction of the radio wave is based on the half line OX
If the counterclockwise direction is positive (see Fig. 14),
By correcting the satellite position error due to the air refractive index, L₁= Nh + {c (T_P-T_A) + HΣ_{i = 1} ⁿ(1 / cos (π + α_i))} Cos α₀ = Nh + {c (T_P-T_A) -HΣ_{i = 1} ⁿ(1 / cos α_i)} Cos α₀ = Nh + {c (T_B-T_P) + HΣ_{i = 1} ⁿ(1 / cos (π + β_i))} Co sβ₀ (6) = nh + {c (T_B-T_p) -HΣ_{i = 1} ⁿ(1 / cos β_i)} Cosβ₀ = Nh + {c (T_C-T_P) + HΣ_{i = 1} ⁿ(1 / cos (π + γ_i))} Co sγ₀ = Nh + {c (T_C-T_p) -HΣ_{i = 1} ⁿ(1 / cos γ_i)} Cosγ₀ L_Two= -HΣ_{i = 1} ⁿtan (π + α_i) + {C (T_P-T_A) + HΣ_{i = 1} ⁿ (1 / cos (π + α_i)} Sin α₀ = -HΣ_{i = 1} ⁿtan α_i+ {C (T_P-T_A) -HΣ_{i = 1} ⁿ(1 / cos α_i)} Sin α₀ (7) L_Four= -HΣ_{i = 1} ⁿtan β_i+ {C (T_B-T_P) -HΣ_{i = 1} ⁿ(1 / cos β_i)} Sinβ₀ (8) L₆= -HΣ_{i = 1} ⁿtan γ_i+ {C (T_C-T_P) -HΣ_{i = 1} ⁿ(1 / ccsγ_i)} Sinγ₀ (9) L_Three= V (T_B-T_A) (10) L₅= V (T_C-T_B) (11) However, n tries to locate the ground surface or the position of the atmosphere.
Divided into layers of thickness h parallel to the horizontal plane where the object
The number of times. c is the radio wave propagation speed. α₀Is the position A of the ground station
From time T_AWhen, the radio waves radiated toward the radio repeater
, When it enters the interface between the spherical layer and the wave rectilinear layer,
At the entry point, the normal and radio wave created at the interface of this parallel plane
The angle formed by. α_iIs time T_APosition A of the ground station at
The radio waves radiated from the radio relay station by the
Parallel to the horizontal plane on which the object
When plunging into the i-th parallel plane layer from the bottom surface of thickness h
Angle of incidence. β₀Is time T from position P of the radio repeater_PNoto
Radiated to the ground station at time T_BWhen is the position of the ground station
The electric wave that has reached the position B reaches the interface between the spherical layer and the radio wave straight traveling layer.
At the time of entry, the field of this parallel plane
The angle between the normal line on the surface and the radio wave. β_iIs time T_pof
Time T from the position P of the radio repeater_BGround station at
The radio waves radiated toward position B of the
Thickness h parallel to the horizontal plane of the object to be stopped
Refraction when entering the i-th parallel plane layer from the bottom surface of the
Horn. γ₀Is time T from position P of the radio repeater_PWhen, the ground
Emitted to the upper station, time T_CAt position C of the ground station
The arriving radio waves rush into the interface between the spherical layer and the radio wave straight-through layer.
At the entry point,
The angle between the normal and the radio wave. γ_iIs time T_pWhen
Time T from the position P of the radio repeater_CPosition of the ground station at
Radio waves radiated to C locate the ground surface or position
Lower surface of thickness h parallel to the horizontal plane where the object
Refraction angle when entering from the to the i-th parallel plane layer. Σ_{i = 1} ⁿ(Sin α₀/ Cos α_i) = Σ_{i = 1} ⁿ{Sin α₀/ (1-sin^Twoα_i)^1/2} = Σ_{i = 1} ⁿ[Sin α₀/ {1- (sin α₀/ N_i)^Two}^1/2] = Σ_{i = 1} ⁿ[Sin α₀/ {(N_i ^Two-Sin^Twoα₀) / N_i ^Two}^{1 / 2} ] = Σ_{i = 1} ⁿ{N_isin α₀/ (N_i ^Two-Sin^Twoα₀)^1/2} ≈ Σ_{i = 1} ⁿ{N_isin α₀/ (1-sin^Twoα₀)^1/2} = Σ_{i = 1} ⁿ(N_isin α₀/ Cos α₀) = Σ_{i = 1} ⁿ(N_itan α₀) In the above equation, n_iBy setting ≈1, an error will occur.
To live. To prevent this error from occurring, n_isin α₀/ (N_i ^Two-Sin^Twoα₀)^1/2  = K {n_isin α₀/ (1-sin^Twoα₀)^1/2} Σ_{i = 1} ⁿ(Sin α₀/ Cos α_i) = KΣ_{i = 1} ⁿ(N_itan α₀) (12) Same as (12)_{i = 1} ⁿ(Sin β₀/ Cos β_i) = KΣ_{i = 1} ⁿ(N_itan β₀) (13) Σ_{i = 1} ⁿ(Sinγ₀/ Cos γ_i) = KΣ_{i = 1} ⁿ(N_itan γ₀) (14) tan α_i= Sinα_i/ Cos α_i = (Sin α₀/ N_i) / {1- (sin α₀/ N_i)^Two}^1/2 = (Sin α₀/ N_i) / {(N_i ^Two-Sin^Twoα₀)^1/2/ N_i} = Sinα₀/ (N_i ^Two-Sin^Twoα₀)^1/2 ≈ sin α₀/ (1-sin^Twoα₀)^1/2 = Sinα₀/ Cos α₀ = Tan α₀ In the above equation, n_iBy setting ≈1, an error will occur.
To live. To prevent this error from occurring, sin α₀/ (N_i ^Two-Sin^Twoα₀)^1/2 = K {sin α₀/ (1-sin^Twoα₀)^1/2} = K (sin α₀/ Cos α₀) Tan α_i= Ktan α₀ (15) tanβ as in (15)_i= Ktan β₀ (16) tan γ_i= Ktanγ₀ (17) where n_iIs an object whose surface or position is to be located
, Which is parallel to the horizontal plane where
Refractive index of radio waves in the row plane layer. From (6) and (12), nh + {c (T_P-T_A) -HΣ_{i = 1} ⁿ(1 / cos α_i)} Cos α₀ = Nh + c (T_P-T_A) Cos α₀−hΣ_{i = 1} ⁿ(1 / cos α_i) Cos α₀ = Nh + c (T_P-T_A) Cos α₀−hΣ_{i = 1} ⁿ(1 / cos α_i) (Sin α₀/ Sinα₀) Cos α₀ = Nh + c (T_P-T_A) Cos α₀−hΣ_{i = 1} ⁿ(Sin α₀/ Cos α_i ) (Cos α₀/ Sinα₀) = Nh + c (T_P-T_A) Cos α₀-KhΣ_{i = 1} ⁿ(N_itan α₀) (1 / tan α₀) = Nh + c (T_P-T_A) Cos α₀-KhΣ_{i = 1} ⁿn_i (18) From (6) and (13), nh + {c (T_B-T_P) -HΣ_{i = 1} ⁿ(1 / cos β_i)} Cosβ₀ = Nh + c (T_B-T_P) Cosβ₀-KhΣ_{i = 1} ⁿn_i (19) From (6) and (14), nh + {c (T_C-T_P) -HΣ_{i = 1} ⁿ(1 / cos γ_i)} Cosγ₀  = Nh + c (T_C-T_P) Cosγ₀-KhΣ_{i = 1} ⁿn_i (20) From (6), (18), and (19), nh + c (T_B-T_P) Cosβ₀-KhΣ_{i = 1} ⁿn_i= Nh + c (T_P -T_A) Cos α₀-KhΣ_{i = 1} ⁿn_i ∴cos β₀= {(T_P-T_A) / (T_B-T_P)} Cos α₀ (21) Similarly, from (6), (18) and (20),₀= {(T_P-T_A) / (T_C-T_P)} Cos α₀(22) From (7), (12), and (15), L_Two= -KhΣ_{i = 1} ⁿtan α₀+ C (T_P-T_A) Sin α₀ -KhΣ_{i = 1} ⁿn_itan α₀ = -Kh (Σ_{i = 1} ⁿ(1 + n_i) Tan α₀+ C (T_P-T_A) Sin α₀ = {-K (h / cosα₀) Σ_{i = 1} ⁿ(1 + n_i) + C (T_P-T_A)} Si nα₀ (23) Similarly, from (8), (13), and (16), L_Four= {-K (h / cosβ₀) Σ_{i = 1} ⁿ(1 + n_i) + C (T_B -T_P)} Sinβ₀ (24) Similarly, from (9), (14), and (17), L₆= {-K (h / cosγ₀) Σ_{i = 1} ⁿ(1 + n_i) + C (T_C -T_P)} Sinγ₀ (25) Now, in order to simplify the calculation, −KhΣ_{i = 1} ⁿ(1 + n_i) = K (26) T_P-T_A= P (27) T_B-T_P= Q (28) T_C-T_P= R (29), from (21), (27) and (28), cos β₀= (P / q) cos α₀ (30) From (22), (27) and (29), cosγ₀= (P / r) cos α₀ (31) From (23) and (27), L_Two= (K / cos α₀+ Cp) sinα₀ (32) From (21), (26), (27), (28), L_Four= (K / cos β₀+ Cq) sinβ₀ = {(Kq / p) (1 / cos α₀) + Cq} {1- (p / q)^Twocos^Twoα₀ }^1/2 (33) From (22), (26), (27), (29), L₆= (K / cosγ₀+ Cr) sinγ₀ = {(Kr / p) (1 / cos α₀) + Cr} {1- (p / r)^Twocos^Twoα₀ }^1/2 (34) From (10), (27), (28), L_Three= V (p + q) (35) From (11), (28), (29), L₅= V (r−q) (36) From (35) and (36), L_Three ^TwoL₅= V^Three(P + q)^Two(R−q) (37) From (33) and (36), L_Four ^TwoL₅= V (r−q) {(k^Twoq^Two/ P^Two) (1 / cos^Twoα₀ ) +2 (ckq^Two/ P) (1 / cos α₀) + C^Twoq^Two-K^Two-2 ckp ・ cos α₀-C^Twop^Twocos^Twoα₀} (38) From (32) and (36), L_Two ^TwoL₅= V (r-q) {k^Two(1 / cos^Twoα₀) + 2ckp (1 / cos α₀) + C^Twop^Two-K^Two-2 ckp cos α₀-C^Twop^Twocos^Two α₀} (39) From (34) and (35), L_ThreeL₆ ^Two= V (p + q) {(k^Twor^Two/ P^Two) (1 / cos^Twoα₀ ) +2 (ckr^Two/ P) (1 / cos α₀) + C^Twor^Two-K^Two-2 ckp ・ cos α₀-C^Twop^Twocos^Twoα₀} (40) From (33) and (35), L_ThreeL_Four ^Two= V (p + q) {(k^Twoq^Two/ P^Two) (1 / cos^Twoα₀ ) + 2ckq^Two/ P (1 / cos α₀) + C^Twoq^Two-K^Two-2 ckp cos α₀ -C^Twop^Twocos^Twoα₀} (41) From (35) and (36), L_ThreeL₅ ^Two= V^Three(P + q) (r-q)^Two (42) (37), (38), (39), (40), (41),
Substituting (42) into (5) gives L_Three ^TwoL₅+ L_Four ^TwoL₅-L_Two ^TwoL₅-L_ThreeL₆ ^Two+ L_ThreeL_Four ^Two+ L_Three L₅ ^{Two = V3} (P + q)^Two(R−q) + V (r−q) {(k^Twoq^Two/ P^Two) (1 / cos^Twoα₀) +2 (ckq^Two/ P) (1 / cos α₀) + C^Twoq^Two-K^Two -2 ckp cos α₀-C^Twop^Twocos^Twoα₀} -V (r-q) {k^Two(1 / cos^Twoα₀) +2 ckp (1 / cos α₀) + C^Twop^Two-K^Two -2 ckp cos α₀-C^Twop^Twocos^Twoα₀} -V (p + q) {(k^Twor^Two/ P^Two) (1 / cos^Twoα₀) +2 (ckr^Two/ P) (1 / cos α₀) + C^Twor^Two-K^Two -2 ckp cos α₀-C^Twop^Twocos^Twoα₀} + V (p + q) {(k^Twoq^Two/ P^Two) (1 / cos^Twoα₀) + 2ckq^Two/ P (1 / cos α₀) + C^Twoq^Two-K^Two -2 ckp cos α₀-C^Twop^Twocos^Twoα₀} + V^Three(P + q) (r-q)^Two = (K^Two/ P^Two) (P + q) (q-r) (r + p) V (1 / cos^Twoα₀) +2 ck (p + q) (q-r) (r + p) V / p (1 / cos α₀) + C^Two(P + q) (q−r) (r + p) V = 0 = (p + q) (q−r) (r + p) V {(k^Two/ P^Two) (1 / cos α₀)^Two+ 2ck / p (1 / cos α₀) + C^Two-V^Two} = 0 From q ≠ r, (k^Two/ P^Two) (1 / cos α₀)^Two+ 2ck / p (1 / cos α₀) + C^Two-V^Two= 0 ∴1 / cos α₀= -Ck / p ± {(ck / p)^Two-(K^Two/ P^Two) (C^Two-V^Two )}^1/2] / (K^Two/ P^Two) ∴1 / cos α₀= (Ck / p ± Vk / p) / (k^Two/ P^Two) = P (c ± V) / k ∴cos α₀= K / p (c ± V) = KhΣ_{i = 1} ⁿ(1 + n_i) / (T_P-T_A ) (C ± V)} (43) Substituting (43) into (21) and (22). cos β₀= {(T_P-T_A) / (T_B-T_P)} {KhΣ_{i = 1} ⁿ(1 + n_i ) / (T_P-T_A) (C ± V)} = {KhΣ_{i = 1} ⁿ(1 + n_i) / (T_B-T_P) (C ± V)} (44) cosγ₀= {KhΣ_{i = 1} ⁿ(1 + n_i) / (T_C-T_P) (C ± V)} (45) Therefore, the time T_AFrom the ground station position A to the radio repeater
Is radiated to the time T_PReach the position P of the radio relay
The elevation angle of the generated radio wave at the ground station position A is π / 2-sin^-1[(1 / n_n) [1- {KhΣ_{i = 1} ⁿ(1 + n_i) / (T_P-T_A) (C ± V)}^1/2] Time T_PRadiation toward the ground station from the position P of the radio repeater
At time T_BThe location of the radio wave that reached the ground station position B when
The elevation angle at the upper station position B is π / 2-sin^-1[(1 / n_n) [1- {KhΣ_{i = 1} ⁿ(1 + n_i ) / (T_B-T_P) (C ± V)}^1/2] Time T_PRadiation toward the ground station from the position P of the radio repeater
At time T_CThe location of the radio wave that reached the ground station position C when
The elevation angle at the upper station position C is π / 2-sin^-1[(1 / n_n) [1- {KhΣ_{i = 1} ⁿ(1 + n_i ) / (T_C-T_P) (C ± V)}^1/2]. However, n_nIs the electric charge of the atmospheric gas layer where the ground station is located.
The refractive index of the wave.

5 Improvement of satellite position accuracy The circumference of the earth is classified into three regions as shown in FIG. Ground surface
The area from the surface to the height of 12 km above the ground is a horizontal layer, above the ground surface.
The area from 12km to 500km in height is spherical
Layer and the area above the ground surface with a height of 500 km or more
We will call it the wave straight layer. Stillness above the equator
Radio waves are radiated from satellites, and these radio waves propagate to the ground surface.
About the route of this radio wave when reaching the ground station above
(See FIG. 12). Satellite position is P, above ground level
Let Q be the position of the ground station. Radio waves emitted from point P
Passes through the radio wave straight layer and enters the point R on the spherical layer interface.
Then, after passing through the spherical layer, pass the point S on the horizontal layer interface.
Then, the position Q of the ground station on the ground surface is reached. Radio communication
A medium parallel to the horizontal plane passing through the point Q and having a thickness h
Divide into layers. From the radio wave straight layer to the point R on the spherical layer interface
Parallel plane at the point R and the traveling direction of the radio wave when entering
The angle formed by the normal to the layer is α₀, Radio wave parallel planes
The refraction angle to the layer is α_i, N is the number of parallel plane layers. point
Let H be the foot of a perpendicular line from P to the horizontal plane passing through point Q.
And PH = nh + {cp−hΣ_{i = 1} ⁿ(1 / cos α_i)} Cos α₀(1) Where C is the speed of the radio wave and p is the radio wave propagation time.
It If the refractive index of the atmosphere is n and the refractive index is N, then n = 1 + N × 10^-6 N depends on the weather conditions at each location,
Experimentally generally N = 77.6 (P / T) + 3.73 × 10⁵(E / T^Two) (NU). Where P is atmospheric pressure (mb) and e is
Water vapor pressure (mb) and T are absolute temperatures (K). The actual
This index of refraction is
It decreases exponentially and its altitude characteristic is experimentally generally N (h) = Ns {exp (−Ce · h)} (NU) Ce = 1_n{Ns / N (1km)} = 1_n{Ns / (Ns + ΔN)} where Ns is the refraction index on the ground surface and h is from the ground surface
Is the height (km). From the above, in each parallel plane layer
The refractive index of atmospheric gas can be calculated. Now each parallel plane layer
Refractive index of atmospheric gas at n_iThen, (1) in the horizontal layer region, from Snell's law,_isin α_i= N₀sin α_{0 ∴sinαi} = (N₀/ N_i) Sin α₀ However, n₀
Is the refractive index of radio waves in a vacuum. ∴cos α_i= (1-sin^Twoα₀)^1/2 = {1- (n₀ ^Two/ N_i ^Two) Sin^Twoα₀}^1/2 Therefore, from equation (1), the path length of the radio wave in the horizontal layer area
Is hΣ_{i = 1} ¹²[1 / {1- (n₀ ^Two/ N_i ^Two) Sin^Twoα₀}^{1 /} 2] (2) (2) In the spherical layer region, from Snell's law, (n_i+ Hi / a) sin α_i= N₀sin α₀ ∴sinα_i= {N₀/ (N_i+ Hi / a)} sin α₀ ∴cos α_i= (1-sin^Twoα₀)^1/2 = [1- {n₀ ^Two/ (N_i+ Hi / a)^Two} Sin^Twoα₀]^1/2 Therefore, from equation (1), the path length of the radio wave in the spherical layer region
Is hΣ_{i = 12} ⁵⁰⁰ [1- {n₀ ^Two/ (N_i+ Hi / a)^Two} S in^Twoα₀]^1/2 (3) (3) In the radio wave straight layer region, hΣ_{i = 500} ⁿ(1 / cos α_i) = HΣ_{i = 500} ⁿ(Cos α₀/ Cos α_i) (1 / cos α₀) = HkΣ_{i = 500} ⁿ(N₀/ Cos α₀) (4) Where k is cos α₀Constant depending on
Is. From equations (2) and (3), parallel horizontal plane layers and parallel spheres
The path length of the radio wave passing through the surface layer is α₀Is determined by
It Now, radio waves passing through the parallel horizontal plane layer and the parallel spherical layer
Let Li be the i-th approximation value of the path length of_{i = 1} ¹²(1 / cos α_i) + Σ_{i = 12} ⁵⁰⁰(1 / cos α_i)} ≠ 0 ∴Li = Σ_{i = 1} ¹²(1 / cos α_i) + Σ_{1 = 12} ^{500 ± x}(1 / cos α_i) Therefore, the radio path length between PQ is Σ_{i = 1} ¹²(1 / cos α_i) + Σ_{i = 12} ⁵⁰⁰(1 / cos α_i ) + Σ_{i = 500} ⁿ(1 / cos α_i) ± Σ_{i = 500} ^x(1 / cos α_i), Compared with the true value of the radio path length between PQ, ± Σ
_{i = 500} ^x(1 / cos α_i) Only different. Therefore, Σ
_{i = 500} ^x(1 / cos α_i) → so that it becomes 0
For example, Σ_{i = 500} ^x(1 / cos α_i) ≈ 0 when α₀Is required α₀Is. cos α₀To
As a parameter, the parallel horizontal plane layer region and the parallel spherical layer region
Expressions (2) and (3) are used to express the path length of radio waves in the region.
It becomes like Fig.15. Put two points A and B on the curve in FIG.
Then, the curve in FIG. 15 is approximated as a straight line passing through the two points A and B.
It Therefore, in the parallel horizontal plane layer area and the parallel spherical surface layer area,
The radio wave path length is a₁cos α₀+ B₁ It is represented by (5). This is defined as the parallel horizontal plane area and the parallel spherical surface area.
It is called the first-order approximation of the path length of radio waves in the area. α₀But
Then, from the refractive index of each parallel plane layer, α_i, Also decided
It Therefore, the path length of the radio wave passing through each parallel plane layer is fixed.
Maru Therefore α₀The only parallel plane layer area and
And the path length of the radio wave in the parallel spherical layer region is determined. Parallel this
Of the radio path length in the horizontal plane layer region and the parallel spherical layer region
Called experimental value. Parallel horizontal plane area and parallel spherical surface area
First order approximation of radio wave path length and parallel horizontal plane region
And the difference between the experimental values of the radio path length in the parallel spherical layer region,
That is, 1 in FIG. 15 is approximated by a parabola. This is c₁cos^Twoα₀+ D₁cos α₀+ E₁ It is expressed as (6). Substituting equations (4), (5) and (6) into equation (1)
Then, PH = nh + cpcosα₀-H {(a₁cos α₀+ B₁)-(C₁ cos^Twoα₀+ D₁cos α₀+ E₁)} Cos α₀-Hk (n-500) (7). However, PH = h (1 + k) n (8) cos α₀= Hk (2n + m) / (c + V) p (9) k = u cos α₀+ W (10) where V is the rotation speed of the earth, m is the parallel horizontal plane layer region and
And the refractive index of the radio wave in the parallel spherical layer region
It is a constant. U and w are cos α₀Constant determined by
Is. Substituting equations (8), (9) and (10) into equation (7)
Then, the left side of equation (7) is cos α₀And the cubic equation of
It That is, cos α₀= X, f (x) = x^Three+ F₁x^Two+ G₁x + h₁= 0 (11) By finding the root of equation (11), cos α₀Is determined
Therefore, n is determined from (9). Cos α just found
₀And n are primary approximations. This cos α₀The first
From the first-order approximation value, in FIG.
Narrowing the range of path length in the parallel spherical layer region, and
sα₀The difference between adjacent values of
Take points C and D and go straight through the curve in FIG.
Make a second approximation as a line. Therefore, the parallel horizontal plane area
The path length of the radio wave in the region and the parallel spherical layer region is a_Twocos α₀+ B_Two  Is approximated by. This is a parallel horizontal plane layer area and a parallel spherical layer.
It is called a second-order approximation of the path length of radio waves in the area. parallel
Radio wave path length in horizontal plane layer and parallel spherical layer region
The quadratic approximation value and the parallel horizontal surface layer area and the parallel spherical surface area
The difference between the experimental value of the radio path length in
It is approximated by a parabola as in the first round. This is c_Twocos^Twoα₀+ D_Twocos α₀+ E_Two It is expressed as (12). By repeating the same process as before, cos
α₀And a second approximation of n. FIG. 15 and Expression (6)
And from (12) c₁cos^Twoα₀+ D₁cos α₀+ E₁> C_Twocos
^Twoα₀+ D_Twocos α₀+ E_Two＞ ・ ・ ・ ・ ・ ・ ・ ・ ＞ c
_icos^Twoα₀+ D_icos α₀+ E_i  And Σ_{i = 500} ^x(1 / cos α_i) Is gradually 0
You can see that you are approaching. Therefore, cos α₀Gradually
To approach the true value. Repeat the above operation
Finally, in the parallel horizontal plane area and the parallel spherical layer area,
I) Approximate i-th order path length and parallel horizontal plane layer area and parallel
The difference from the experimental value of the radio path length in the spherical layer region is a parabola
Is not approximated by
Becomes difficult to obtain. At this point, cos α₀of
The experimental value is represented by a straight line by reducing the width before and after the i-th approximation.
Within the range of parallel horizontal plane layer and parallel spherical layer layer
To find the path length of the radio wave in. That is, cos next to each other
α₀Δh is reduced by the two values x and x + Δh of
In the horizontal horizontal layer area and the parallel spherical surface area.
The i-th approximation of the path length of the radio wave
Limit the difference from the experimental value of the path length of the radio wave in the spherical region
You can get closer to 0, so this way
sα₀And n will approach their true value. That conclusion
As a result, it was found that the position of the satellite approaches its true value infinitely.
It

6 Measurement of azimuth angle Time T_AFrom the position A of the ground station at
Emit radio waves toward the repeater. The time when the radio wave propagates
T_PAt this time, it is assumed that the radio relay device is reached. And
Simultaneously when the radio wave from the ground station arrives at the radio repeater
Radio waves are radiated from the radio repeater toward the ground station every moment.
To be done. This radio wave propagates at time T_BWhen the above ground
A station is reached and the position of the ground station at this time is B.
(Refer to FIG. 16) Put the foot of the perpendicular line from point P on the XY-plane.
Let's call it Q. To point A of the radio wave radiated from point A to point P
Elevation angle at α_n, Radio waves radiated from point P to point B
The elevation angle at point B of_nRefraction of atmospheric gases on the ground surface
Rate n_nAnd Also, radiation was emitted from point A to point P.
The refraction angle of the radio wave from the atmosphere to the outside is α₀, From point P
Radio waves radiated toward point B from outside the atmosphere to the atmosphere
Angle of incidence β₀And (A'B'Q 'plane is the boundary of the atmosphere
It is in the sky about 500km above the XY plane. )
The rotation direction of the earth and the Y axis are parallel. Straight line AQ, B
The angle between Q and the X axis is the coordinates of γ, δ, and point P, respectively.
Is P (X, Y, Z), [-hΣ_{i = 1} ⁿtan α_i+ {C (T_P-T_A) -HΣ_{i = 1} ⁿ (1 / cos α_i)} Sin α₀] Cosγ = [− hΣ_{i = 1} ⁿtan β_i+ {C (T_B-T_P) -HΣ_{i = 1} ⁿ(1 / cos sβ_i)} Sinβ₀] Cos δ (1) [−hΣ_{i = 1} ⁿtan α_i+ {C (T_P-T_A) -HΣ_{i = 1} ⁿ(1 / cos α_i)} Sin α₀] Sinγ + V (T_B-T_A) = [− HΣ_{i = 1} ⁿtan β_i+ {C (T_B-T_P) -HΣ_{i = 1} ⁿ(1 / cos sβ_i)} Sinβ₀] Sin δ (2) where α_i, Β_iIs the XY-plane through ground stations A and B
The angle of incidence of radio waves passing through a plane-parallel layer of thickness h parallel to
Is the angle of refraction. −hΣ_{i = 1} ⁿtan α_i+ {C (T_P-T_A) -HΣ_{i = 1} ⁿ(1 / cos α_i)} Sin α₀= A-hΣ_{i = 1} ⁿtan β_i+ {C (T_B-T_P) -HΣ_{i = 1} ⁿ(1 / c osβ_i)} Sinβ₀= BV (T_B-T_A) = C. However, V is the rotation speed of the earth. (1) is Acosγ = Bcosδ (3) (2) is Asinγ + C = Bsinδ (4) cosγ = (1-sin^Twoγ)^1/2, Cos δ = (1
-Sin^Twoδ)^1/2To (3). A (1-sin^Twoγ)^1/2= B (1-sin^Twoδ)^1/2 (5) Square both sides of (5), and^Two(1-sin^Twoγ) = B^Two(1-sin^Twoδ) A^Two-A^Twosin^Twoγ = B^Two-B^Twosin^Twoδ (6) Substituting (4) into (6), A^Two-A^Twosin^Twoγ = B^Two-B^Two{(Asinγ + C) / B)^Two= B^Two-(A^Twosin^Twoγ + 2AC sinγ + C^Two) 2ACsinγ = B^Two-C^Two  -A^Two ∴ sin γ ＝ (B^Two-C^Two-A^Two) / 2AC (7) From (4), sinγ = (Bsinδ−C) / A (8) Substituting (8) into (6), A^Two-A^Two{(Bsin δ-C) / A}^Two= B^Two-B^Twosin^Twoδ A^Two-(B^Twosin^Twoδ-2BC sinδ + C^Two) = B^Two-B^Twosin^Twoδ 2BCsin δ = B^Two-A^Two+ C^Two ∴ sin δ = (B^Two-A^Two+ C^Two) / 2BC (9) Time T_A, T_B, T_P, Is confirmed, C, α₀，
β₀, Α_iAnd β_iIs confirmed. Therefore, A and B are
Therefore, γ and δ are determined from (8) and (9).

[Brief description of drawings]

(A) FIG. 1 is a diagram showing a radio wave propagation control method for knowing a radio wave propagation time between a ground station and a radio repeater when an electronic computer is not connected to the ground station. (B) FIG. 2 is a diagram showing a method for measuring an azimuth angle. In this figure, point P represents the position of the satellite and points A and B represent the position of the ground station. Further, γ and δ are angles formed by a straight line connecting the foot of a perpendicular line dropped from the satellite to the XY plane and each ground station and the X axis perpendicular to the rotation direction of the earth. (C) FIG. 3 is a diagram showing a propagation control method of radio waves radiated from the object and the fixed ground station. P _ij represents the position of the satellite at time T _ij , M _ij represents the position of the object at time T _ij , and W _ij represents the position of the fixed ground station at time T _ij . (D) FIG. 4 is a diagram showing a method for obtaining the shortest distance in a state where there is a radio wave propagating between the object and the radio repeater. (E) FIG. 5 is a diagram showing a radio wave selection method for obtaining the shortest distance in a certain state between the fixed ground station and the radio relay station. L ₆ represents the shortest distance between the fixed ground station and the radio repeater in a certain state. (F) FIGS. 6 and 7 are diagrams showing the shortest distance between the object, the radio repeater, and the fixed ground station when the radio wave path length is measured using radio wave propagation control. In FIG. 6, Mx and Mxx represent the position of the object at each time, and Pxx represents the position of the radio relay device at each time. Lxx represents the shortest distances between the object and the radio repeater, between the objects, and between the radio repeaters. Figure 7
In FIG. 6, W × and Wxx represent the position of the fixed ground station at each time point, and the others are the same as in FIG. (G) FIG. 8 is a diagram for synchronizing the aging mechanism of the object and the aging mechanism of the fixed ground station by utilizing radio wave propagation control. P _ij , M _ij and W _ij represent the positions of the radio repeater, the object and the fixed ground station at time T _ij . (H) FIG. 9 is a diagram for synchronizing the aging mechanism of the radio repeater and the aging mechanism of the fixed ground station using radio wave propagation control. P _ij , M _ij and W _ij represent the positions of the radio repeater, the object and the fixed ground station at time T _ij . (I) FIG. 10 shows that when the radio repeater is at point P12,
It is a figure showing the elevation angle and azimuth angle of the electric wave in coordinate XYZ which makes the position in the fixed ground station in the time of some origin. (J) FIG. 11 is a diagram when the circumference of the earth is divided into three layers. 1 is the earth, 2 is a plane parallel layer, 3 is a spherical layer, and 4 is a radio wave rectilinear layer. (K) FIG. 12 is a diagram showing a radio wave path until a radio wave emitted from a satellite (or a ground station) reaches the ground station (or a satellite). (L) FIG. 13 is a diagram when obtaining the elevation angle of a radio wave from the radio wave propagation time. Point P represents the position of the satellite at time T _P. Point Q is a foot of a perpendicular line drawn from the point P to the XY plane, and points A, B, and C are positions of the ground station at times T _A , T _B, and T _C. (M) FIG. 14 is a diagram showing an angle formed by a radio wave path and a normal line standing on an interface parallel to the ground surface when a radio wave plunges from a spherical layer into a radio wave straight layer (or vice versa). Is. The counterclockwise angle from this normal is positive. (N) FIG. 15 is a graph in which when a radio wave rushes from the spherical layer into the radio wave straight-ahead layer (or vice versa), the cosine of the angle between the normal line to the interface at the rush point and the radio wave traveling direction is the X axis FIG. 4 is a diagram showing a change in radio wave path length when the path length of a radio wave passing through the spherical layer and the parallel horizontal plane layer is represented by the Y axis. (O) FIG. 16 is a diagram showing a method for measuring an azimuth angle.
Point P is the position of the satellite, point A is the position of the ground station at time T _A , and point B is the position of the ground station at time T _B. In addition, the point Q is a perpendicular leg dropped from the point P to the XY plane, the point A ′,
B'is the point where the radio wave enters the interface between the radio wave rectilinear layer and the spherical layer, and point Q'is the straight line PQ is the intersection point between the wave rectilinear layer and the spherical layer. γ and δ represent the azimuth angles of the ground station when the ground station positions are points A and B, respectively. α ₀ and β ₀ are angles formed by the normal line of the radio wave entering the interface between the radio wave straight traveling layer and the spherical layer and the radio wave traveling direction. (P) FIG. 17 shows a basic radio relay device provided in a communication satellite for receiving a digital time code, determining the reception time of the code, and transmitting a radio signal after an arbitrary time has elapsed. .. The incoming radio signal is received by the antenna 1 and sent to the receiver 3 via the diplexer 2. Next, the arrival time of the received wireless signal is counted and confirmed by the timekeeping mechanism 4, the wireless signal is edited by the processing device 5, and stored in the internal storage device 6 for a specified time. After a specified time, the signal is combined in the mixer 8 with the intermediate frequency generated by the local oscillator 7. The output signal of the mixer has a frequency different from that of the received signal, is sent to the diplexer 2 through the transmitter 9, and is emitted from the antenna 1. (Q) FIG. 18 is a schematic diagram showing an electronic device provided on an object which attempts to locate a position for monitoring a three-dimensional position by transmitting and receiving radio waves at appropriate intervals using one communication satellite. .. This device can be unattended. The control program in the processing device sequentially repeats the reception mode and the transmission mode at certain time intervals. In the transmission mode, the control program in the processing device receives the time signal from the timekeeping mechanism, and the time generation program in the processing device 19 outputs the digital time signal in consideration of the delay time until the radiation from the antenna. generate.
The signal is generated as a digital time signal by the digital time signal generator 18, and the transmitter 19 and the diplexer 11 are generated.
It is radiated from the antenna 10 via the. In the reception mode, the incoming radio signal is received by the antenna 10 and sent to the receiver 12 via the diplexer 11. Next, the clock mechanism 13
Thus, the arrival time of the received wireless signal is counted and the received data is transferred to the received data buffer. And
The processing device corrects this counting result in consideration of the delay time from the reception of the antenna to the arrival of the aging mechanism. Editing work is performed by adding the correction result to the end of the digital time code stored in the received data buffer.
Then, at the time of the next transmission, the time counting mechanism 13 edits the digital time code considering the delay time to the antenna,
It is added to the end of the edited digital time code, converted into a digital time code by the digital time signal generator 18, this converted signal is modulated by the intermediate frequency generated by the local oscillator 17, and this modulated output, that is, the mixer. Is radiated from the antenna 10 via the diplexer 11 via the transmitter 19. (R) FIG. 19 shows a schematic diagram of an electronic device provided in a fixed ground station. A radio wave repeater installed on a satellite that receives a digital time signal, determines the time when the received digital time code arrives at a fixed ground station, processes these received signals by a radio wave propagation control program in a computer processor, and mounts them on a satellite. It is provided in the fixed ground station in order to observe and count the position of each time point and the distance between the fixed ground station and each object whose position is to be determined, and to determine the three-dimensional position of the object. 1 is a schematic diagram of a basic electronic device. A control program in the processing device switches between a transmission mode and a reception mode at certain time intervals. Now, in the reception mode, the incoming radio signal is received by the receiver 21 via the antenna 20.
This reception signal is counted by the clock mechanism 24 at the reception time of the incoming radio wave signal. The count result is received by the time generation program in the computer processing device, and the reception time of the incoming radio wave signal at the fixed ground station is corrected in consideration of the delay time from the antenna 20 to the clock mechanism. Next, the editing program in the processing device 24 adds the correction value of the reception time of the incoming radio signal at the fixed ground station to the end of the digital time code represented by the incoming radio signal. Then, the data signal is stored in the storage device 25. In the transmission mode, the processing device 2 takes into consideration the delay time until the processing device 24 radiates the digital time signal read by the clock mechanism from the antenna.
The radio wave emission time is corrected by the time generation program in 4, the digital time signal generator encodes the digital time, sends it to the transmitter 29, and emits it from the antenna 30. In addition, 22 is a mixer and 26 is a local oscillator. (S) Table 1 shows the temporal positions of the transmitter, the radio repeater, and the fixed ground station. (T) Table 2 shows arrival and departure times of radio waves. (U) Table 3 shows the emission time of the radio wave emitted from the fixed ground station. (V) Table 4 represents the data stored in the receive data buffer when the object is in receive mode. (W) Table 5 shows a radio wave route and a radio wave propagation time.

The three-dimensional position of an arbitrary point can be instantly known within a distance measuring accuracy of 1 mm.

─────────────────────────────────────────────────── ───

[Procedure amendment]

[Submission date] February 25, 1992

[Procedure Amendment 1]

[Document name to be amended] Statement

[Name of item to be corrected] Full text

[Correction method] Change

[Correction content]

[Document name] Statement

[Title of Invention] Three-dimensional position measurement by communication satellite

[Claims]

Detailed Description of the Invention

[0001]

SUMMARY OF THE INVENTION The present invention relates to a wireless position measurement system using an artificial earth satellite, and more specifically to a method for monitoring position using one communication satellite. One satellite is sufficient to locate the position of objects on the ground and in the air by distance measurement. The position and distance are determined from the propagation delay time when a wireless signal travels at the speed of light and is transmitted and received between an object via a satellite and a fixed station on the ground. If the time position of the satellite is known, the position line of the object can be calculated from one satellite having a different time position, and the observation position is at the intersection of the three position lines. The distance measurement accuracy at the observation position is within 1 mm.

[0002]

2. Description of the Related Art Considering the use of a communication satellite for wireless measurement in which position observation is performed by using a wireless signal, often requiring two satellites is a difficulty. The present invention overcomes this difficulty by requiring only one communication satellite. Further, there is an observation position determination system which is performed by one communication satellite (and active range finder satellite), but there is a drawback that two timing signal satellites are further required to exhibit the same function. Moreover, the ranging accuracy of the observation position is 100 m to 1500 m.

[0003]

BACKGROUND OF THE INVENTION The present invention is intended to provide early position monitoring, ie, tracking of human, vehicle and aircraft positions, at fixed ground stations using current or potential satellites. Is influential in. Possible applications include length, area and height measurements, ie surveying, location monitoring of oil tankers and other dangerous cargo-laden vessels, for disaster prevention and environmental protection. Effective monitoring of foreign vessels within 200 nautical miles, offshore surveillance of aircraft for traffic control, navigation of commercial vessels from land and vessel location, and location of land mobile vehicles. .. Others include position control of intercontinental ballistic bullets, satellite orbit correction and attitude control, and tracking of missiles. This method can spread its service on a global scale, can achieve high accuracy, and is cheaper than other proposed schemes.

[0004]

[Means for solving the problem]

[Operation] 1. Radio wave propagation control (1) Propagation control of radio waves radiated from the object The transmitter antenna position of the object whose position is to be determined (hereinafter referred to as the transmitter antenna position) is time T.
_{At M11} , it is at point M11. The antenna position of the radio repeater mounted on the satellite (hereinafter referred to as the radio repeater antenna position) is point P11 at time T _M11 .
It is in. The antenna position of the fixed ground station is at point W11 at time T _M11 . At time T _M11 , a radio wave is radiated from the transmitter antenna position, and the time when the radio wave reaches the radio repeater antenna position is T _P12 . During time (T _P12 -T _M11 ), the transmitter antenna position changes from point M11 to point M12, the radio repeater antenna position changes from point P11 to point P12, and the fixed ground station antenna position changes from point W11 to point W11. Move to W12. Assuming that the radio relay time of the radio repeater is Δτ, the radio wave reaching the radio repeater at time T _P12 is emitted from the radio repeater at time (T _P12 + Δτ). Time (T _P12 + Δ
τ), the transmitter antenna position moves to point M13, the radio repeater antenna position moves to point P13, and the fixed ground station antenna position moves to point W13. Time (T _P12
+ Δτ), the time when the radio wave radiated from the radio repeater antenna position reaches the fixed ground station antenna position is T
_W14 . At time T _W14 , the transmitter antenna position is at point M14, and the radio repeater antenna position is at point P1.
4, the antenna position of the fixed ground station moves to point W14. The above is summarized in Table 1. Further, the above is illustrated in FIG. At time T _MX , when the time when the radio wave radiated from the transmitter antenna position reaches the radio repeater antenna position is (T _P12 + Δτ), when the radio repeater moves from point P12 to point P13 Since it is a radio wave that has just reached, the error in the radio wave path length due to the refractive index of atmospheric gas is ignored, and C ((T _P12 + Δ
τ) -T _MX ) is the distance between the point MX and the point P13.
(In the time column when the radio wave reaches the radio repeater antenna in Table 2, the radio wave equal to T _P12 + Δτ corresponds to this.) In order to determine the time T _MX , first, from the transmitter antenna position, Radio waves are radiated toward a radio relay station for a certain time period and at a certain time interval, and these radio waves reach a fixed ground station via the radio wave relay station. In the fixed ground station, these received radio waves are stored in the storage device of the electronic computer connected to the fixed ground station as shown in Table 2. Using Table 2,
The distance between the point MX and the point P13 is determined according to the flow chart of FIG.

(2) Propagation Control of Radio Waves Emitted from Fixed Ground Stations The time when radio waves are radiated from the fixed ground station is T _WX , and the position of the fixed ground station at this time T _WX is point WX. The time when this radio wave returns to the fixed ground station again is T
_WY , the position of the fixed ground station at this time T _WY is defined as point WY. The time when the radio wave is radiated from the transmitter antenna position is T
The radio wave of _M11 reaches the fixed ground station at time T _W14 . The position of the fixed ground station at this time is point W14.
If time T _WY is the same as time T _W14 , time T
After reaching the radio repeater, the radio wave radiated from the fixed ground station in _WX passes the same route as the radio wave radiated from the transmitter antenna position at time T _M11 . In order to determine the time _TWX , first, radio waves are radiated from the fixed ground station at a fixed time and at a fixed time interval, and these radio waves are displayed on a storage device of a computer installed in the fixed ground station. It is stored like 3. Using Table 3, the distance between the point WX and the point P12 can be calculated according to the flow chart of FIG.

(3) Radio wave propagation control in the object and the fixed ground station in the reception mode In the object and the fixed ground station, the transmission mode and the reception mode are sequentially repeated. When in the transmission mode, the incoming radio wave is not received and either the radio wave is radiated or nothing is performed. When in the receive mode, no radio waves are emitted and either incoming radio waves are received or nothing is done. (A) When the object is in the reception mode. When the radio wave arrives at the antenna, the incoming radio wave is stored in the reception data buffer via the diplexer. Next, the time when the radio wave arrives at the antenna is determined by considering the delay time from the antenna to the reception data buffer by the aging mechanism provided in the object. Then, the radio wave arrival time is added to the end of the data stored in the received data buffer. When the object is switched to transmit mode, the contents of the received data buffer are sent to the transmitter and further radiated from the antenna via the diplexer. In addition, received data
The data in the buffer is guaranteed until the object goes from receive mode to send mode and then to the next receive mode. The data stored in the received data buffer is as shown in Table 4. (B) Radio wave propagation control of the fixed ground station in the reception mode: The arrival time of the incoming radio wave is determined by the aging mechanism in the fixed ground station, and the content of the received radio wave is stored in the electronic equipment connected to the fixed ground station. Process by computer.

(4) Radio wave path using radio wave propagation control
Measuring the length L The distance between point M11 and point P12 is L₁(Fig. 6
reference). To the influence of the refractive index of atmospheric gas (including the ionosphere)
Than L₁= [[HΣ_{i = 1} ⁿtan α_1i+ {C (T_P12-T_M11) −hΣ_{i = 1} ⁿ(1 / cos α_1i)} Sin α₁₀]^Two + [Nh + {c (T_P12-T_M11) -HΣ_{i = 1} ⁿ(1 / cos α_1i)} Cos α₁₀]^Two]^1/2 nh is the refractive index of atmospheric gas in units of 1 km in height from point M11
The height when dividing up to a height of 1 parallel to the ground surface
The difference is usually h = 1 and n = 500. c is in vacuum
Propagation speed of radio waves in T_P12Is from point M11 to time T
_M11When the radiated radio waves reach the radio repeater
Tick, T_M11Is the time when the radio wave was radiated from the point M11, α
_1i(I = 1 to n) is the radio wave to each parallel plane layer of thickness h
Angle of incidence, α₁₀Is a flat in the sky above the height nhkm from the point M11
It is the refraction angle of the radio wave to the row plane layer. From Snell's law,
In the plane-parallel layer (n = 1 to 12), n_1Bsin α_1B= N₁₁sin α₁₁= N₁₂si
nα₁₂＝ ・ ・ ・ ・ ・ ＝ n_1isin α_1i= ...
・ ＝ n₁₁₂sin α₁₁₂= N₁₀sin α₁₀  n₁₀Is a known value of the refractive index of radio waves in a vacuum. or,
n_1BIs the refractive index of atmospheric gas at point M11, and
For measuring atmospheric pressure, vapor pressure and absolute temperature of M11
Get more. n₁₁, N₁₂・ ・ ・ ・ ・ ・ ・ ・ N_1i...
..N₁₁₂Is n_1BAnd the atmosphere 1 km above the point M11
If the refraction index of the gas is known, it can be obtained from an empirical formula. Parallel sphere
In the layer (n = 12 to 500), (n₁₁₂+ 12 / a) sin α₁₁₂= (N₁₁₃+
13 / a) sin α₁₁₃＝ ・ ・ ・ ・ ・ ・ ＝ (n_1i+
i / a) sin α_1i＝ ・ ・ ・ ・ ・ ＝ (n₁₅₀₀+5
00 / a) sin α₁₅₀₀= N₁₀sin α₁₀  Where a is the radius of the earth and n₁₁₂, N₁₁₃...
n_1i・ ・ ・ ・ ・ ・ ・ ・ N₁₅₀₀Is the large stratosphere and ionosphere
It is the refractive index of air gas, and is more than the refractive index of atmospheric gas in the troposphere.
It is stable, and the method described in Japanese Patent Application No. 3-128489 is used.
I ask for it. Also, α₁₀Is calculated from the elevation angle,Get more. However, V is the rotation speed of the earth, k_iIs α₁₀
Is a proportional constant corresponding to. From the above, L₁Is determined.
That is, the shortest distance between the point M11 and the point P12 is determined.
It The distance between points P13 and W14 is L_Three(Fig. 7
reference). Effect of refractive index of atmospheric gas (including ionosphere)
By L_Three= [[HΣ_{i = 1} ⁿtan α_3i+ {C (T_W14-(T_P12+ Δ τ))-hΣ_{i = 1} ⁿ(1 / cos α_3i)} Sin α_Thirty]^Two + [Nh + {c (T_W14-(T_P12+ Δτ))-hΣ_{i = 1} ⁿ(1 / cos α_3i)} Cos α_Thirty]^Two]^1/2 nh is the refractive index of atmospheric gas at a height of 1 km from the ground surface
Altitude when dividing up to the height of 1 parallel to the ground surface
The difference is usually h = 1 and n = 500. c is in vacuum
Propagation speed of radio wave, T_P12Is from point M11 to time T
_M11When the radiated radio waves reach the radio repeater
Tick, T_M11Is the time when the radio wave was radiated from the point M11, T
_W14Is from point M11 to time T_M11Electric energy emitted when
Waves are transmitted to the fixed ground station antenna position W14 via the radio repeater.
Time of arrival, α_3i(I = 1 to n) is each parallel of thickness h
Refraction angle of the radio wave to the plane layer, α_ThirtyIs the height from the ground surface nh
It is the incident angle of the radio wave on the parallel plane layer above the km. Sune
According to Le's law, in parallel plane layers (i = 1 to 12)
Is n_3Bsin α_3B= N₃₁sin α₃₁= N₃₂si
nα₃₂＝ ・ ・ ・ ・ ・ ＝ n_3isin α₃₁...
= N₃₁₂sin α₃₁₂= N_Thirtysin α_Thirty  n_ThirtyIs a known value of the refractive index of radio waves in a vacuum. or,
n_3BIs the refractive index of the atmospheric gas at W14, and the point W
By measuring the atmospheric pressure, vapor pressure and absolute temperature of 14
I can get it. n₃₁, N₃₂・ ・ ・ ・ ・ ・ ・ ・ N_3i...
・ N₃₁₂Is n_3BAnd the atmospheric gas 1 km above the point W14
If the index of refraction of the film is known, it can be obtained from an empirical formula. Parallel spherical layer
In (i = 12 to 500), (n₃₁₂+ 12 / a) sin α₃₁₂= (N₃₁₃+
13 / a) sin α₃₁₃＝ ・ ・ ・ ・ ・ ＝ (n_3i+ I
/ A) sin α_3i＝ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ＝ (n
₃₅₀₀+ 500 / a) sin α₃₅₀₀= N_Thirtysi
nα_Thirty Where a is the radius of the earth and n₃₁₂, N₃₁₃...
・ N_3i... n₃₅₀₀Is the large stratosphere and ionosphere
It is the refractive index of air gas, and is more than the refractive index of atmospheric gas in the troposphere.
It is stable, and the method described in Japanese Patent No. 3-128489 is used.
I ask for it. Also, α_ThirtyIs calculated from the elevation angle,Get more. However, V is the rotation speed of the earth, k_iα_ThirtyTo
Is the corresponding proportionality constant. From the above, L_ThreeIs determined. Immediately
Then, the shortest distance between the point P13 and the point W14 is determined. The distance between point WX and point W14 is L₅(See Fig. 7)
See). L₅= V (T_W14-T_WX) V is the rotation speed of the earth. T_W14Is the transmitter antenna position M
11 to time T_M11The radio waves emitted during
When the fixed ground station antenna position W14 via the relay is reached
Ticks. T_WXHas reached the position P12 of the radio repeater antenna
Time is T_P12Fixed ground station antenna position, as in
The emission time of the radio wave emitted from WX. T_P12Is the transmitter
From antenna position M11, time T_M11Is radiated when
When the radio wave reaches the radio repeater antenna position P12
Ticks. The distance between the point P12 and the point WX is L₆(See Fig. 7)
See). In the influence of the refractive index of atmospheric gas (including the ionosphere)
Than L₆= [[HΣ_{i = 1} ⁿtan_6i+ {C (T_P12-T_WX) -HΣ_i-1 ⁿ (1 / cos α_6i)} Sin α₆₀]^Two + [Nh + {c (T_P12-T_WX) -HΣ_{i = 1} ⁿ(1 / cos α_6i)} Cos α₆₀]^Two]^1/2 nh is the refractive index of atmospheric gas at a height of 1 km from the ground surface
Altitude when dividing up to the height of 1 parallel to the ground surface
The difference is usually h = 1 and n = 500. c is in vacuum
Propagation speed of radio wave, T_P12Is the point M₁₁From time T
_M11When the radiated radio waves reach the radio repeater
Tick, T_WXHas reached the position P12 of the radio repeater antenna
Time is T_P12Fixed ground station antenna position, as in
The emission time of the radio wave emitted from WX. α_6i(I = 1 to 1
n) is the incident angle of the radio wave on each parallel plane layer of thickness h, α₆₀
Is the radio wave from the ground surface to the parallel plane layer above the height nhkm
Is the refraction angle of. From Snell's law, parallel plane layers (i =
1 to 12), n_6Bsin α_6B= N₆₁sin α₆₁= N₆₂si
nα₆₂= ・ ・ ・ ・ = N_6isin α_6i＝ ・ ・ ・ ・ ＝
n₆₁₂sin α₆₁₂= N₆₀sin α₆₀ n₆₀Is a known value of the refractive index of radio waves in a vacuum. or,
n_6BIs the refractive index of atmospheric gas at point WX,
By measuring the atmospheric pressure, vapor pressure and absolute temperature of
Maru n₆₁, N₆₂・ ・ ・ ・ ・ ・ ・ ・ N_6i... n
₆₁₂Is n_6BAnd bending of atmospheric gas 1 km above the point WX
If the folding index is known, it can be obtained from an empirical formula. Parallel spherical layer (i =
12-500), (n₆₁₂+ 12 / a) sin α₆₁₂= (N₆₁₃+
13 / a) sin α₆₁₃＝ ・ ・ ・ ・ ・ ＝ (n_6i+ I
/ A) sin α_6i＝ ・ ・ ・ ・ ・ ・ ・ ・ ＝＝ (n₆₅₀₀
+ 500 / a) sin α₆₅₀₀= N₆₀sin α₆₀ Where a is the radius of the earth and n₆₁₂, N₆₁₃...
・ N_6i... n₆₅₀₀Is the large stratosphere and ionosphere
It is the refractive index of air gas, and is more than the refractive index of atmospheric gas in the troposphere.
It is stable and can be obtained by the method described in Japanese Patent Application No. 3-128489.
I will keep it. Also, α₆₀Is calculated from the elevation angle,Get more. However, V is the rotation speed of the earth, k_iIs α₆₀
Is a proportional constant corresponding to. From the above, L₆ Is determined
It That is, the shortest distance between the point P12 and the point WX is determined.
It The distance between the point P13 and the point MX is L₇(See Fig. 6)
See). In the influence of the refractive index of atmospheric gas (including the ionosphere)
Than L₇= [[HΣ_{i = 1} ⁿtan_7i+ {C ((T_P12+ Δτ) -T_M X) -hΣ_{i = 1} ⁿ(1 / cos α_7i)} Sin α₇₀]^Two + [Nh + {c ((T_P12+ Δτ) -T_MX) -HΣ_{i = 1} ⁿ(1 / cos α_7i )} Cos α₇₀]^Two]^1/2 nh is the refractive index of atmospheric gas in units of 1 km in height from point M11
The height when dividing up to a height of 1 parallel to the ground surface
The difference is usually h = 1 and n = 500. c is in vacuum
Propagation speed of radio waves in T_P12Is from point M11 to time T
_M11When the radiated radio waves reach the radio repeater
Tick, T_MXHas reached the position P13 of the radio repeater antenna
Time is T_P12Transmitter antenna position as + Δτ
The emission time of the radio waves emitted from the MX. α_7i(I = 1
~ N) is the incident angle of the radio wave on each parallel plane layer of thickness h, α
₇₀From the point MX to the parallel plane layer above the height nhkm
It is the refraction angle of the radio wave. From Snell's law, parallel plane layers
In (i = 1 to 12), n_7Bsin α_7B= N₇₁sin α₇₁= N₇₂si
nα₇₂＝ ・ ・ ・ ・ ・ ＝ n_7isin α_7i= ...
・ ・ ・ ・ ・ ・ ＝ n₇₁₂sin α₇₁₂= N₇₀sin
α₇₀ n₇₀Is a known value of the refractive index of radio waves in a vacuum. or,
n_7BIs the refractive index of atmospheric gas at point M11, and
For measuring atmospheric pressure, vapor pressure and absolute temperature of M11
Get more. n₇₁, N₇₂・ ・ ・ ・ ・ ・ ・ ・ N_7i...
..N₇₁₂Is n_7BAnd the atmosphere 1 km above the point M11
If the refraction index of the gas is known, it can be obtained from an empirical formula. Parallel sphere
In the layer (i = 12 to 500), (n₇₁₂+ 12 / a) sin α₇₁₂= (N₇₁₃+
13 / a) sin α₇₁₃＝ ・ ・ ・ ・ ・ ＝ (n_7i+ I
/ A) sin α_7i＝ ・ ・ ・ ・ ・ ・ ・ ・ ＝＝ (n₇₅₀₀
+ 500 / a) sin α₇₅₀₀= N_{70 sin α 70} Where a is the radius of the earth and n₇₁₂, N₇₁₃...
・ N_7i... n₇₅₀₀Is the large stratosphere and ionosphere
It is the refractive index of air gas, and is more than the refractive index of atmospheric gas in the troposphere.
It is stable, and the method described in Japanese Patent No. 3-128489 is used.
I ask for it. Also, α₇₀Is calculated from the elevation angle,Get more. However, V is the rotation speed of the earth, k₁Is α₇₀
Is a proportional constant corresponding to. From the above, L₇Is determined.
That is, the shortest distance between the point P13 and the point MX is determined. The distance between points M11 and MY is L₉, Point P12 and point
The distance between MY and L₁₀(See FIG. 6). Time T
_M11When, the radio wave relay from the transmitter antenna position M11
The electric wave radiated toward the machine is time T_P12When this
Reach the radio repeater. This time T_P12When this
Released from the radio repeater to the surveyor in reception mode on the ground
Select the radio wave to be emitted. This selected radio wave
Time to reach the surveyor in the reception mode of T_MYTosu
It Also, time T_MYWhen in the reception mode on the ground when
The position of the measurer is defined as a point MY. L₉= V (T_MY-T_M11) V is the rotation speed of the earth. T_M11Is the transmitter antenna position M
The time when the radio wave was emitted from 11 to the radio repeater. Big
Due to the influence of the refractive index of gas (including the ionosphere), L₁₀= [[HΣ_{i = 1} ⁿtan_10i+ {C ((T_MY-T_P12 ) -HΣ_{i = 1} ⁿ(1 / cos α_10i)} Sin α₁₀₀]^Two + [Nh + {c (T_MY-T_P12) -HΣ_{i = 1} ⁿ(1 / cos α_10i)} Cos α₁₀₀]^Two]^1/2 nh is the refractive index of atmospheric gas in units of 1 km in height from point M11
The height when dividing up to a height of 1 parallel to the ground surface
The difference is usually h = 1 and n = 500. c is in vacuum
Propagation speed of radio waves in T_P12Is from the point M11
Tick T_M11When the radio wave radiated reaches the radio repeater
Time, α_10i(I = 1 to n) are parallel planes of thickness h
Refraction angle of radio wave to the layer, α₁₀₀Is height nh from point M11
It is the incident angle of the radio wave on the parallel plane layer above the km. Sune
In the parallel plane layer (i = 1 to 12) from Le's law, n_10Bsin α_10B= N₁₀₁sin α₁₀₁= N
₁₀₂sin α₁₀₂・ ・ ・ ・ ・ ＝ n_10isin α
_10i＝ ・ ・ ・ ・ ・ ＝ n₁₀₁₂sin α₁₀₁₂= N
₁₀₀sin α₁₀₀ n₁₀₀Is a known value of the refractive index of radio waves in a vacuum.
Also, n_10BIs the refractive index of atmospheric gas at point MX
Measure the atmospheric pressure, vapor pressure and absolute temperature at point M11.
It can be obtained by things. n₁₀₁, N₁₀₂・ ・ ・ ・ ・ ・ ・ ・ N
_10i... n₁₀₁₂Is n_10BAnd at point M11
If you know the refraction index of atmospheric gas 1km above the sky,
I want it. In the parallel spherical layer (i = 12 to 500), (n₁₀₁₂+ 12 / a) sin α₁₀₁₂= (N
₁₀₁₃+ 13 / a) sin α₁₀₁₃＝ ・ ・ ・ ・ ・ ＝
(N_10i+ I / a) sinα_10i= ...
... = (n₁₀₅₀₀+ 500 / a) sin α
₁₀₅₀₀= N₁₀₀sin α₁₀₀ Where a is the radius of the earth and n₁₀₁₂, N₁₀₁₃・ ・ ・
... n_10i... n₁₀₅₀₀Is the stratosphere and electricity
The refractive index of atmospheric gas in the delaminating layer, which is the refractive index of atmospheric gas in the troposphere.
It is more stable than the folding rate and described in Patent Request 3-128489.
Method. Also, α₁₀₀Is the elevation angle calculation method
,Get more. However, V is the rotation speed of the earth, k_iIs α
₁₀₀Is a proportional constant corresponding to. From the above, L₁₀Is
Determined. That is, the shortest distance between the point P12 and the point MY is
Set. The distance between the point M11 and the point P13 is L₈(Fig. 6
reference). The distance between points M11 and MX is L₁₁Tosu
It L₁₁= V (T_MX-T_M11) V is the rotation speed of the earth. T_MXIs a satellite-mounted radio repeater
The time when the antenna position P13 is reached is T_P12+ Δτ
Radio wave is emitted from the transmitter antenna position MX.
Time By the second law of the cosine of the triangle, L₁₀ ^Two= L₁ ^Two+ L₉ ^Two-2L₁L₉cos∠P12 ・ M11 ・ MY ∴cos∠P12 ・ M11 ・ MY = (L₁ ^Two+ L₉ ^Two-L₁₀ ^Two) / 2L₁L₉ (B-1) The distance between point P12 and point MX is L₁₂Then, L₁₂ ^Two= L₁ ^Two+ L₁₁ ^Two-2L₁L₁₁ccs∠P12 · M11 · MY ········ (B-2) Substituting equation (B-1) into equation (B-2). L₁₂ ^Two= L₁ ^Two+ L₁₁ ^Two-(2L₁L₁₁) ・ {(L₁ ^Two+ L₉ ^Two -L₁₀ ^Two) / 2L₁L₉} = L₁ ^Two+ L₁₁ ^Two-L₁₁(L₁ ^Two+ L₉ ^Two-L₁₀ ^Two) / L₉·········· (B-3) From the formula (B-3), the distance L between the point P12 and the point MX.
₁₂Is confirmed. ∠P13 ・ P12 ・ MX = γ, ∠M1
1 · P12 · MX = δ. L₇ ^Two= L_Two ^Two+ L₁₂ ^Two-2L_TwoL_{12 cosγ} ∴ cosγ = (L_Two ^Two+ L₁₂ ^Two-L₇ ^Two) / 2L_TwoL₁₂・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ (B-4) L₁₁ ^Two= L₁ ^Two+ L₁₂ ^Two-2L₁L_{12 cos δ} ∴cos δ = (L₁ ^Two+ L₁₂ ^Two-L₁₁ ^Two) / 2L₁L₁₂·········· (B-5) ∠M11 · P12 · P13 = γ + δ. L₈ ^Two= L₁ ^Two+ L_Two ^Two-2L₁L_Twocos (γ + δ) = L₁ ^Two+ L_Two ^Two-2L₁L_Two(Cos γ cos δ-sin γ sin δ) ... (B-6) sin γ = (1-cos^Twoγ)^1/2= [1-{(L_Two ^Two+ L₁₂ ^Two-L₇ ^Two ) / (2L_TwoL₁₂)}^Two]^1/2(B-7) sin δ = (1-cos^Twoδ)^1/2= [1-{(L₁ ^Two+ L₁₂ ^Two-L₁₁ ^Two ) / (2L₁L₁₂)}^Two]^1/2(B8) Formulas (B-4), (B-5), (B-7) and (B-8)
Is substituted into equation (B-6). L₈ ^Two= L₁ ^Two+ L_Two ^Two-2L₁L_Two[{(L_Two ^Two+ L₁₂ ^Two-L₇ ^Two) / (2L_TwoL₁₂)} {L₁ ^Two+ L₁₂ ^Two-L₁₁ ^Two) / (2L₁L₁₂)}-[1-{(L_Two ^Two+ L₁₂ ^Two-L₇ ^Two) / (2L_TwoL₁₂)}^21/2・ [1-((L₁ ^Two+ L₁₂ ^Two-L₁₁ ^Two) / (2L₁L₁₂)}^Two]^1/2] L₈= <L₁ ^Two+ L_Two ^Two-2L₁L_Two[{(L_Two ^Two+ L₁₂ ^Two-L₇ ^Two) / (2 L_TwoL₁₂)} {(L₁ ^Two+ L₁₂ ^Two-L₁₁ ^Two) / (2L₁L₁₂)}-[1-{(L_Two ^Two+ L₁₂ ^Two-L₇ ^Two) / (2L_TwoL₁₂)}^Two]^1/2・ [1-{(L₁ ^Two+ L₁₂ ^Two-L₁₁ ^Two) / (2L₁L₁₂)}^Two]^1/2]^{1 / Two} >^1/2 From the above, L₈Is confirmed. The distance between point WY and point W14 is L₂₁(Fig. 7
reference). L₂₁= V (T_W14-T_WY) V is the rotation speed of the earth. T_W14Is the transmitter antenna position M
11 to time T_M11The radio waves emitted during
When the fixed ground station antenna position W14 via the relay is reached
Ticks. T_WYIs time T_P12When the radio repeater antenna position
Radio waves radiated from P12 reach fixed ground station position WY
The time reached. The distance between point P12 and point WY is L₂₀(Fig. 7
reference). Effect of refractive index of atmospheric gas (including ionosphere)
By L₂₀= [[HΣ_{i = 1} ⁿtan α_20i+ {C (T_WY-T_P12 ) -HΣ_{i = 1} ⁿ(1 / cos α_20i)} Sin α₂₀₀]^Two + [Nh + {c (T_WY-T_P12) -HΣ_{i = 1} ⁿ(1 / cos α_20i)} Cos α₂₀₀]^Two]^1/2 nh is the refractive index of atmospheric gas at a height of 1 km from the ground surface
Altitude difference when dividing up to a height of 1 parallel to the ground surface
Therefore, normally, h = 1 and n = 500. c is in vacuum
Propagation speed of radio wave, T_P12Is from point M11 to time T
_M11When the radiated radio wave reaches the radio repeater
Tick, α_20i(I = 1 to n) is for each parallel plane layer of thickness h
Refraction angle of radio wave, α₂₀₀Is nhkm high from point MY
It is the incident angle of the radio wave to the parallel plane layer in the sky. Snell's Law
From the rule, in the parallel plane layer (i = 1 to 12), n_20Bsin α_20B= N₂₀₁sin α₂₀₁= N
₂₀₂sin α₂₀₂＝ ・ ・ ・ ・ ・ ・ ＝ n_20isin
α_20i＝ ・ ・ ・ ・ ・ ・ ＝ n₂₀₁₂sin α₂₀₁₂
= N₂₀₀sin α₂₀₀ n₂₀₀Is a known value of the refractive index of radio waves in a vacuum.
Also, n_20BIs the refractive index of atmospheric gas at point MY
To measure the atmospheric pressure, vapor pressure and absolute temperature at point MY.
Determined by n₂₀₁, N₂₀₂・ ・ ・ ・ ・ ・ ・ ・ N
_20i... n₂₀₁₂Is n_20BAnd above the point MY
If the refraction index of the atmospheric gas at 1 km in the sky is known, it can be obtained from the experimental formula.
Maru In the parallel spherical layer (i = 12 to 500), (n₂₀₁₂+ 12 / a) sin α₂₀₁₂= (N
₂₀₁₃+ 13 / a) sin α₂₀₁₃= ...
= (N_20i+ I / a) sinα_20i= ...
・ ・ ・ ・ ・ ・ ＝ (n_20,500+ 500 / a) sin α
_20,500= N₂₀₀sin α₂₀₀ Where a is the radius of the earth and n₂₀₁₂, N₂₀₁₃・ ・ ・
... n_20i... n_20,500Is the stratosphere and electricity
The refractive index of atmospheric gas in the delaminating layer, which is the refractive index of atmospheric gas in the troposphere.
It is more stable than the folding rate and described in Patent Request 3-128489.
Method. Also, α₂₀₀Is the elevation angle calculation method
,Get more. However, V is the rotation speed of the earth, k_iIs α
₂₀₀Is a proportional constant corresponding to. From the above, L₂₀Is
Determined. That is, the shortest distance between the point P12 and the point WY is
Set. (10) Set the distance between point P12 and point W14 to L_ThirteenTosu
(See FIG. 7). Coordinates of point P12 with point W14 as the origin
Is P12 (X, Y). (X-L₅)^Two+ Y_Two ^Two= L₆ ^Two・ ・ ・ ・ ・ ・ ・ ・ (C-1) (X-L₂₁)^Two+ Y^Two= L₂₀ ^Two(C-2) From the formulas (C-1) and (C-2), X = (L₆ ^Two-L₂₀ ^Two-L₅ ^Two+ L₂₁ ^Two) / 2 (L₂₁-L₅) ... (C-3) Substituting equation (C-3) into equation (C-1). Y = [L₆ ^Two-{(L₆ ^Two-L₂₀ ^Two+ L₂₁ ^Two-2L₅L₂₁+ L₅ ^Two ) / 2 (L₂₁-L₅)}^Two]^1/2..... (C-4) From formulas (C-3) and (C-4), L_Thirteen ^Two= X^Two+ Y^Two= {(L₆ ^Two-L₂₀ ^Two-L₅ ^Two+ L₂₁ ^Two) / 2 (L₂₁-L₅)}^Two+ [[L₆ ^Two-{(L₆ ^Two-L₂₀ ^Two+ L₂₁ ^Two-2 L₅L₂₁+ L₅ ^Two) / 2 (L₂₁-L₅)}^Two]^1/2]^Two ∴L_Thirteen= [{(L₆ ^Two-L₂₀ ^Two-L₅ ^Two+ L₂₁ ^Two) / 2 (L₂₁ -L₅)}^Two + [L₆ ^Two-{(L₆ ^Two-L₂₀ ^Two+ L₂₁ ^Two-2L₅L₂₁+ L₅ ^Two ) / 2 (L₂₁-L₅)}^Two]]^1/2 From the above, L_ThirteenIs determined. That is, point P12 and point W14
The shortest distance between and is fixed. (11) Time T_W14Position W14 of fixed ground station at
With the origin as time T_P12Position of the radio repeater when
Set the coordinates of P12 to P12 (X_P12, Y_P12，
Z_P12) (See FIG. 7). Radiated from point P12
Radio waves when they reach the fixed ground station position WY
The elevation angle of β_20nThen the angle β_20nIs certain
I have decided. X_P12 ^Two+ Y_P12 ^Two+ Z_P12 ^Two= L_Thirteen ^Two・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ (G-1) X_P12 ^Two+ (Y_P12-L₂₁)^Two+ Z_P12 ^Two= L₂₀ ^Two・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ (G-2) Z_P12= L₂₀sin β_20n········ (G-3) From the formulas (G-1) and (G-2), Y_P12= (L_Thirteen ^Two-L₂₀ ^Two+ L₂₁ ^Two) / 2L₂₁········· (G-4) From the formulas (G-1), (G-3) and (G-4), X_P12= [L_Thirteen ^Two-{(L_Thirteen ^Two-L₂₀ ^Two+ L₂₁ ^Two) / (2 L₂₁)}^Two-L₂₀ ^Twosin^Twoβ_20n]^1/2.. (G-5) L_Thirteen, L₂₀, L₂₁And β_20nIs confirmed
Coordinate P12 (X_P12, Y_P12, Z
_P12) Is also confirmed. (12) Set the distance between point WZ and point P13 to L₁₈To
(See Figure 7). Refractive index of atmospheric gas (including ionosphere)
Due to the effect of L₁₈= [[HΣ_{i = 1} ⁿtan α_18i+ {C ((T_P12+ Δτ) -T_WZ ) -HΣ_{i = 1} ⁿ(1 / cos α_18i)} Sin α₁₈₀]^Two + [Nh + {c ((T_P12+ Δτ) -T_WZ) -HΣ_{i = 1} ⁿ(1 / cos α_18i)} Cos α₁₈₀]^Two]^1/2 nh is the refractive index of atmospheric gas at a height of 1 km from the ground surface
Altitude when dividing up to the height of 1 parallel to the ground surface
The difference is usually h = 1 and n = 500. c is in vacuum
Propagation speed of radio wave, T_P12Is from point M11 to time T
_M11When the radiated radio wave reaches the radio repeater
Tick, T_WZHas reached the position P13 of the radio repeater antenna
Time is T_P12Fixed ground station antenna
The emission time of the radio wave emitted from the position WZ. α
_18i(I = 1 to n) is the radio wave to each parallel plane layer of thickness h
Incident angle of, α₁₈₀Is above the height nhkm above the ground
It is the refraction angle of the radio wave to the plane parallel layer. Snell's law
In the parallel plane layer (i = 1 to 12), n_18Bsin α_18B= N₁₈₁sin α₁₈₁= N
₁₈₂sin α₁₈₂・ ・ ・ ・ ・ ・ ＝ n_18isin α
_18i＝ ・ ・ ・ ・ ・ ・ ＝ n₁₈₁₂sin α₁₈₁₂=
n₁₈₀sin α₁₈₀ n₁₈₀Is a known value of the refractive index of radio waves in a vacuum.
Also, n_18BIs the refractive index of atmospheric gas at point W14
Measure the atmospheric pressure, vapor pressure and absolute temperature at point W14
It can be obtained by things. n₁₈₁, N₁₈₂... n
_18i..... n₁₈₁₂Is n_18BAnd point W14
If you know the refraction index of atmospheric gas 1 km above
I can get it. In the parallel spherical layer (i = 12 to 500)
Is (n₁₈₁₂+ 12 / a) sin α₁₈₁₂= (N
₁₈₁₃+ 13 / a) sin α₁₈₁₃= ...
= (N_18i+ I / a) sinα_18i= ...
= (N₁₈₅₀₀+ 500 / a) sin α₁₈₅₀₀=
n₁₈₀sin α₁₈₀ Where a is the radius of the earth and n₁₈₁₂, N₁₈₁₃...
... n_18i..... n₁₈₅₀₀Is the stratosphere and
Refractive index of atmospheric gas in the ionosphere, and that of atmospheric gas in the troposphere
It is more stable than the refractive index, and the patent request is 3-128489.
I will ask for it using the method described below. Also, α₁₈₀Is the elevation angle calculation method
FromGet more. However, V is the rotation speed of the earth, k_iIs α
₁₈₀Is a proportional constant corresponding to. From the above, L₁₈Is
Determined. That is, the distance L between the point WZ and the point P13₁₈But
Determine. (13) Set the distance between point WZ and point W14 to L₂₂To
(See Figure 7). L₂₂= V (T_W14-T_WZ) V is the rotation speed of the earth. T_W14Is the transmitter antenna position M
11 to time T_M11The radio waves emitted during
The time when the antenna reaches the ground station antenna position W14 via the relay. T
_WZIs the time when it reached the radio repeater antenna position P13
T_P12Fixed ground station antenna position as + Δτ
The emission time of the radio wave emitted from WZ. From the above, L₂₂
Is determined. That is, the shortest distance between the point WZ and the point W14 is
Determine. ▲ 14 ▼ Time T_W14Position W14 of fixed ground station at
With the origin as time T_P12Radio repeater when + Δτ
The coordinates of position P13 of P13 (X_P13, Y_P13, Z
_P13) (See FIG. 7). Emitted from point P13
Radio wave when it reaches the fixed ground station position W14
The elevation angle of β_3nThen, from the term, the elevation angle β_3nIs confirmed
I'm doing so, X_P13 ^Two+ Y_P13 ^Two+ Z_P13 ^Two= L_Three ^Two・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ (H-1) X_P13 ^Two+ (Y_P13-L₂₂)^Two+ Z_P13 ^Two= L₁₈ ^Two・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ (H-2) Z_P13= L_Threesin β_3n(H-3) From formulas (H-1) and (H-2), Y_P13= (L_Three ^Two-L_Thirteen ^Two+ L₂₂ ^Two) / 2L₂₂(H-4) From formulas (H-1), (H-3) and (H-4), X_P13= [L_Three ^Two-{(L_Three ^Two-L_Thirteen ^Two+ L₂₂ ^Two) / 2L₂₂ }^Two-L_Three ^Twosin^Twoβ_Threen]^1/2・ ・ ・ ・ ・ ・ ・ ・ ・ ・ (H-5) L_Three, L₁₈, L₂₂And β_3nHas been confirmed,
Coordinate P13 (X_P13, Y_P13，
Z_P13) Is also confirmed. (15) Set the distance between points P12 and P13 to L_TwoTo
(See Figure 7). L_Two= {(X_P12-X_P13)^Two+ (Y_P12-Y_P13)^Two＋ (Z_P12-Z_P13)^Two}^1/2 Since the coordinates of the points P12 and P13 are fixed, L_Two
Is also confirmed. (16) Draw a vertical line from the point P12 to the horizontal plane that passes through the point MY.
Then, the foot is designated as point Q12. Time T_M11When
It is radiated from the receiver antenna position M11 toward the radio repeater.
Radio wave at time T_P12When, reach this radio repeater
To do. This time T_P12At this time,
Select the radio wave radiated to the surveyor in the reception mode above.
Choose. This selected radio wave is in the ground reception mode.
Time to reach the surveyor_MYAnd Point P12 and point
The distance to Q12 is L_10ZThen, L_10Z= Nh + {c (T_MY-T_P12) -HΣ_{i = 1} ⁿ(1 / c os α_10i)} Cos α₁₀₀ nh is the refractive index of atmospheric gas at a height of 1 km from point MY.
Altitude when dividing up to the height of 1 parallel to the ground surface
The difference is usually h = 1 and n = 500. c is in vacuum
Propagation speed of radio wave, T_P12Is from point M11 to time T
_M11When the radiated radio waves reach the radio repeater
Tick, α_10i(I = 1 to n) is for each parallel plane layer of thickness h
Refraction angle of radio wave, α₁₀₀Is nhkm above the ground
It is the incident angle of the radio wave to the parallel plane layer in the sky. Therefore, L
_10ZIs confirmed.

(5) Determining the three-dimensional position of the object by radio wave propagation control With the point W14 as the origin, the coordinates M11 (X,
Y, Z) is calculated. The point M11 is an intersection point of a circle formed by intersecting a sphere having a center of a point P12, a radius of L ₁ and a center of a point P13, and having a radius of L _{8 with} a horizontal plane passing through the point MY, and thus ^{_{P12) 2 + (Y-Y}} P12) 2 + (Z-Z P12) 2 = L 1 2 ···················· (K-1) (X -X _P13 ) ² + (Y-Y _P13 ) ² + (Z-Z _P13 ) ² = L ₈ ² ... K-2) Z = Z _P12- L _{10Z ...} (K-3) (K-1) ), (K-2), 2 (X _P13 −X _P12 ) X + 2 (Y _P13 −Y _P12 ) Y + 2 (Z _P13 −Z _P12 ) Z = L ₁₂ ² −L ₈ ² − (X _{P 12} ² + Y _{P 12} ² + _{Z P ^{2 2) + (X P1 3}} 2 + Y P13 2 + Z P13 2) ······ (K-4) ▲ 11 ▼ than ^{_{section, X P12 2 + Y P12 2}} + Z P12 2 = L 13 2 ····・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ (K-5) From item (15), X _P13 ² + Y _P13 ² + Z _P13 ² = L ₃ ² (K-6) Substituting (K-5) and (K-6) into (K-4), ( _XP13) −X _P12 ) X + (Y _P13 −Y _P12 ) Y + (Z _P13 −Z _P12 ) Z = (L ₁ ² −L ₈ ² −L ₁₃ ² + L ₃ ² ) / 2 ... _{·············· (K-7) X P12} , X P13, Y P12, Y P13, Z P12 and _{Z P13} is, ▲ 11 ▼ claim, ▲ 15 Term and ▲ 12 ▼
Because they confirm the _{claim, X P13 -X P12 = a,} Y
Putting the P ₁₃ -Y _P12 = b and _{Z P13 -Z P12 = d, (} K-7) ^{_{is, aX + bY + dZ = (}} L 1 2 -L 8 2 -L 13 2 + L 3 2) / 2 Y = {( L ₁ ² −L ₈ ² −L ₁₃ ² + L ₃ ² ) / 2−aX−dZ} / b ... (K -8) Z is determined from (K-3) and item (17) on page 29. (K-3) a (K-1), (K -2) is substituted ^{_{into, (X-X P12) 2}} + (Y-Y P12) 2 + (Z P12 -L 10Z - Z P12) 2 = L ₁ ² ... (K-9) (X-X _P13 ) ² + (Y-Y _P13 ) ² + (Z _P12- L _10Z -Z _P13 ) ² = L ₈ ² ... (K-10) From (K-9), (X-X _P12 ) ² + (Y-Y _P12 ) ² + L _10Z ² = L ₁ ² ... (K-11) From (K-10), (X-X _P13 ) ² + (Y-Y
^{_{P13) 2 + (Z P12 -Z}} P13) 2 -2 (Z P12
^{_{-Z P13) L 10Z + L 10Z}} 2 = L 8 2 Z P13 -
From ^{_{Z P12 = d, (X-}} X P13) 2 + (Y-Y P13) 2 + d 2 + 2dL 10Z + L 10Z 2 = L 8 2 ············ (K-12) ( K-11) - (from ^{_{K-12), 2aX + 2bY}} = L 1 2 -L 8 2 + 2dL 10Z + d 2 + a (X P1 2 + X P13) + b (Y P12 + Y P13) ······ (K-13 _{) X P12 + X P13 = e} , when the _{Y P12 + Y P13 = f,} (K-13) ^{_{may, 2aX + 2bY = L 1 2}} -L 8 2 + 2dL 10Z + d 2 + ae + bf Y = (L 1 2 -L 8 2 + 2dL 10Z + D ² + ae + bf-2aX) / 2b ... (K-14) Substitute (K-14) into (K-1). To do. ^{_{(X-X P12) 2 +}} {(L 1 2 -L 8 2 + 2dL 10Z + d 2 + a e + bf-2aX) / 2b-Y P12} 2 + (Z P12 -L 10Z -Z P12) 2 = L 1 2 ( _{^{1 + a 2 / b 2)}} X 2 +2 {(a / b) (L 1 2 -L 8 2 + 2dL 10Z + d 2 + ae + bf-2bY P12 X- P12)} X + (L 1 2 -L 8 2 + 2dL 10Z + d 2 ^{_{+ ae + bf-2bY P12)}} 2/4 b 2 + X P12 2 + L 10Z 2 -L 1 2 = 0 X = [- (a / b) (L 1 2 -L 8 2 + 2dL 10Z + d 2 + ae + bf- 2bY P12 -X P12 ) ± ^{_{[{(a / b) (L}} 1 2 -L 8 2 + 2dL 10Z + d 2 + ae + bf -2bY P12 -X P12)} 2 - (1 + a 2 / b 2) {(L 1 2 ^{_{L 8 2 + 2dL 10Z + d}} 2 + ae + bf-2bY P12) 2 / 4b 2) + X P12 2 + L 10Z 2 -L 1 2} ] ^{1/2] / (1 + a 2} / b 2) ········ ... (K-15) Substitute (K-15) into (K-8). Y = (L ₁ ² −L ₈ ² −L ₁₃ ² + L ₃ ² ) / 2 −a [− (a / b) (L ₁ ² −L ₈ ² + 2dL _10Z + d ² + ae + bf-2bY _P12 −X _P12 ) ± ^{_{[{(a / b) (L}} 1 2 -L 8 2 + 2dL 10Z + d 2 + ae + bf-2bY P12 -X P12)} 2 - (1 + a 2 / b 2) {(L 1 2 -L 8 2 + 2dL 10Z ^{_{+ d 2 + a e + bf}} -2bY P12) 2 / 4b 2) + X P12 2 + L 10Z 2 -L 1 2} ] ^1/2] Accordingly, the position of the point M11 is determined.

2 How to synchronize the timekeeping mechanism: Fixed ground station, radio repeater mounted on satellite and position
The objects that try to find the
Have a structure. Now, let's see how to synchronize these clocks.
Explain. (1) A timekeeping mechanism and a fixed mechanism for the object whose position is to be determined.
Synchronization with the timekeeping mechanism of the fixed ground station The object whose position is to be determined (hereinafter referred to as the aforementioned object)
To do. ) And a fixed ground station (hereinafter referred to as the fixed ground station)
It ) And the radio repeater mounted on the satellite at the same time from
(Hereinafter, referred to as the above-mentioned radio repeater.)
Shoot. These two radio waves pass through the radio repeater and
It is received at the fixed ground station and the object. From the object M11
The radiated radio wave propagates and reaches the radio repeater P12.
When it reaches the fixed ground station W1Y from the radio repeater
Select the radio waves radiated toward. This selected radio wave
Radiation time T from the radio repeater of_P12, The fixed land
Arrival time T to the upper station_W1Y, Azimuth β_W1YAnd elevation α
_W1YIs a computer connected to the fixed ground station
Is recorded on the storage device. The radio wave is the radio repeater
When the radio relay time elapses after reaching
Radio waves are emitted from aircraft P13 to the fixed ground station W14.
Be done. Time T at which this radio wave is emitted from the radio repeater
_P13, The arrival time T at the fixed ground station_W14And the above
Elevation angle α at fixed ground station_W14And azimuth β_W14To
Computer storage device connected to the fixed ground station
Remember above. Radiation from the fixed ground station W11
The propagated radio wave propagates and reaches the radio repeater P22.
From the radio repeater to the fixed ground station W2Y
Select the radio wave to be radiated. In front of this selected radio wave
Radiation time T from the radio repeater_P22, The fixed ground station
Arrival time T_W2Y, Azimuth β_W2YAnd elevation α
_W2YIs a storage device of a computer connected to a fixed ground station
Recorded above. After the radio wave reaches the radio repeater,
Radiation toward the object M24 when the radio relay time has elapsed
Radiated to the fixed ground station W3Y in addition to the radio waves
There are radio waves that are generated. Radiation to this fixed ground station
Time T at which the radio wave is emitted from the radio repeater_P23, The above
Arrival time T at the fixed ground station_W3YAnd at the fixed ground station
Angle of elevation α_W3Y, Azimuth β_W3YThe fixed ground station
Stored in the storage device of the computer connected to
Ku. (Refer to Table 5) The coordinates when the point W1Y of the point P12 is the origin is P12.
(X_P12, Y_P12, Z_P12), Point W1 of point P13
The coordinates when 4 is the origin are P13 (X_P13, Y
_P13, Z_P13), The point W2Y of the point P22 was used as the origin.
The coordinates at time P22 (X_P22, Y_P22, Z_P22)
And the coordinate when the point W3Y of the point P23 is the origin is P2.
3 (X_P23, Y_P23, Z_P23). Atmospheric gas
Neglecting the error of the radio path length due to the refractive index of
The apparent shortest distance between the point P12 and the point W1Y is c.
(T_W1Y-T_P12), So X_P12= C (T_W1Y-T_P12) Cos α_W1Y・ Sin β_W1 Y Y_P12= C (T_W1Y-T_P12) Cos α_W1Y・ Cos β_{W1 Y} Z_P12= C (T_W1Y-T_P12) Sin α_W1Y T_W1Y-T_P12= T_W3Y-T_P23, Α_W1Y= Α_W3Y (1) T_W2Y-T_P22= T_W14-T_P13, Α_W14= Α_W2Y (2) If so, the radio path M11 → P12 → P13 → W14
Wave paths W11 → P22 → P23 → M24 are equal in time
And the arrival time T of the radio wave to the object_M24And fixed land
Arrival time T of the radio wave to the upper station_W14There is a difference between
For example, when the difference is between the above-mentioned object and each time-dependent mechanism of the fixed ground station
There will be a gap between them. Therefore, the relationship of the above equations (1) and (2)
Satisfy the radio wave to the electric power connected to the fixed ground station.
Select from the storage device of the child computer, and store the object over time.
Synchronize the aging mechanism between the structure and the fixed ground station.

(2) Synchronization of the radio repeater mounted on the satellite (see FIG. 9) At time T _M01 , the object emits a radio wave toward the radio repeater. The time when the radio wave reaches the radio repeater is T _P02 . Also, from the fixed ground station in the previous period, time T
_{When W01,} a radio wave is radiated toward the radio repeater.
It is assumed that the radio wave is radiated from the fixed ground station so that the time when the radio wave reaches the radio wave repeater becomes T _P02 . Let L ₁ be the distance between the object and the radio repeater. or,
_Let L ₂ be the distance between the position of the radio relay station at the time T _P02 + α and the fixed ground station at the time T _W04 . Here, α is the radio relay time of the radio repeater, and T _W04 is the time when the radio wave radiated from the object at time T _M01 reaches the fixed ground station via the radio repeater. L ₁ = c (T _P02 −T _M01 ) (4) L ₂ = c (T _P02 −T _W01 ) (5) L ₁ + L ₂ = c (T _W04 −T _M01 −α) (6) (4), From (5) and (6), T _P02 = (T _W04 + T _W01 −α) / 2 Therefore, since T _W04 , T _W01, and α are known, the true value at time T _P02 is determined. Therefore, the true value corrects the aging mechanism of the radio repeater. However, when the radio wave radiated from the object reaches the radio wave repeater and the position of the radio wave repeater, and when the radio wave relay time of the radio wave repeater elapses after the radio wave reaches the radio wave repeater. The position of the radio wave repeater of 1 is relative to the fixed ground station, and the radio wave at the same position is selected. That is, two radio waves having the same radio wave propagation time and elevation angle are selected.

3. Correction of satellite position error due to atmospheric refractive index (see FIG. 20) The space through which radio waves pass is divided into plane layers of thickness h parallel to the ground surface passing through the fixed ground station Q _n . The refractive indices of the parallel plane layers are n ₀ , n ₁ , ..., N _n , respectively. Let P1 be the actual position of the satellite and P2 be the apparent position of the satellite. The incident point of the radio wave radiated from the actual position P1 of the satellite from the medium with the refractive index n _{0 to} the medium with the refractive index n ₁ is Q ₀ ,
Let Q be the incident point from the medium of refractive index n _{1 to} the medium of refractive index n _2.
1 , the incident point from the medium having the refractive index n _{2 to} the medium having the refractive index n ₃ is Q ₂ , the incident point from the medium having the refractive index n _{3 to} the medium having the refractive index n ₄ is Q ₃ , ... Index n _1-1 to refractive index n _1
Let Q _{1-1 be} the incident point of the medium on the medium, and _let Q _n be the incident point on the ground surface, that is, the position of the fixed ground station. The foot of a perpendicular line drawn from the point Q ₀ to the interface between the refractive indices n ₁ and n ₂ is N ₁ ,
The perpendicular leg dropped from the point Q ₁ to the interface between the refractive indices n ₂ and n ₃ is N ₂ , the perpendicular leg dropped from the point Q ₂ to the interface between the refractive indices n ₃ and n ₄ is N ₃ , ...・ Refractive index n _{i + 1} from point Q _i
And the leg of the perpendicular line dropped on the interface of n _{i +2} is N _{i + 1} ...
Foot of the perpendicular line drawn from the ... point _{Q n-1} on the ground surface of the _N n,
Also, let I be the foot of the perpendicular line drawn from the point Q ₀ to the ground surface.
Refractive index n _{0 of the} radio wave radiated from the actual position P1 of the satellite
Medium the refractive index n ₁ of alpha ₁ to the incident angle alpha ₀ refraction angle at the interface of the _medium, refraction angle alpha ₂ to the interface of the medium refractive index n ₂ and a medium of refractive index n _1, a refractive index n The refractive angle to the interface between the medium of No. _{2 and} the medium of refractive index n ₃ is α ₃ , ..., The refractive index n
a _i-1 of the medium refraction angle at the interface of the medium of refractive index n _i alpha
_i , ... Let α _{n be} the refractive index at the interface between the medium having the refractive index n _{n−1 and} the medium having the refractive index n _n . If that emits radio waves toward the ground surface to the satellite Conversely, at in the medium from the refractive index n ₁ to n _n, may be replaced refraction angle to the incident angle. Further, the refraction angle to the medium having the refractive index n ₀ is α ₀ . When radio wave radiated from the actual position P1 of the satellite is incident on the medium having a refractive index n ₁ from a medium of refractive index n _0, the incident point Q
_It is assumed that the incident point on the ground surface is J, assuming that the light has not been refracted at ₀ and has proceeded straight to reach the ground surface. IJ / IQ ₀ = tanα ₀ ∴IJ = IQ ₀ tanα ₀ = nh · tanα ₀ N ₁ Q ₁ / N, where n is the number of parallel plane layers with a thickness h from the interface with a refractive index n ₀ to the ground surface. ₁ Q ₀ = tan α ₁ ∴N ₁ Q ₁ = N ₁ Q ₀ tanα ₁ = h · tan α ₁ N ₂ Q ₂ / N ₂ Q ₁ = tan α ₂ ∴N ₂ Q ₂ = N ₂ Q ₁ tanα ₂ = h · tanα N ₃ Q ₃ / N ₃ Q ₂ = tan α ₃ ∴N ₃ Q ₃ = N ₃ Q ₂ tanα ₃ = h · tanα ₃ ··· N _i Q _i / N _i Q _i-1 = tan α _i ∴N _i Q _i = N _i Q _i-1 tanα _i = h · tanα _i ··· N _n Q _n / N _n Q _n-1 = tan α _n ∴N _n Q _n = N _n Q _n-1 tanα _n = h · tan α _n IQ _n = N ₁ Q ₁ + N ₂ Q ₂ + N ₃ Q ₃ + ... + N _i Q _i + ... + N _n Q _n = h (tan α ₁ + tan α ₂ + tan α ₃ + ... + tan α _i + ... + tan α _n ) JQ _n = IJ-IQ _n = nh. tan α ₀ −h (tan α ₁ + tan α ₂ + tan α ₃ + ... + tan α _i + ... tan α _n ) = h {nt a α ₀ − (tan α ₁ + tan α ₂ + tan α ₃ + ・ ・ ・ ・ ・ + tan α _i + ・ ・ ・ ・ ・ + Tanα _n )} N ₁ Q ₀ / Q ₀ Q ₁ = cos α ₁ ∴Q ₀ Q ₁ = N ₁ Q ₀ / cosα ₁ = h / cosα ₁ Radio waves pass through Q ₀ Q ₁ . Let t ₁ be the time required for ct ₁ = Q ₀ Q ₁ ∴t ₁ = Q ₀ Q ₁ / c = h (cosα ₁ · c) N ₂ Q ₁ / Q ₁ Q ₂ = _{cosα 2 ∴Q 1 Q 2 = N} 2 ₁ / _{cosα 2} = h / co
When the time required for the sα ₂ radio wave to pass through Q ₁ Q ₂ is t ₂ , ct ₂ = Q ₁ Q ₂ ∴t ₂ = (N ₂ Q ₁ / cos α ₂ ) / c = when the radio wave propagation speed is c. h / (cosα ₂ · c) N ₃ Q ₂ / Q ₂ Q ₃ = cos α ₃ ∴Q ₂ Q ₃ = N ₃ Q ₂ / cos α ₃ = h / cos α ₃ Required for the radio wave to pass through Q ₂ Q _3. If the time is t ₃ , the radio wave propagation velocity is c, and ct ₃ = Q ₂ Q ₃ ∴t ₃ = Q ₂ Q ₃ / c = h / (cos α ₃ · c) ··· N _i Q _i-1 / Q _{i −1} Q _i = cos α _i ∴Q _i-1 Q _i = N _i Q _i-1 / cos α _i = h / cos αi Let t _i be the time required for the radio wave to pass through Q _i-1 Q _i. ct _i the speed of _{c = Q i-1 Q i} ∴t i = Q i-1 Q i = h / (cosα _{· C) · · N n Q} n-1 / Q n-1 Q n = cosα n ∴Q n-1 Q n = N n Q n-1 / ccsa n = h / cosα n radio waves _{Q n-1} Q Letting t _n be the time required to pass _n , ct _n = Q _n−1 Q _n ∴t _n = Q _n−1 Q _n / c = h / (cos α _n
· C) radio wave the time required to pass between the points P1 and Q ₀ and T _p. The emission time of the radio wave at the point P1 is T _p1 ,
When the in radio wave arrival time to the point _{Q n} and _{T qn, T qn -T p1 =} (t 1 + t 2 + t 3 + ··· + t i + ··· + t n) + T p ∴T p = (T _{qn -T p1) - (t 1} + t 2 + t 3 + ··· + t i + ·· · t n) = (T qn -T p1) - {h / (cosα 1 · c) + h / (cos α 2・ C) + h / (cosα ₃ · c) + ・ ・ ・ + h / (cosα _i · c) + ・ ・ ・ + h / (cosα _n · c)} = (T _qn −T _p1 ) − (h / c) (1 / cosα ₁ + 1 / cosα ₂ + 1 / cosα ₃ + ... + 1 / cosα _i + ... + 1 / cosα _n ) _Let L _p1q0 be the distance between the point P1 and the point Q ₀ . the refractive index is _{n 0 (= 1), L} p1q0 = c · T p = c (T qn -T p1) -h (1 / c When _{sα 1 + 1 / cosα 2 +} 1 / cosα 3 + ···· + 1 / cosα i + · ·· + 1 / radio wave radiated from the cos [alpha] _n) point P1, assuming straight without being refracted at the point _{Q 0,} the point Let L be the distance between Q ₀ and point J
_{Assuming JQ0} , the time T _jq0 from when the radio wave passes through the point Q ₀ until it reaches the point J on the ground surface is T _jq0 = L because the refractive index of the medium is n ₀ (= 1). _{jq0 / c = JQ 0 / c} = (1 / c) (IQ 0 / cosα 0) = nh / radio wave radiated from (cosα ₀ · c) the actual position of the satellite P1 is, the refractive index n
_The time to reach the ground surface through the medium of ₀ (= 1) is T
_{If j} , the medium is all uniform and the refractive index is n _0. T _j = P1Q ₀ / c + JQ ₀ / c = L _p1q0 / c + L _jq0 / c = (T _qn −T _p1 ) + (h / c) {n / cosα ₀ − (1 / c osα ₁ + 1 / cosα ₂ + 1 / cosα ₃ + ... + 1 / coscos _i + ... + 1 / cosα _n )} From the actual position P1 of the satellite The radiated radio wave has a refractive index n
₀ (= 1) times the refractive index _n 0 required to pass through the uniform _{medium, n 1, n 2, n} 3, ·····, n i, ···
.. and n _n , where T _s is the difference from the time required to pass through the medium, T _s = T _j − (T _qn −T _p1 ) = (h / c) {n / cos α ₀ − (1 / Cosα ₁ + 1 / cosα ₂ + 1 / cosα ₃ + ···· + 1 / cosα _i + ···· + 1 / cosα _n ) The elevation angle of the radio wave radiated from the satellite's apparent position P2 at the fixed ground station ( π / 2-α _n ) The elevation angle at the point Q ₀ of the radio wave radiated from the actual position P1 of the satellite is (π / 2-α ₀ ).
Then, from Snell's law, n ₀ sin α ₀ = n _n sin α _n ∴sin α ₀ = (n _n / n ₀ ) sin α _n ∴α ₀ = sin ⁻¹ {(n _n / n ₀ ) sin
α _n } Therefore, the actual position of the satellite is the rear point J of the fixed ground station.
Then, the distance from the fixed ground station is h {n · tan α ₀ − (tan α ₁ + tan α ₂ + ta
nα ₃ + ・ ・ ・ ・ ・ + tan α _i + ・ ・ ・ ・ ・ + tan
α _n )}, the elevation angle is π / 2-sin ⁻¹ {(n _n / n ₀ ) sin α _n } The arrival time of the radio wave is compared to the time until the radio wave reaches the fixed ground station. Then, (h / c) {n / cos α ₀ − (1 / cos α ₁ + 1 /
cosα ₂ + 1 / cosα ₃ + ... + 1 / cosα _i
+ ... + 1 / cos α _n ) increases. With the position Q _n of the fixed ground station as the origin, the points Q _n-1 , Q _n-2 , ..., Q _i ,.
_{Q 3, Q 2, Q 1} , Q 0, and the coordinates of P1, respectively _{(X n-1, Y n} -1), (X n-2, Y n-2), ·
..., (X _i , Y _i ), ... (X ₃ ,
Y ₃ ), (X ₂ , Y ₂ ), (X ₁ , Y ₁ ), (X ₀ , Y
₀ ) and (X _p1 , Y _p1 ). X _n-1 = N _n Q _n = N _n Q _n-1 tan α _n = h · tan α _n Y _n-1 = N _n Q _n-1 = h X _n-2 = N _n Q _n + N _n-1 Q _n-1 = h · tan α _n + h · tan α _n-1 Y _n-2 = N _n Q _n-1 + N _n-1 Q _n-2 = 2h X _i = N _n Q _n + N _n-1 Q _n-1 + ... + N _{i + 1} Q _{i + 1} = h (tanα _n + tanα _n-1 + ... + tanα _{i + 1} ) Y _i = N _n Q _n-1 + N _n-1 Q _n-2 + ... + N _{i + 1} Q _i = (n-i) h X ₃ = N _n Q _n + N _n-1 Q _n-1 + ... + N _{i + 1} Q _{i + 1} + ... ... + N ₄ Q ₄ = h ( _{tanα n + tanα n-1 +} ······ + tanα i + 1 + ····· + tanα 4) Y 3 = n n Q n-1 + _{n-1 Q n-2 +} ····· + N i + 1 Q i + · ···· + N 4 Q 3 = (n-3) h X 2 = N n Q n + N n-1 Q n-1 +・ ・ ・ ・ ・ + N _{i + 1} Q _{i + 1} + ・ ・ ・ ・ + N ₄ Q ₄ + N ₃ Q _{3 = h (tanα n} + tanα _n-1 + ・ ・ ・ ・ ・ ・ + tanα _{i + 1} + ・ + tanα ₄ + tanα _{3) Y 2 = n n Q} n-1 + n n-1 Q n-2 + ····· + n i + 1 Q i + · ···· + n 4 Q 3 + n 3 Q 2 = (n-2) h _{X 1 = N n Q n +} N n-1 Q n-1 + ····· + N i + 1 Q i + 1 + · ···· + N 4 Q 4 + N 3 Q 3 + N 2 Q 2 = h (tanα n + tanα n _{-1 + ······ + tanα i + 1} + ····· + tanα 4 + tanα 3 + tanα 2) Y _{= N n Q n-1 +} N n-1 Q n-2 + ····· + N i + 1 Q i + · ·· + N 4 Q 4 + N 3 Q 3 + N 2 Q 2 + N 1 Q 1 = (n-1 _{) h X 0 = N n Q} n + N n-1 Q n-1 + ····· + N i + 1 Q i + 1 + · ···· + N 4 Q 4 + N 3 Q 3 + N 2 Q 2 + N 1 Q 1 = h (tanα _n + tanα _n-1 + ... + tanα _{i + 1} + ... + tanα ₄ + tanα ₃ + tanα ₂ + tanα ₁ ) Y ₀ = N _n Q _n-1 + N _n-1 Q _n-2 +・ ・ ・ ・ ・ + N _{i + 1} Q _i + ・ ・ ・ ・ + N ₄ Q ₃ + N ₃ Q ₂ + N ₂ Q ₁ + N ₁ Q ₀ = nh X _p1 = X ₀ + P 1Q ₀ sin α ₀ = hΣ _{i = 1} ⁿ tanα _i + L ^{_{p1q0 sinα 0 = hΣ i = 1}} n ta nα i + {c ^{_{T qn -T p1) -hΣ i =}} 1 n (1 / cosα i)} sinα 0 Y p1 = Y 0 + P1Q 0 cosα 0 = nh + {c (T qn -T p1) -hΣ i = 1 n (1 / cosα _i )} cosα _{0 The} radio wave radiated from the actual position of the satellite toward the ground station or the observation point, or the radio wave radiated from the ground station or the observation point toward the satellite, has a refractive index n ₀ to a refractive index n ₁ The origin is the point of incidence of radio waves on the interface parallel to the ground surface that changes to or opposite to, and at this origin, the refractive index n ₀ changes to the refractive index n ₁ or the opposite interface is parallel to the ground surface. The radio wave from the actual position of the satellite to the ground station or observation point on the XY-plane, where the normal is the X-axis, and the Y-axis is the straight line orthogonal to the X-axis in the plane formed by this X-axis and the radio wave path. the horizontal distance _{L XP1} and vertical path length of When determining the release _{L YP1,} angle of incidence, the reference line angle of refraction and the positive direction of the X axis ^{_{L XP1 = hΣ i = 1 n}} tan (π + α i) + {c (T qn -T p1) + hΣ i = 1 n (1 / cos (π + α i))} sinα 0 = hΣ i = 1 n tanα i + {c (T qn -T p1) -hΣ i = 1 n (1 / cosα i)} sinα 0 L YP1 = nh + { c (T _qn −T _p1 ) + hΣ _{i = 1} ⁿ (1 / (cos (π + α _i ))} cosα ₀ = nh + {c (T _qn −T _p1 ) −hΣ _{i = 1} ⁿ (1 / cos α _i ). } Cos α ₀ Therefore, if the shortest distance between the actual position P1 of the satellite and the position Q _n of the fixed ground station is L _p1qn , then L _p1qn = (L _Xp1 ² + L _Yp1 ² ) ^1/2 = [[hΣ _{i = 1} ⁿ tanα _i + {c (T _qn −T _p1 ) −h Σ ^{_{i = 1 n (1 / cosα}} i)} sinα 0 ] ² + _{[nh + {c (T qn -T} p1) -hΣ i = 1 n (1 / c osα i)} cosα 0 ] ^{2] 1/2}

4. Determination of elevation angle The circumference of the earth is classified into three regions as shown in FIG. Ground surface
The area from the surface to the height of 12 km above the ground is the horizontal layer or the ground surface.
From the height of 12 km to 500 km in the spherical layer,
Then, the area over 500 km above the ground surface is directly
I'll call it Shinda. Radio waves from satellites in the sky now
Is radiated, and this radio wave propagates and the ground station on the ground surface
Consider the path of this radio wave when it reaches.
(See Fig. 12) The medium through which the radio waves pass is the water passing through the ground station.
Divide into parallel plane layers of thickness h parallel to the plane. Point A is time T_APosition of the ground station at time point B is time T_BPosition C of the ground station at time T_CThe position of the ground station at time point P is time T_PThe position of the radio relay station mounted on the satellite at_AThen the elevation angle (π /
2-α_n) Is emitted toward the radio repeater at time T_PNoto
The radio wave dotted line PB reaching the radio wave repeater position P is the time T_PFrom the radio relay station position P to the ground station
Is emitted toward the time T_BAngle of elevation (π / 2-β_n)
The radio wave dotted line PC reaching the ground station position B at time T_PFrom the radio relay station position P to the ground station
Is emitted toward the time T_CAngle of elevation (π / 2-γ_n)
The radio wave AP reaching the ground station position C at_AGround station position A and time T_Pof
The shortest distance between the radio relay station position P and the thick line PB is the time T_BGround station position B and time T_Pof
Position PThick line PC is time T_CGround station position C and time T_Pof
Shortest distance L from the radio relay station position P₁Is time T_PHeight of position P of the radio repeater when_TwoIs time T_AGround station position A and time T_PWhen
Horizontal distance from the radio relay station position P_FourIs time T_BGround station position B and time T_PWhen
Horizontal distance from the radio relay station position P₆Is time T_CGround station position C and time T_PWhen
The horizontal distance δ from the radio relay station position P is_BGround station position B and time T_PWhen
The foot of the perpendicular line dropped from the position P of the radio repeater to the XY-plane.
Angle L formed by the straight line connecting Q and the positive direction of the Y-axis_ThreeIs time T_AGround station position A and time T_BWhen
Shortest distance from the ground station position B of L₅Is time T_BGround station position B and time T_CWhen
Shortest distance from the ground station position C of (above, refer to FIG. 13).
From the second law, L_Two ^Two= L_Three ^Two+ L_Four ^Two-2L_ThreeL_Fourcos δ (1) In ΔBCQ, from the second law of cosine, L₆ ^Two= L_Four ^Two+ L₅ ^Two-2L_FourL₅cos (π−δ) = L_Four ^Two+ L₅ ^Two + 2L_FourL₅From cos δ (2) (1), 2L_ThreeL_Fourcos δ = L_Three ^Two+ L_Four ^Two-L_Two ^Two ∴cos δ = (L_Three ^Two+ L_Four ^Two-L_Two ^Two) / 2L
_ThreeL_Four (3) From (2), 2L_FourL₅cos δ = L₆ ^Two-L_Four ^Two-L₅ ^Two ∴cos δ = (L₆ ^Two-L_Four ^Two-L₅ ^Two) / 2L
_FourL₅ (4) From (3) and (4), (L_Three ^Two+ L_Four ^Two-L_Two ^Two) / 2L_ThreeL_Four= (L₆ ^Two-L_Four ^Two-L₅ ^Two ) / 2L_FourL₅ L_Three ^TwoL₅+ L_Four ^TwoL₅-L_Two ^TwoL₅-L_ThreeL₆ ^Two+ L_ThreeL_Four ^Two+ L_Three L₅ ^Two= 0 (5) Radio waves radiated from the satellite position P
It is assumed that a point O on the interface YY 'with the layer is entered. At point O
At the interface YY 'between the radio wave rectilinear layer and the spherical layer
Be XX '. The traveling direction of the radio wave is based on the half line OX
Then, (1) radio waves are radiated from the satellite toward the observation point on the ground.
14-1, the incident angle of the radio wave on the interface YY ′; α₀ The radio wave of the i-th parallel plane layer from the interface YY '
Refraction angle; α_i+ Π From Snell's law, n₀sin α₀= -N_isin (α_i+ Π) (∵n₀sin α₀= N_isin α_i) (2) Radio waves radiate from the ground observation point to the satellite
14-2, the refraction angle of the radio wave from the interface YY ′; α₀Incident angle of radio wave from the + π interface YY ′ to the i-th parallel plane layer;
α_i From Snell's law, n_isin α_i= -N₀sin (α₀+ Π) (∵n₀sin α₀ = N_isin α_i) By correcting the satellite position error due to atmospheric refractive index, L₁= Nh + {c (T_P-T_A) + HΣ_{i = 1} ⁿ(1 / cos (π + α_i))} Cos α₀ = Nh + {c (T_P-T_A) -HΣ_{i = 1} ⁿ(1 / cos α_i)} Cos α₀ (6-1) = nh + {c (T_B-T_P) + HΣ_{i = 1} ⁿ(1 / cos (π + β_i))} C osβ₀ = Nh + {c (T_B-T_P) -HΣ_{i = 1} ⁿ(1 / cos β_i)} Cosβ₀ (6-2) = nh + {c (T_C-T_P) + HΣ_{i = 1} ⁿ(1 / cos (π + γ_i))} Cosγ₀ = Nh + {c (T_C-T_P) -HΣ_{i = 1} ⁿ(1 / cos γ_i)} Cosγ₀ (6-3) L_Two= HΣ_{i = 1} ⁿtan (π + α_i) + {C (T_P-T_A) + HΣ_{i = 1} ⁿ (1 / cos (π + α_i))} Sinα₀ (7) L_Four= HΣ_{i = 1} ⁿtan (π + β_i) + {C (T_B-T_P) + HΣ_{i = 1} ⁿ (1 / cos (π + β_i))} Sinβ₀ (8) L₆= HΣ_{i = 1} ⁿtan (π + γ_i) + {C (T_C-T_P) + HΣ_{i = 1} ⁿ (1 / cos (π + γ_i))} Sinγ₀ (9) L_Three= V (T_B-T_A) (10) L₅= V (T_C-T_B) (11) where n is the atmospheric gas layer and ionosphere,
Thickness h parallel to the horizontal plane of the object to be stopped
The number when divided into layers. c is the radio wave propagation speed. α₀Is
Time T from position A of the ground station_AWhen facing,
The radiated radio waves plunge into the interface between the ionosphere and the radio wave straight layer.
At the entry point,
Angle between the normal OX 'and the radio wave (see Figure 14-2)
See). α_iIs time T_AFrom the position A of the ground station at
Radio waves radiated toward the repeater may hit the ground surface or position.
Of the thickness h parallel to the horizontal plane where the object to be stopped exists
Incident angle when entering the i-th parallel plane layer from the bottom surface
(See FIG. 14-2). β₀Is from position P of the radio repeater
Tick T_PAt the time T_BWhen
The radio waves that have reached position B of the ground station are in the ionosphere and radio wave straight-ahead layers.
When it rushes into the interface with the
The angle formed by the radio wave and the normal OX created at the interface of the row plane (Fig.
14-1). β_iIs time T_POf the radio repeater when
Time from position P to time T_BRadiation toward position B of the ground station at
The electromagnetic waves that are used to locate the ground surface or position
I-th from the bottom of the thickness h parallel to the horizontal plane of the body
Refraction angle when entering the plane-parallel layer (see Figure 14-1)
See). γ₀Is time T from position P of the radio repeater_PWhen,
Emitted to the ground station at time T_CPosition C of ground station
Waves arriving at rush into the interface between the ionosphere and the rectilinear layer
Then, at this entry point, at the interface of this parallel plane layer
The angle between the vertical axis OX and the radio wave (see Figure 14-1)
See). γ_iIs time T_PFrom the position P of the radio repeater when
Time T_CRadio waves radiated toward position C of the ground station at
However, the existence of an object that seeks to locate the ground surface or position
I-th parallel plane layer from the bottom with thickness h parallel to the horizontal plane
Refraction angle when entering (see FIG. 14-1). Σ_{i = 1} ⁿ(Sin α₀/ Cos α_i) = Σ_{i = 1} ⁿ{Sin α₀/ (1 / sin^Twoα_i)^1/2} = Σ_{i = 1} ⁿ[Sin α₀/ {1- (sin α₀/ N_i)^Two}^1/2  ] = Σ_{i = 1} ⁿ[Sin α₀/ {(N_i ^Two-Sin^Twoα₀) / N_i ^Two}^1/2 ] = Σ_{i = 1} ⁿ{N_isin α₀/ (N_i ^Two-Sin^Twoα₀)^1/2} ≈ Σ_{i = 1} ⁿ{N_isin α₀/ (1-sin^Twoα₀)^1/2} = Σ_{i = 1} ⁿ(N_isin α₀/ Cos α₀) = Σ_{i = 1} ⁿ(N_itan α₀) In the above equation, n_iBy setting ≈1, an error will occur.
To live. To prevent this error from occurring, n_isin α₀/ (N_i ^Two-Sin^Twoα₀)^1/2 = K_i{N_isin α₀/ (1-sin^Twoα₀)^1/2} Σ_{i = 1} ⁿ(Sin α₀/ Cos α_i) = Σ_{i = 1} ⁿk_i(N_itan α₀) (12) This k_iDepends on the location of the receiving / transmitting station, and
Even if the location of the transmitting station is the same, the parallel plane layer
Each is different. Similar to (12) Σ_{i = 1} ⁿ(Sin β₀/ Cos β_i) = Σ_{i = 1} ⁿl_i(N_itan β₀) (13) Σ_{i = 1} ⁿ(Sinγ₀/ Cos γ_i) = Σ_{i = 1} ⁿm_i(N_itan γ₀) (14) tan α_i= Sinα_i/ Cos α_i = (Sin α₀/ N_i) / {1- (sin α₀/ N_i)^Two}^1/2 = (Sin α₀/ N_i) / {(N_i ^Two-Sin^Twoα₀)^1/2/ N_i} = Sinα₀/ (N_i ^Two-Sin^Twoα₀)^1/2 ≈ sin α₀/ (1-sin^Twoα₀)^1/2 = Sinα₀/ Cos α₀ = Tan α₀ In the above equation, n_iBy setting ≈1, an error will occur.
To live. To prevent this error from occurring, sin α₀/ (N_i ^Two-Sin^Twoα₀)^1/2 = K_i{Sin α₀/ (1-sin^Twoα₀)
^1/2} = K_i(Sin α₀/ Cos α₀) Tan α_i= K_itan α₀ (15) tanβ as in (15)_i= L_itan β₀ (16) tan γ_i= M_itan γ₀ (17) where n_iIs an object whose surface or position is to be located
, Which is parallel to the horizontal plane where
Refractive index of radio waves in the row plane layer. From (6-1) and (12), nh + {c (T_P-T_A) -HΣ_{i = 1} ⁿ(1 / cos α_i)} Cos α₀ = Nh + c (T_P-T_A) Cos α₀−hΣ_{i = 1} ⁿ(1 / cos α_i) C os α₀ = Nh + c (T_P-T_A) Cos α₀−hΣ_{i = 1} ⁿ(1 / cos α_i) (Sin α₀/ Sinα₀) Cos α₀ = Nh + c (T_P-T_A) Cos α₀−hΣ_{i = 1} ⁿ(Sin α₀/ Cos α_i) (Cos α₀/ Sinα₀) = Nh + c (T_P-T_A) Cos α₀−hΣ_{i = 1} ⁿk_i(N_itan α₀ ) (1 / tan α₀) = Nh + c (T_P-T_A) Cos α₀−hΣ_{i = 1} ⁿk_in_i  (18) From (6-2) and (13), nh + {c (T_B-T_P) -HΣ_{i = 1} ⁿ(1 / cos β_i)} Cosβ₀ = Nh + c (T_B-T_P) Cosβ₀−hΣ_{i = 1} ⁿl_in_i (19) From (6-3) and (14), nh + {c (T_C-T_P) -HΣ_{i = 1} ⁿ(1 / cos γ_i)} Cosγ₀ = Nh + c (T_C-T_P) Ccsγ₀−hΣ_{i = 1} ⁿm_in_i (20) From (6-1), (6-2), (18), and (19), nh + c (T_B-T_P) Cosβ₀−hΣ_{i = 1} ⁿl_in_i= Nh + c (T_P-T_A) Cos α₀−hΣ_{i = 1} ⁿk_in_i ∴cos β₀= {(T_P-T_A) / (T_B-T_P)} Cos α₀ (∵l_i≒ k_i) (21) Similarly, (6-1), (6-3), (18), (2
From 0), cosγ₀= {(T_P-T_A) / (T_C-T_P)} Cos α₀ (∵m_i≒ k_i) (22) From (7), (12), (15), L_Two= HΣ_{i = 1} ⁿtan (π + α_i) + {C (T_P-T_A) + HΣ_{i = 1} ⁿ (1 / cos (π + α_i))} Sinα₀ = HΣ_{i = 1} ⁿ{Sin (π + α_i) / Cos (π + α_i)} + {C (T_P-T_A) + HΣ_{i = 1} ⁿ(1 / cos (π + α_i))} Sinα₀ = HΣ_{i = 1} ⁿsin (π + α_i) / {1-sin^Two(Π + α_i)}^1/2 + {C (T_P-T_A) + HΣ_{i = 1} ⁿ(1 / cos (π + α_i))} Sinα₀ (22-1) However, from Snell's law,₀sin α₀= N_isin α_i Therefore, sin (π + α_i) = Sin π cos α_i+ Cosπsinα_i = -Sin α_i =-(N₀/ N_i) Sin α₀ = -Sin α₀/ N_i (22-2) From (22-1) and (22-2), L_Two= HΣ_{i = 1} ⁿ(-Sin α₀/ N_i) / {1-(-sin α₀ / N_i)^Two}^1/2 + {C (T_P-T_A) -HΣ_{i = 1} ⁿ(1 / cos α_i)} Sin α₀ = HΣ_{i = 1} ⁿ(-Sin α₀/ N_i) / (1-sin^Twoα₀/ N_i ^Two )^1/2 + {C (T_P-T_A) -HΣ_{i = 1} ⁿ(1 / cos α_i)} Sin α₀  = HΣ_{i = 1} ⁿ{-Sin α₀/ (N_i ^Two-Sin^Twoα₀)^1/2  } + {C (T_P-T_A) -HΣ_{i = 1} ⁿ(1 / cos α_i)} Sin α₀ = -HΣ_{i = 1} ⁿ{Sin α₀/ (N_i ^Two-Sin^Twoα₀)^1/2 } (Cos α₀/ Cos α₀) + {C (T_P-T_A) -HΣ_{i = 1} ⁿ(1 / cos α_i)} Sin α₀ = -HΣ_{i = 1} ⁿ{Cos α₀/ (N_i ^Two-Sin^Twoα₀)^1/2 } (Sin α₀/ Cos α₀) + {C (T_P-T_A) -HΣ_{i = 1} ⁿ(1 / cos α_i)} Sin α₀ (22-3) By the way, k_i= (1-sin^Twoα₀) / (N_i ^Two-Sin^Twoα₀)^1/2 (22-4) From (22-3) and (22-4), L_Two= -HΣ_{i = 1} ⁿk_itan α₀+ {C (T_P-T_A) -HΣ_{i = 1} ⁿ (1 / cos α_i)} Sin α₀ = -HΣ_{i = 1} ⁿk_itan α₀+ C (T_P-T_A) Sin α₀-H Σ_{i = 1} ⁿ(Sin α₀/ Cos α_i) From (22-5) (22-5) and (12), L_Two= -HΣ_{i = 1} ⁿk_itan α₀+ C (T_P-T_A) Sin α₀− HΣ_{i = 1} ⁿk_in_itan α₀ = -HΣ_{i = 1} ⁿk_i(1 + n_i) Tan α₀+ C (T_P-T_A) S in α₀ = {-(H / cosα₀) Σ_{i = 1} ⁿk_i(1 + n_i) + C (T_P -T_A)} Sin α₀ (23) Similarly, from (8), (13), and (16), L_Four= {-(H / cosβ₀) Σ_{i = 1} ⁿl_i(1 + n_i) + C (T_B -T_P)} Sinβ₀ (24) Similarly, from (9), (14), and (17), L₆= {-(H / cosγ₀) Σ_{i = 1} ⁿm_i(1 + n_i) + C (T_C -T_P)} Sinγ₀ (25) To simplify the calculation now, (∵k_i≒ l_i≒ m_i) −hΣ_{i = 1} ⁿk_i(1 + n_i) ≒ -hΣ_{i = 1} ⁿl_i(1 + n_i) ≈ hΣ_{i = 1} ⁿm_i(1 + n_i) = K (26) T_P-T_A= P (27) T_B-T_P= Q (28) T_C-T_P= R (29), from (21), (27) and (28), cos β₀= (P / q) cos α₀ (30) From (22), (27) and (29), cosγ₀= (P / r) cos α₀ (31) From (23) and (27), L_Two= (K / cos α₀+ Cp) sinα₀ (32) From (21), (26), (27), (28), L_Four= (K / cos β₀+ Cq) sinβ₀ = {(Kq / p) (1 / cos α₀) + Cq} {1- (p / q)^Two cos^Twoα₀}^1/2 (33) From (22), (26), (27), (29), L₆= (K / cosγ₀+ Cr) sinγ₀ = {(Kr / p) (1 / cos α₀) + Cr} {1- (p / r)^Two cos^Twoα₀}^1/2 (34) From (10), (27), (28), L_Three= V (p + q) (35) From (11), (28), (29), L₅= V (r−q) (36) From (35) and (36), L_Three ^TwoL₅= V^Three(P + q)^Two(R−q) (37) From (33) and (36), L_Four ^TwoL₅= V (r−q) {(k^Twoq^Two/ P^Two) (1 / cos^Twoα₀ ) +2 (ckq^Two/ P) (1 / cos α₀) + C^Twoq^Two-K^Two -2ckp / cos α0^{-C Two}p^Two cos^Twoα₀} (38) From (32) and (36), L_Two ^TwoL₅= V (r-q) {k^Two(1 / cos^Twoα₀) + 2ckp (1 / cos α₀) + C^Twop^Two-K^Two-2 ckp cos α₀ -C^Twop^Twocos^Twoα₀} (39) From (34) and (35), L_ThreeL₆ ^Two= V (p + q) {(k^Twor^Two/ P^Two) (1 / cos^Twoα₀ ) +2 (ckr^Two/ P) (1 / cos α₀) + C^Twor^Two-K^Two -2 ckp cos α₀-C^Twop^Two cos^Twoα₀} (40) From (33) and (35), L_ThreeL_Four ^Two= V (p + q) {(k^Twoq^Two/ P^Two) (1 / cos^Twoα₀ ) + 2ckq^Two/ P (1 / cos α₀) + C^Twoq^Two-K^Two -2 ckp cos α₀-C^Two p^Twocos^Twoα₀} (41) From (35) and (36), L_ThreeL₅ ^Two= V^Three(P + q) (r-q)^Two (42) (37), (38), (39), (40), (41),
Substituting (42) into (5) gives L_Three ^TwoL₅+ L_Four ^TwoL₅-L_Two ^TwoL₅-L_ThreeL₆ ^Two+ L_ThreeL_Four ^Two+ L_Three L₅ ^Two = V^Three(P + q)^Two(R−q) + V (r−q) {(k^Twoq^Two/ P^Two) (1 / cos^Twoα₀) +2 (ckq^Two/ P) (1 / cos α₀) + C^Twoq^Two-K^Two -2 ckp cos α₀-C^Twop^Twocos^Twoα₀} -V (r-q) {k^Two(1 / cos^Twoα₀) +2 ckp (1 / cos α₀) + C^Twop^Two-K^Two -2 ckp cos α₀-C^Twop^Twocos^Twoα₀} -V (p + q) {(k^Twor^Two/ P^Two) (1 / cos^Twoα₀) +2 (ckr^Two/ P) (1 / cos α₀) + C^Twor^Two-K^Two -2 ckp cos α₀-C^Twop^Twocos^Twoα₀} + V (p + q) {(k^Twoq^Two/ P^Two) (1 / cos^Twoα₀) + 2ckq^Two/ P (1 / cos α₀) + C^Twoq^Two-K^Two -2 ckp cos α₀-C^Twop^Twocos^Twoα₀} + V^Three(P + q) (r-q)^Two = (K^Two/ P^Two) (P + q) (q-r) (r + p) V (1 / cos^Twoα₀ ) + 2ck (p + q) (q-r) (r + p) V / p (1 / cosα₀) + C^Two(P + q) (q−r) (r + p) V = 0 = (p + q) (q−r) (r + p) V {(k^Two/ P^Two) (1 / cos α₀ )^Two+ 2ck / p (1 / cos α₀) + C^Two-V^Two} = 0 From q ≠ r, (k^Two/ P^Two) (1 / cos α₀)^Two+ 2ck / p (1 / cos α₀) + C^Two-V^Two= 0 ∴1 / cos α₀= -Ck / p ± {(ck / p)^Two-(K^Two/ P^Two) (C^Two -V^Two)}^1/2] / (K^Two/ P^Two)Substituting (43) into (21) and (22).Therefore, time T_AFrom the ground station position A to the radio repeater
Is emitted at time T_PWhen the radio relay station position P is reached
The elevation angle of the radio wave at the ground station position A isTime T_PRadiation toward the ground station from the position P of the radio repeater
At time T_BThe location of the radio wave that reached the ground station position B when
The elevation angle at the upper station position B isTime T_PRadiation toward the ground station from the position P of the radio repeater
At time T_CThe location of the radio wave that reached the ground station position C when
The elevation angle at the upper station position C isIs. However, n_nIs the electric charge of the atmospheric gas layer where the ground station is located.
The refractive index of the wave.

5 Improvement of satellite position accuracy The circumference of the earth is classified into three regions as shown in FIG. Ground surface
The area from the surface to the height of 12 km above the ground is a horizontal layer, above the ground surface.
The area from 12km to 500km in height is spherical
Layer and the area above the ground surface with a height of 500 km or more
We will call it the wave straight layer. From a satellite in the sky now
Radio waves are radiated, propagated, and are on the ground surface
Consider the path of this radio wave when it reaches the ground station
(See FIG. 12). Satellite position is P, ground station on the ground surface
Let Q be the position of. The radio waves emitted from point P are directly
It passes through the progression layer, rushes to the point R on the spherical layer interface, and then
After passing through the spherical layer and the point S on the horizontal layer interface,
The position Q of the ground station on the plane is reached. The medium through which radio waves pass
Divide into parallel plane layers of thickness h parallel to the horizontal plane passing through the point Q
It When entering the point R on the spherical layer interface from the radio wave straight layer
Standing in the plane parallel layer at the point R and the traveling direction of the radio wave
The angle formed by the normal is α₀, Refraction of radio waves into each parallel plane layer
The angle is α_i, N is the number of parallel plane layers. Point P to point Q
Let H be the foot of the perpendicular drawn to the horizontal plane passing through, PH = nh + {cp−hΣ_{i = 1} ⁿ(1 / COSα_i)} COSα₀  (1) Where c is the speed of the radio wave and p is the radio wave propagation time.
It If the refractive index of the atmosphere is n and the refractive index is N, then n = 1 + N × 10^-6 N depends on the weather conditions at each location,
Experimentally generally N = 77.6 (P / T) + 3.73 × 10⁵(E / T^Two) (NU). Where P is atmospheric pressure (mb) and e is
Water vapor pressure (mb) and T are absolute temperatures (K). The actual
This index of refraction is
It decreases exponentially and its altitude characteristic is empirically generally: N (h) = Ns {exp (−Ce · h)} (NU) Ce = 1_n{Ns / N (1km)} = 1_n{Ns / (Ns + ΔN)} where Ns is the refraction index on the ground surface and h is from the ground surface
Is the height (km). From the above, in each parallel plane layer
The refractive index of atmospheric gas can be calculated. Atmosphere gas, ionosphere
The refractive index of radio waves in Japan is described in Japanese Patent Application No. 3-128489.
Obtained by the method listed. Atmospheric gas in each parallel plane layer
Index of refraction_iThen, (1) in the horizontal layer region, from Snell's law,_isin α_i= N₀sin α₀  ∴ sin α_i= (N₀/ N_i) Sin α₀ However
Then n₀Is the refractive index of radio waves in a vacuum. ∴ cos α_i= (1-sin^Twoα_i)^1/2 = {1- (n₀ ^Two/ N_i ^Two) Sin^Twoα₀}
^1/2 Therefore, from equation (1), the path length of the radio wave in the horizontal layer area
Is hΣ_{i = 1} ¹²[1 / {1- (n₀ ^Two/ N_i ^Two) Sin^Twoα₀}
^1/2(2) (2) In the spherical layer region, from Snell's law, (n_i+ Hi / a) sin α_i= N₀sin α₀ ∴ sin α_i= {N₀/ (N_i+ Hi / a)} sin α₀ ∴ cos α_i= (1-sin^Twoα_i)^1/2 = [1- {n₀ ^Two/ (N_i+ Hi / a)^Two} Sin^Twoα₀]^1/2 Therefore, from equation (1), the path length of the radio wave in the spherical layer region
Is hΣ_{i = 12} ⁵⁰⁰[1- {n₀ ^Two/ (N_i+ Hi / a)^Two} Sin^Two α₀]^1/2 (3) (3) In the radio wave straight layer region, k_i= 1, n₀= 1
From hΣ_{i = 500} ⁿ(1 / cos α_i) = HΣ_{i = 500} ⁿ(Cos α₀/ Cos α_i) (1 / cos α₀ ) = HΣ_{i = 500} ⁿk (n₀/ Cos α₀) = HΣ_{i = 500} ⁿ(1 / cos α₀) (4) From equations (2) and (3), parallel horizontal plane layers and flat
The path length of the radio wave passing through the spherical layer is α₀By one
Determined. Now pass through the parallel horizontal plane layer and the parallel spherical layer
Let Li be the i-th approximation of the path length of the radio wave, then Li- {Σ_{i = 1} ¹²(1 / cos α_i) + Σ_{i = 12} ⁵⁰⁰(1 / cos α_i)} ≠ 0 ∴Li = Σ_{i = 1} ¹²(1 / cos α_i) + Σ_{i = 12} ^{500 ± x}(1 / cos α_i) Therefore, the radio path length between PQ is Σ_{i = 1} ¹²(1 / cos α_i) + Σ_{i = 12} ⁵⁰⁰(1 / cos α_i ) + Σ_{i = 500} ⁿ(1 / cos α_i) ± Σ_{i = 500} ^x(1 / cos α_i), Compared with the true value of the radio path length between PQ, ± Σ
_{i = 500} ^x(1 / cos α_i) Only different. Therefore, Σ
_{i = 500} ^x(1 / cos α_i) → so that it becomes 0
For example, Σ_{i = 500} ^x(1 / cos α_i) ≈ 0 when α₀Is required α₀Is. cos α₀To
As a parameter, the parallel horizontal plane layer region and the parallel spherical layer region
Expressions (2) and (3) are used to express the path length of radio waves in the region.
It becomes like Fig.15. Put two points A and B on the curve in FIG.
Then, the curve in FIG. 15 is approximated as a straight line passing through the two points A and B.
It Therefore, in the parallel horizontal plane layer area and the parallel spherical surface layer area,
The radio wave path length is a₁cos α₀+ B₁ It is represented by (5). This is defined as the parallel horizontal plane area and the parallel spherical surface area.
It is called the first-order approximation of the path length of radio waves in the area. α₀But
Then, from the refractive index of each parallel plane layer, α_iIs also determined.
Therefore, the path length of the radio wave passing through each parallel plane layer is determined.
It Therefore α₀Corresponding to the only parallel plane layer area and
The path length of the radio wave in the parallel spherical layer region is determined. Parallel this
The actual path length in the plane layer area and the parallel spherical layer area.
Called the test value. Parallel horizontal layer area and parallel spherical layer area
First-Order Approximation of Radio Wave Length and Parallel Horizontal Plane Region in Japan
And the difference between the experimental values of the radio path length in the parallel spherical layer region,
The 1 in FIG. 15 is approximated by a parabola. This is c₁cos^Twoα₀+ D₁cos α₀+ E₁ It is expressed as (6). Substituting equations (4), (5) and (6) into equation (1)
Then, PH = nh + cp cos α₀-H {(a₁cos α₀+ B₁)-(C₁cos^Twoα₀+ D₁cos α₀+ E₁)} Cos α₀-H (n-500) (7). However, PH = hΣ_{i = 1} ⁿ(1 + k_i) (8)Also, 35 ° ≦ α₀For ≤45 °, experimentally, in general, k_i= 0.96 (10) Expressions (8) and (9) are calculated from Expression (10) as follows: PH = h (1 + k) n (8-1)Here, V is the rotation speed of the earth, m is the parallel horizontal plane layer region and
And the refractive index of the radio wave in the parallel spherical layer region
It is a constant. Equations (8-1), (9-1) and (10) are
Substituting into equation (7), the left side of equation (7) is cos α₀of
It becomes a cubic equation. That is, cos α₀= X, f (x) = x^Three+ F₁x^Two+ G₁x + h₁= 0 (11) By finding the root of equation (11), cos α₀Is determined
Therefore, n is determined from the equation (9). Cos just sought
α₀And n are primary approximations. This cos α₀of
From the first-order approximation value, in FIG.
Narrows the range of path length in the parallel spherical layer region, and c
osα₀The difference between adjacent values of
Take two points C and D and go through the curve of FIG. 15 through two points C and D
Approximate the second time as a straight line. Therefore, parallel horizontal plane layers
The path length of the radio wave in the area and the parallel spherical layer area is a_Twocos α₀+ B_Two Is approximated by. This is a parallel horizontal plane layer area and a parallel spherical layer.
It is called a second-order approximation of the path length of radio waves in the area. parallel
Radio wave path length in horizontal plane layer and parallel spherical layer region
The quadratic approximation value and the parallel horizontal surface layer area and the parallel spherical surface area
The difference between the experimental value of the radio path length in
It is approximated by a parabola as in the first round. This is c_Twocos^Twoα₀+ D_Twocos α₀+ E_Two It is expressed as (12). By repeating the same process as before, cos
α₀And a second approximation value of n is obtained. FIG. 15 and equation (6) and
From (12) c₁cos^Twoα₀+ D₁cos α₀+ E₁> C_Twocos
^Twoα₀+ D_Twocos α₀+ E_Two＞ ・ ・ ・ ・ ・ ・ ・ ・ ＞ c
_icos^Twoα₀+ D_icos α₀+ E_i And Σ_{i = 500} ^x(1 / cos α_i) Is gradually 0
You can see that you are approaching. Therefore, cos α₀Gradually
To approach the true value. Repeat the above operation
Finally, in the parallel horizontal plane area and the parallel spherical layer area,
I) Approximate i-th order path length and parallel horizontal plane layer area and parallel
The difference from the experimental value of the radio path length in the spherical layer region is a parabola
Is not approximated by
Becomes difficult to obtain. At this point, cos α₀of
The experimental value is represented by a straight line by reducing the width before and after the i-th approximation.
Within the range of parallel horizontal plane layer and parallel spherical layer layer
To find the path length of the radio wave in. That is, cos next to each other
α₀Δh is reduced by the two values x and x + Δh of
In the horizontal horizontal layer area and the parallel spherical surface area.
The i-th approximation of the path length of the radio wave
Limit the difference from the experimental value of the path length of the radio wave in the spherical region
You can get closer to 0, so this way
sα₀And n will approach their true value. That conclusion
As a result, it was found that the position of the satellite approaches its true value infinitely.
It

6 Measurement of Azimuth Angle From position A of the ground station at time T _A , a radio wave is radiated toward a radio relay device mounted on the satellite. It is assumed that the radio wave propagates and reaches the position P of the radio repeater at time T _P.
Then, at the same time when the radio wave from the ground station reaches the radio relay station, the radio wave is radiated from the radio relay station toward the ground station. This radio wave propagates and reaches the ground station at time T _B , and the position of the ground station at this time is set to B
And (Refer to FIG. 16) Let Q be a foot of a perpendicular line from the point P to the XY-plane. Point A
The elevation angle at point A of the radio wave radiated toward point P is α
_{Let n be} the elevation angle at point B of the radio wave radiated from point P toward point B, be β _n , and be the refractive index of atmospheric gas on the ground surface be n _n . Also, the refraction angle of the radio wave radiated from the point A toward the point P when passing through the interface between the ionosphere and the radio wave straight traveling layer is α ₀ , and the point P is
The incident angle of the radio wave radiated toward the point B when it enters the interface between the ionosphere and the radio wave rectilinear layer is β ₀ . (A'B '
The Q'plane is the interface between the ionosphere and the radio wave rectilinear layer, and is about 500 km above the XY-plane. The Y-axis is parallel to the rotation direction of the earth. The angles formed by the straight lines AQ and BQ and the X axis are respectively γ and δ, and the coordinates of the point P are P (X, Y,
When Z), ^{_{[hΣ i = 1 n tanα i +}} {c (T P -T A) -hΣ i = 1 n (1 / cosα i)} sinα 0 ] ^{_{cosγ = -hΣ i = 1 n tanβ}} i + {C (T _B −T _P ) −hΣ _i = 1 ⁿ (1 / cos β _i )} sin β ₀ ] cos δ (1) [hΣ _{i = 1} ⁿ tan α _i + {c (T _P −T _A ) −hΣ _{i ^{= 1 n (1 / cosα i}} )} sinα 0 ] _{sinγ + V (T B -T A} ) = ^{_{[hΣ i = 1 n tanβ i +}} {c (T B -T P) -hΣ i = 1 n (1 / cosβ _i )} sinβ ₀ ] sinδ (2) where α _i and β _i are incident angles or refraction angles of radio waves passing through a plane parallel layer having a thickness h parallel to the XY-plane passing through the ground stations A and B. is there. ^{_{hΣ i = 1 n tanα i +}} {c (T P -T A) -hΣ i = 1 n (1 / cosα i)} sinα 0 = A hΣ i = 1 n tanβ i + {c (T B -T P ^{_{) -hΣ i = 1 n (1}} / cosβ i)} sinβ 0 = B V (T B -T a) = and C. However, L and V are the rotation speeds of the earth. (1) is Acosγ = Bcosδ (3) (2) is Asinγ + C = Bsinδ (4) cosγ = (1-sin ² γ) ^1/2 , cosδ = (1
Substitute −sin ² δ) ^1/2 into (3). A (1-sin ² γ) ^1/2 = B (1-sin ² δ) ^1/2 (5) Square both sides of (5) to obtain A ² (1-sin ² γ) = B ² (1 −sin ² δ) A ² −A ² sin ² γ = B ² −B ² sin ² δ (6) Substituting (4) into (6), A ² −A ² sin ² γ = B ² −B ^{2 {(Asinγ + C) /} B) 2 = B 2 - (A 2 sin 2 γ + 2ACsinγ + C 2) 2ACsinγ = B 2 -C 2 -A 2 ∴ sinγ = (B 2 -C 2 -A 2) / 2AC (7) ( From 4), sinγ = (Bsinδ−C) / A (8) Substituting (8) into (6), A ² −A ² {(Bsinδ−C) / A} ² = B ² −B ² sin ^{2 δ A 2 - (B 2} sin 2 δ-2BCsinδ + C 2) = B 2 -B 2 si n 2 δ 2BCsinδ = ^{2 -A 2 + C 2 ∴ sinδ} = (B 2 -A 2 + C 2) / 2BC (9) the time _{T A, T B,} if _{T P} is _{determined, C, α 0, β 0} ,
α _i and β _i are determined. Therefore, since A and B are determined, γ and δ are determined from (8) and (9). However,
It is assumed that the air gas and the ionosphere have known radio wave refractive indices.
In addition, the measuring method of the radio wave refractive index is Japanese Patent Application No. 3-1284.
See 89.

EFFECTS OF THE INVENTION Distance measurement accuracy of 1 mm for three-dimensional position of arbitrary point
You can know instantly within.

[Brief Description of Drawings] (a) FIG. 1 is a diagram showing a radio wave propagation control method for knowing a radio wave propagation time between a ground station and a radio repeater when a computer is not connected to the ground station. is there. (B) FIG. 2 is a diagram showing a method for measuring an azimuth angle. In this figure, point P represents the position of the satellite and points A and B represent the position of the ground station. Further, γ and δ are angles formed by a straight line connecting the foot of a perpendicular line dropped from the satellite to the XY plane and each ground station and the X axis perpendicular to the rotation direction of the earth. (C) FIG. 3 is a diagram showing a propagation control method of radio waves radiated from the object and the fixed ground station. P _ij represents the position of the satellite at time T _ij , M _ij represents the position of the object at time T _ij , and W _ij represents the position of the fixed ground station at time T _ij . (D) FIG. 4 is a diagram showing a method for obtaining the shortest distance in a state where there is a radio wave propagating between the object and the radio repeater. (E) FIG. 5 is a diagram showing a radio wave selection method for obtaining the shortest distance in a certain state between the fixed ground station and the radio relay station. L ₆ represents the shortest distance between the fixed ground station and the radio repeater in a certain state. (F) FIGS. 6 and 7 are diagrams showing the shortest distance between the object, the radio repeater, and the fixed ground station when the radio wave path length is measured using radio wave propagation control. In FIG. 6, Mx and Mxx represent the position of the object at each time, and Pxx represents the position of the radio relay device at each time. Lxx represents the shortest distances between the object and the radio repeater, between the objects, and between the radio repeaters. Figure 7
In FIG. 6, W × and Wxx represent the position of the fixed ground station at each time point, and the others are the same as in FIG. (G) FIG. 8 is a diagram for synchronizing the aging mechanism of the object and the aging mechanism of the fixed ground station by utilizing radio wave propagation control. P _ij , M _ij and W _ij represent the positions of the radio repeater, the object and the fixed ground station at time T _ij . (H) FIG. 9 is a diagram for synchronizing the aging mechanism of the radio repeater and the aging mechanism of the fixed ground station using radio wave propagation control. P _ij , M _ij and W _ij represent the positions of the radio repeater, the object and the fixed ground station at time T _ij . (I) FIG. 10 shows that when the radio repeater is at point P12,
It is a figure showing the elevation angle and azimuth angle of the electric wave in coordinate XYZ which makes the position in the fixed ground station in the time of some origin. (J) FIG. 11 is a diagram when the circumference of the earth is divided into three layers. 1 is the earth, 2 is a plane parallel layer, 3 is a spherical layer, and 4 is a radio wave rectilinear layer. (K) FIG. 12 is a diagram showing a radio wave path until a radio wave emitted from a satellite (or a ground station) reaches the ground station (or a satellite). (1) FIG. 13 is a diagram when obtaining the elevation angle of a radio wave from the radio wave propagation time. Point P represents the position of the satellite at time T _P. Point Q is a foot of a perpendicular line drawn from the point P to the XY plane, and points A, B, and C are positions of the ground station at times T _A , T _B, and T _C. (M) Fig. 14-1 shows the normal line and radio wave path set up at the interface parallel to the ground surface when the radio wave radiated from the satellite toward the observation point on the ground enters the interface between the radio wave rectilinear layer and the ionosphere. It is a figure showing the defining method of the incident angle and refraction angle of a radio wave from the angle which is formed. In addition, Fig. 14-2 shows the normal line and the radio path of the radio wave radiated toward the satellite from the observation point on the ground when it penetrates into the interface between the ionosphere and the radio wave rectilinear layer. It is a figure showing the definition method of the incident angle and refraction angle of a radio wave from the angle formed. In addition, indicates a region of the radio wave straight traveling layer, and indicates a region of the ionosphere and the atmospheric gas layer. (N) FIG. 15 is a graph in which when a radio wave rushes from the spherical layer into the radio wave straight-ahead layer (or vice versa), the cosine of the angle between the normal line to the interface at the rush point and the radio wave traveling direction is the X axis FIG. 4 is a diagram showing a change in radio wave path length when the path length of a radio wave passing through the spherical layer and the parallel horizontal plane layer is represented by the Y axis. (O) FIG. 16 is a diagram showing a method for measuring an azimuth angle.
Point P is the position of the satellite, point A is the position of the ground station at time T _A , and point B is the position of the ground station at time T _B. or,
Point Q is a perpendicular foot from point P on the XY plane, point A ',
B'is the point where the radio wave enters the interface between the radio wave rectilinear layer and the spherical layer, and point Q'is the straight line PQ is the intersection point between the wave rectilinear layer and the spherical layer. γ and δ represent the azimuth angles of the ground station when the ground station positions are points A and B, respectively. α ₀ and β ₀ are angles formed by the normal line of the radio wave entering the interface between the radio wave straight traveling layer and the spherical layer and the radio wave traveling direction. (P) FIG. 17 shows a basic radio relay device provided in a communication satellite for receiving a digital time code, determining the reception time of the code, and transmitting a radio signal after an arbitrary time has elapsed. .. The incoming radio signal is received by the antenna 1 and sent to the receiver 3 via the diplexer 2. Next, the arrival time of the received wireless signal is counted and confirmed by the timekeeping mechanism 4, the wireless signal is edited by the processing device 5, and stored in the internal storage device 6 for a specified time. After a specified time, the signal is combined in the mixer 8 with the intermediate frequency generated by the local oscillator 7. The output signal of the mixer has a frequency different from that of the received signal, is sent to the diplexer 2 through the transmitter 9, and is emitted from the antenna 1. (Q) FIG. 18 is a schematic diagram showing an electronic device provided on an object which attempts to locate a position for monitoring a three-dimensional position by transmitting and receiving radio waves at appropriate intervals using one communication satellite. .. This device can be unattended. The control program in the processing device sequentially repeats the reception mode and the transmission mode at certain time intervals. In the transmission mode, the control program in the processing device receives the time signal from the timekeeping mechanism, and the time generation program in the processing device 19 outputs the digital time signal in consideration of the delay time until the radiation from the antenna. generate.
The signal is generated as a digital time signal by the digital time signal generator 18, and the transmitter 19 and the diplexer 11 are generated.
It is radiated from the antenna 10 via the. In the reception mode, the incoming radio signal is received by the antenna 10 and sent to the receiver 12 via the diplexer 11. Next, the clock mechanism 13
Thus, the arrival time of the received wireless signal is counted and the received data is transferred to the received data buffer. And
The processing device corrects this counting result in consideration of the delay time from the reception of the antenna to the arrival of the aging mechanism. Editing work is performed by adding the correction result to the end of the digital time code stored in the received data buffer.
Then, at the time of the next transmission, the time counting mechanism 13 edits the digital time code considering the delay time to the antenna,
It is added to the end of the edited digital time code, converted into a digital time code by the digital time signal generator 18, this converted signal is modulated by the intermediate frequency generated by the local oscillator 17, and this modulated output, that is, the mixer. Is radiated from the antenna 10 via the diplexer 11 via the transmitter 19. (R) FIG. 19 shows a schematic diagram of an electronic device provided in a fixed ground station. A radio wave repeater installed on a satellite that receives a digital time signal, determines the time when the received digital time code arrives at a fixed ground station, processes these received signals by a radio wave propagation control program in a computer processor, and mounts them on a satellite. It is provided in the fixed ground station in order to observe and count the position of each time point and the distance between the fixed ground station and each object whose position is to be determined, and to determine the three-dimensional position of the object. 1 is a schematic diagram of a basic electronic device. A control program in the processing device switches between a transmission mode and a reception mode at certain time intervals. Now, in the reception mode, the incoming radio signal is received by the receiver 21 via the antenna 20.
This reception signal is counted by the clock mechanism 24 at the reception time of the incoming radio wave signal. The count result is received by the time generation program in the computer processing device, and the reception time of the incoming radio wave signal at the fixed ground station is corrected in consideration of the delay time from the antenna 20 to the clock mechanism. Next, the editing program in the processing device 24 adds the correction value of the reception time of the incoming radio signal at the fixed ground station to the end of the digital time code represented by the incoming radio signal. Then, the data signal is stored in the storage device 25. In the transmission mode, the processing device 2 takes into consideration the delay time until the processing device 24 radiates the digital time signal read by the clock mechanism from the antenna.
The radio wave emission time is corrected by the time generation program in 4, the digital time signal generator encodes the digital time, sends it to the transmitter 29, and emits it from the antenna 30. In addition, 22 is a mixer and 26 is a local oscillator. (S) In FIG. 20, the area from the observation point to 500 km above the sky is divided into parallel plane layers of thickness h (1 km) parallel to the horizontal plane passing through the observation point, and the paths of radio waves passing through the respective parallel plane layers are shown. FIG. (T) Table 1 shows the temporal positions of the transmitter, the radio repeater, and the fixed ground station. (U) Table 2 shows arrival and departure times of radio waves. (V) Table 3 shows the emission time of the radio wave emitted from the fixed ground station. (W) Table 4 represents the data stored in the receive data buffer when the object is in receive mode. (X) Table 5 shows radio wave paths and radio wave propagation times.

[Table 1]

[Table 2]

[Table 3]

[Table 4]

[Table 5]

[Procedure Amendment 2]

[Document name to be corrected] Drawing

[Correction target item name] All drawings

[Correction method] Change

[Correction content]

[Figure 1]

[Figure 3]

[Fig. 2]

[Figure 4]

[Figure 9]

FIG. 11

[Figure 5]

[Figure 6]

[Fig. 14-1]

FIG. 17

[Figure 7]

[Figure 8]

[Fig. 14-2]

[Figure 10]

FIG. 18

FIG. 19

[Fig. 12]

FIG. 15

[Fig. 13]

FIG. 16

FIG. 20

Claims (6)

[Claims] 1. A radio wave propagation control device 1. Using a single satellite (hereinafter referred to as the satellite) whose position is unknown, equipped with a radio wave repeater (hereinafter referred to as the radio wave repeater). In a method of determining a three-dimensional position of an object to be located (hereinafter referred to as the object), (1). Propagation control of radio waves radiated from the object (a) A signal including data indicating the time when the radio waves are radiated from the object is radiated from the object to the radio repeater mounted on the satellite. The "signal including data representing the time when the radio wave is radiated from the object" is hereinafter referred to as "time signal radiated from the object". (B) The radio relay device receives a time signal emitted from the object from the object, determines a reception time of the time signal emitted from the object, and determines a time signal emitted from the object. A signal including data indicating the time when the radio wave relay receives the time signal radiated from the object is added to the end of the. The "signal including the data indicating the time when the radio wave repeater receives the time signal radiated from the object" is hereinafter referred to as "the reception time signal from the object of the radio wave repeater". (C) The radio relay device receives the time signal radiated from the object, and after the radio relay time of the radio relay device elapses, the time signal radiated from the object and the object of the radio relay device. A series of signals composed of reception time signals from the antenna are radiated to a fixed ground station (hereinafter referred to as the fixed ground station). (D) The fixed ground station receives a series of signals including a time signal radiated from the object and a reception time signal from the object of the radio repeater. (E) The fixed ground station determines a reception time at the fixed ground station of a series of signals including a time signal radiated from the object and a reception time signal from the object of the radio repeater. (F) In the fixed ground station, the elevation angle of the radio wave emitted from the object and arriving at the radio wave repeater when transmitted from the object, the time signal emitted from the object, and the object of the radio wave repeater. The elevation angle when the radio wave carrying the reception time signal is received by the fixed ground station is determined by the elevation angle calculation method described later. (G) In the fixed ground station, the azimuth angle of the radio wave radiated from the object and arriving at the radio wave repeater when transmitted from the object, the time signal radiated from the object, and the object of the radio wave repeater. The azimuth when the fixed ground station of the radio wave carrying the reception time signal from is received by the azimuth calculation method described later. (H) Time signal radiated from the object, reception time signal from the object of the radio repeater, time signal radiated from the object to the fixed ground station, and reception from the object of the radio repeater A signal including data representing the time when the time signal is received is stored in the storage device of the electronic computer connected to the fixed ground station. In addition, "a signal including data representing the time when the fixed ground station radiates a time signal radiated from the object and a reception time signal from the object of the radio repeater" is hereinafter referred to as "the fixed ground station The reception time signal from the object and the radio repeater ". (I) An elevation angle of a radio wave emitted from the object and arriving at the radio wave repeater when transmitted from the object, and a time signal emitted from the object and a reception time signal from the object of the radio wave repeater The elevation angle at the time of receiving the fixed ground station is stored in the storage device of the electronic computer connected to the fixed ground station. (J) An azimuth angle of a radio wave emitted from the object and arriving at the radio repeater when transmitted from the object, a time signal emitted from the object, and a reception time of the radio repeater from the object. An azimuth angle of a radio wave carrying a signal when the fixed ground station is received is stored in a storage device of an electronic computer connected to the fixed ground station. (2). Propagation control of radio waves radiated from the fixed ground station (a) A signal including data indicating the time when the radio waves are radiated from the fixed ground station is radiated from the fixed ground station to the radio relay station. However, the frequency of the radio wave radiated from the fixed ground station is set to be different from the frequency of the radio wave radiated from the object. The "signal including the data indicating the time when the radio wave is radiated from the fixed ground station" is hereinafter referred to as "the time signal radiated from the fixed ground station".
Further, the elevation angle and azimuth angle of the radio wave carrying the time signal radiated from the fixed ground station toward the radio relay station when the fixed ground station is transmitted are determined by the elevation angle and azimuth angle calculation method described later. (B) The radio repeater receives the time signal radiated from the fixed ground station from the fixed ground station. And
The radio relay determines the reception time of the time signal radiated from the fixed ground station, and the reception time of the time signal radiated from the fixed ground station at the end of the time signal radiated from the fixed ground station. A signal including data representing is added.
The "signal including the data representing the reception time of the time signal radiated from the fixed ground station" is hereinafter referred to as the "reception time signal of the radio relay station from the fixed ground station". (C) The radio repeater receives the time signal radiated from the fixed ground station, and after the radio relay time of the radio repeater from the time signal received, the time signal radiated from the fixed ground station and the radio repeater A series of signals, which are reception time signals from the fixed ground station, are radiated to the fixed ground station. (D) The fixed ground station receives a series of signals composed of a time signal radiated from the fixed ground station and a reception time signal of the radio relay station from the fixed ground station. (E) The fixed ground station determines a reception time at the fixed ground station of a series of signals including a time signal radiated from the fixed ground station and a reception time signal of the radio relay station from the fixed ground station. .. (F) A time signal radiated from the fixed ground station, a reception time signal from the fixed ground station of the radio relay station, and a time signal radiated from the fixed ground station to the fixed ground station and the radio relay station. A signal including data representing the time when a series of signals consisting of the reception time signal from the fixed ground station and a time signal radiated from the fixed ground station toward the radio relay station are further fixed. The elevation angle and the azimuth angle at the time of transmitting the ground station are determined by the elevation angle calculation method and the azimuth angle calculation method described later, and are stored in the storage device of the electronic computer connected to the fixed ground station. In addition, "The fixed ground station
A signal containing data representing the time at which a series of signals consisting of a time signal radiated from the fixed ground station and a reception time signal from the fixed ground station of the radio repeater was received, "hereinafter" The reception time signal from the fixed ground station and the radio repeater is referred to as ". (G) In the fixed ground station, the time signal radiated from the fixed ground station and the fixed ground station of the radio repeater from the fixed ground station. The elevation angle of the radio wave carrying the reception time signal when the fixed ground station is received is determined by the elevation angle calculation method described below: (h) In the fixed ground station, the time signal radiated from the fixed ground station and the radio relay The azimuth angle of the radio wave carrying the reception time signal from the fixed ground station of the aircraft when the fixed ground station is received is determined by the azimuth angle calculation method described below: (i) Time signal radiated from the fixed ground station And the above An elevation angle and an azimuth angle of a radio wave carrying a reception time signal from the fixed ground station of the wave repeater at the time of receiving the fixed ground station are accumulated in a storage device of an electronic computer connected to the fixed ground station. j) The time signal radiated from the previous fixed ground station, which is stored in the storage device of the electronic computer connected to the fixed ground station, the reception time signal from the fixed ground station of the radio repeater, and the fixed signal. From a series of signals consisting of reception time signals from the fixed ground station and the radio relay station of the ground station, the time when the radio relay station receives the time signal radiated from the fixed ground station is from the object. A signal at the same time as the time when the radiated time signal is received is selected. (3) Propagation control of radio waves of the object and the fixed ground station in the reception mode. Radiated from The time signal emitted from the object and the reception time signal from the object of the radio repeater after a lapse of the radio relay time of the radio repeater after receiving the time signal of And (b) at the object and the fixed ground station, a series of signals consisting of a time signal emitted from the object and a reception time signal from the object of the radio repeater are sent to the object and the fixed ground station. (C) At the object and the fixed ground station, a series of signals including a time signal radiated from the object and a reception time signal from the object of the radio repeater are received by the radio repeater. (D) at the end of the time signal emitted from the object and the time signal received from the object of the radio repeater at the end of the time when the object emits A signal including data indicating the time when a series of signals including a time signal and a reception time signal from the object of the radio repeater is received is added. still,"
A signal including data representing the time signal radiated from the object and the time at which the reception time signal from the object of the radio repeater is received will be referred to as "hereinafter," reception time of the object from the object and the radio repeater. (E) In the object, the time signal radiated from the object, the reception time signal from the object of the radio repeater, and the reception time signal of the object from the object and the radio repeater. At the end of the, a series of signals to which the signal including the data representing the time at which the radio wave is emitted from the object switched from the reception mode to the transmission mode is added is radiated toward the radio relay device. The content of the radio wave, that is, the time signal radiated from the object, the radio wave, which is received by the fixed ground station via the radio relay station and is stored in the storage device of the computer connected to the fixed ground station. A reception time signal from the object of the repeater, a reception time signal of the object from the object and the radio wave repeater, a time when radio waves are radiated from the object whose reception mode is switched to the transmission mode, and the like are accumulated. In addition, the elevation angle and azimuth angle when the object receives a radio wave carrying a series of signals consisting of a time signal radiated from the object and a reception time signal from the object of the radio repeater The value is determined by a calculation method, and the value is stored in the storage device of the electronic computer connected to the fixed ground station (f) The value is stored in the storage device of the electronic computer connected to the fixed ground station From the radio wave in the previous section (e)
When the radio relay time of the radio repeater elapses from the reception time of the radio repeater from the object, it happens that the radio wave emitted from the object reaches the radio repeater. .. (G) The radio wave emitted from the object reaches the radio wave repeater when the radio wave relay time of the radio wave repeater elapses after the radio wave repeater receives the time signal emitted from the object. As described above, the time, time and interval of radiation from the object are appropriately adjusted so that the object can emit radio waves. (H) When the radio repeater receives the time signal radiated from the fixed ground station, directs the time signal from the object and the object of the radio repeater toward the fixed ground station from the radio repeater. The time, time, and time interval for radiating radio waves from the object and the fixed ground station are adjusted so as to radiate a series of signals including the reception time signal from the. (4). Distance Measurement Using Radio Wave Propagation Control By performing the radio wave propagation control in the above items 1, 2, and 3 at a certain fixed time interval without changing the position of the object, (however, the position of the object "Unchanged" means that the relative position of the object and the earth does not change.) (A) The position of the object when a radio wave is radiated from the object and the radio wave repeater in which the radio wave propagates. The shortest distance to the position of the radio repeater when the radio wave arrives at is obtained. (B) The position of the radio relay when the radio relay time of the radio relay elapses after the radio waves radiated from the object propagate and reach the radio relay, and the radio The shortest distance to the position of the fixed ground station when it reaches the fixed ground station via the radio repeater is obtained. (C) The position of the fixed ground station when the radio wave radiated from the fixed ground station reaches the fixed ground station via the radio relay station, and the radio relay station of the radio wave radiated from the fixed ground station. So that the arrival time at the arrival time coincides with the arrival time of the radio wave radiated from the object at the radio relay device,
The shortest distance to the position of the fixed ground station when radio waves are radiated from the fixed ground station is obtained. (D) From the fixed ground station so that the arrival time of the radio waves radiated from the fixed ground station at the radio relay station matches the arrival time of the radio waves radiated from the object at the radio relay station. The shortest distance between the position of the fixed ground station when the radio wave is radiated and the position of the radio wave repeater when the radio wave propagates and reaches the radio wave repeater is obtained. (E) After the arrival of the time signal from the object to the radio repeater, the radio waves emitted from the object reach the radio repeater at the same time when the radio relay time of the radio repeater has elapsed. , The shortest distance between the position of the object when the radio wave is radiated from the object and the position of the radio wave repeater when the radio wave propagates and reaches the radio wave repeater. (F) After the arrival of the time signal from the fixed ground station to the radio relay station, at the same time when the radio relay time of the radio relay station has passed, the radio wave radiated from the fixed ground station or the radio relay station Of the position of the fixed ground station when radio waves are radiated from the fixed ground station so as to reach the aircraft, and the position of the radio relay station when the radio waves propagate and reach the radio relay station. Find the shortest distance between. (G) At the same time as the position of the object when the radio wave is radiated from the object and at the same time when the radio wave propagates and arrives at the radio wave repeater, the radio wave happens to be directed from the radio wave repeater to the object. The shortest distance from the position of the object when it is radiated and the radio wave propagates and reaches the object is obtained. (H) From the radio wave repeater to the object, at the same time when the radio wave from the object reaches the radio wave repeater and at the same time when the radio wave from the object reaches the radio wave repeater. A radio wave is radiated toward the object, the radio wave propagates, and the shortest distance from the position of the object when reaching the object is obtained. (I) The position of the object when a radio wave is emitted from the object to the radio relay device, and the radio relay time of the radio relay device after the radio wave emitted from the object reaches the radio relay device. When the time elapses, the shortest distance between the position of the object and the position where the object emits the radio wave so that the radio wave happens to reach the radio repeater is obtained. (J) The position of the radio relay device when the time signal emitted from the object reaches the radio relay device, and the radio wave emitted from the object reaches the radio relay device,
The shortest distance to the position of the object when the radio wave is radiated from the object so that the radio wave reaches the radio wave repeater after the radio wave relay time has elapsed. (K) The position of the object when the time signal is radiated from the object, and the position of the radio relay device after the radio relay time elapses after the radio wave radiated from the object reaches the radio relay device. Find the shortest distance between and. (L) The position of the radio wave repeater when the radio wave is emitted from the radio wave repeater toward the fixed ground station at the same time when the time signal emitted from the object reaches the radio wave repeater, and The shortest distance between the position of the fixed ground station when the radio wave propagates and reaches the fixed ground station is obtained. (M) At the same time when the time signal emitted from the object reaches the radio relay station, a radio wave is emitted from the radio relay station toward the fixed ground station, and the radio wave propagates to the fixed ground station. The shortest distance between the position of the fixed ground station when it reaches the position and the position of the fixed ground station when the radio wave radiated from the object reaches the fixed ground station via the radio relay station is obtained. (N) The position of the radio wave repeater when the radio wave emitted from the object reaches the radio wave repeater and the radio wave emitted from the object when the radio wave emitted from the object reaches the fixed ground station via the radio wave repeater. Find the distance to the location of the fixed ground station. (O) X- at the position of the radio repeater when the radio wave radiated from the object propagates and reaches the radio repeater.
The YZ coordinate is obtained with the position of the fixed ground station when the radio wave reaches the fixed ground station via the radio relay station as an origin (0,0,0). (P) The XYZ coordinates of the position of the radio repeater when the radio relay time of the radio repeater has passed after the radio wave radiated from the object propagates and reaches the radio repeater. , The origin of the position of the fixed ground station when the radio wave reaches the fixed ground station via the radio repeater (0, 0, 0)
Ask as. (Q) The position of the radio repeater when the radio wave radiated from the object propagates and reaches the radio repeater, and the radio wave relay of the radio repeater after the radio wave reaches the radio repeater. The shortest distance to the position of the radio repeater when the time has elapsed is obtained. (R) The radio wave radiated from the fixed ground station reaches the radio relay when the radio relay time of the radio relay elapses after the radio wave radiated from the object reaches the radio relay. The position of the fixed ground station when the radio wave is radiated from the fixed ground station, and the position of the fixed ground station when the radio wave radiated from the object reaches the fixed ground station via the radio relay station Find the distance between. (5). Determining the three-dimensional position of the object by radio wave propagation control (a) Position of the radio wave repeater when the time signal emitted from the object reaches the radio wave repeater and when the time signal is emitted The first position plane is calculated from the shortest distance between the position of the object and the position of the radio repeater when the time signal reaches the radio repeater. (B) The position of the radio relay when the radio relay time of the radio relay elapses after the time signal emitted from the object reaches the radio relay, and the time signal is the object. From the shortest distance between the position of the object when radiated from and the position of the radio relay when the time relay reaches the radio relay after the time signal reaches the radio relay. , Calculate the second position plane. (C) At the same time when the time signal radiated from the object reaches the radio repeater, the radio repeater emits a radio wave toward the object. Since the height of the horizontal plane passing through the object from the fixed ground station when the radio wave propagates and reaches the object is determined, the horizontal plane passing through the object is defined as the third position plane (d) The intersection of the first position plane, the second position plane, and the third position plane is the three-dimensional position of the object. 2. Synchronization of time-dependent mechanisms 1. Synchronizing the aging mechanism of the object and the aging mechanism of the fixed ground station At the same time, the object and the fixed ground station radiate radio waves to the radio repeater. Then, the radiated radio waves are received by the fixed ground station and the object, respectively.
Now, let us consider a route in which the radio waves emitted from the object reach the fixed ground station via the radio relay device. When the radio wave emitted from the object reaches the radio relay station, the radio wave emitted from the radio relay station toward the fixed ground station is selected. The emission time of this radio wave from the radio repeater, the arrival time at the fixed ground station, the elevation angle and the azimuth angle at the fixed ground station are stored in the storage device of the electronic computer connected to the fixed ground station. Remember. This radio wave
When the radio relay time elapses after reaching the radio relay station, radio waves are emitted from the radio relay station toward the fixed ground station again. The emission time of this radio wave from the radio repeater, the arrival time at the fixed ground station, and the elevation angle and azimuth angle at the fixed ground station are stored in the storage device of the electronic computer connected to the fixed ground station. Remember. Next, consider a route in which the radio waves radiated from the fixed ground station reach the object via the radio relay device. When the radio wave radiated from the fixed ground station reaches the radio relay station, the radio wave radiated from the radio relay station toward the fixed ground station is selected. The emission time of this radio wave from the radio repeater, the arrival time at the fixed ground station, and the elevation angle and azimuth angle at the fixed ground station are stored in the storage device of the computer connected to the fixed ground station. Remember. After the radio wave reaches the radio relay station, when the radio relay time elapses, there is a radio wave radiated to the fixed ground station in addition to a radio wave radiated to the object. The radiation time of the radio wave radiated toward the fixed ground station from the radio repeater, the arrival time at the fixed ground station, and the elevation angle and azimuth angle at the fixed ground station are connected to the fixed ground station. It is stored in the storage device of the computer. The above operation is executed quite a number of times. In this way, among the innumerable radio waves stored in the storage device of the computer connected to the fixed ground station, the radio waves radiated from the object reach the radio repeater, and Among the radio waves emitted from the radio relay station to the fixed ground station, the difference between the emission time from the radio relay station and the arrival time to the fixed ground station and the elevation angle are the radio waves emitted from the fixed ground station. However, after reaching the radio relay station, when the radio relay time elapses, in addition to the radio waves emitted from the radio relay station toward the object, the radio waves emitted from the radio relay station toward the fixed ground station are transmitted from the radio relay station. The same radio wave is selected for each of the difference between the emission time and the arrival time at the fixed ground station and the elevation angle. With one of the two selected radio waves, the radio wave emitted from the object is
When the radio relay time elapses after reaching the radio relay,
Again, the difference between the emission time of the radio wave radiated from the radio repeater toward the fixed ground station and the arrival time at the fixed ground station and the elevation angle are the other radio waves When the radio wave radiated from the station reaches the radio relay station, the time when the radio wave emitted from the radio relay station to the fixed ground station is emitted from the radio relay station and reaches the fixed ground station. If the time difference and the elevation angle are the same, the temporal path lengths of the two selected radio waves are the same. Therefore, by selecting these two radio waves, the difference between the reception times of these two radio waves between the fixed ground station and the object causes a time lag between the aging mechanism of the object and the aging mechanism of the fixed ground station. Becomes Such work is performed several times, and the aging mechanism of the object is corrected based on the aging mechanism of the fixed ground station based on the average value. (See FIG. 8) 2. Synchronizing the aging mechanism of the radio repeater After synchronizing the aging mechanism of the object and the fixed ground station, the main synchronization is performed. Radio waves are radiated from the object and the fixed ground station toward the radio relay station so that the radio waves from the object and the fixed ground station reach the radio relay station at the same time. .. The true value of the time when the radio wave arrives at the radio repeater can be obtained from the time when the radio wave is emitted from the fixed ground station, the time when the radio wave arrives at the fixed ground station, and the radio relay time of the radio repeater.
With this true value, the aging mechanism of the radio repeater is synchronized. However, when the radio wave emitted from the object reaches the radio relay station, the radio wave is emitted from the radio relay station toward the fixed ground station. When this radio wave propagates and reaches the fixed ground station, the relative position of the radio wave emitted from the object from the position of the fixed ground station with respect to the radio relay station when reaching the radio relay station is When the radio wave relay time elapses after the radio wave emitted from the object reaches the radio wave repeater, the radio wave repeater again emits a radio wave toward the fixed ground station, and the radio wave propagates to the fixed earth station. A radio wave is selected which passes through a route having the same relative position of the radio repeater when the radio relay time has elapsed from the position of the fixed ground station when reaching the ground station. (Fig. 9
See) Fixed ground stations, satellite-borne radio repeaters, and objects whose position is to be located have very sophisticated time-lapse mechanisms. When the object whose position you want to locate starts communicating with the fixed ground station, and sometimes after the communication starts, the radio wave propagation control controls the radio relay onboard the satellite based on the time-dependent mechanism of the fixed ground station. The time-dependent mechanism of the machine is synchronized with the time-dependent mechanism of the object whose position is to be determined. 3. Correction of satellite position error due to atmospheric refractive index It has been experimentally proved that the refractive index of atmospheric gas changes stepwise according to the height above the ground surface. As a result, when the radio waves emitted from the satellite enter the atmosphere,
Due to the influence of atmospheric gas, a refraction phenomenon occurs, and the radio waves radiated from the actual position of the satellite reach the fixed ground station on the ground surface, and the radio path is not a straight line but rather a curve. Therefore, it is calculated that the radio wave goes straight from the time when the radio wave is emitted from the actual position of the satellite, the time when the radio wave reaches the fixed ground station on the ground surface, and the elevation angle of the radio wave which reaches the fixed ground station on the ground surface. Then the result of the calculation deviates considerably from the shortest distance between the actual position of the satellite and the position of the fixed ground station on the ground surface. 1. The space between the entry point of the radio wave radiated from the actual position of the satellite into the atmosphere and the position of the fixed ground station on the ground surface is divided into the case where the height is less than 12 km and the case where the height is 12 km or more. The actual position of the satellite is calculated from the time when the radio wave is emitted from the position, the time when the radio wave arrives at a fixed ground station on the ground surface, and the angle between the normal line at the entry point of the radio wave into the atmosphere and the incoming radio wave. On the contrary, when the radio wave is radiated to the satellite from a fixed station or a mobile station on the ground surface, the correction of the satellite position error can be performed by this method. 2. The space through which radio waves pass is divided into parallel plane layers of thickness h parallel to the ground surface that passes through ground stations or observation points, and the radio wave refractive index of each parallel plane layer is obtained. 3. Obtain the horizontal and vertical distances of each radio wave path length passing through each parallel plane layer from the ground surface to the interface where the refractive index changes from n ₁ to n ₀ , and then calculate the sum of the horizontal distance and the vertical distance of each radio wave path length. The sum of distances is calculated (where n ₀ is the refractive index of radio waves in vacuum). 4. The point where the radio wave radiated from the actual position of the satellite, or the radio wave radiated to the satellite from the ground station or observation point enters the interface parallel to the ground surface where the refractive index n ₀ changes to the refractive index n _1. Set as the origin. Then, at this origin, the normal to the interface parallel to the ground surface where the refractive index n ₀ changes to the refractive index n ₁ is defined as the X-axis, and the X-axis is orthogonal to the X-axis in the plane formed by the radio wave path. In the XY plane with the straight line as the Y-axis, the angle of incidence of the radio wave when passing through each parallel plane layer by the horizontal and vertical distances of the path length of the radio wave from the actual position of the satellite to the ground station or observation point. And the refraction angle, the radio wave propagation time between the satellite and the ground station or the observation point, and the number of parallel plane layers. In addition, the reference line of the incident angle and the refraction angle is the positive X axis, and the counterclockwise direction is positive. (See Figure 14) 4. Determination of elevation angles of incoming radio waves and radiated radio waves. Measurement of radio wave propagation time between ground station and radio repeater (1) When a computer is connected to the ground station. It emits radio waves from the ground station to the radio relay station onboard the satellite. At the same time when the radio wave propagates and reaches the radio repeater,
The radio wave radiated from this radio repeater to the ground station is selected. Measure the time of sending and receiving radio waves at the ground station and the time of sending and receiving radio waves at the radio relay station by the timekeeping mechanism installed in each. Then, this measurement data is stored in the electronic computer connected to the ground station. (2) When a computer is not connected to the ground station.
(Refer to FIG. 1) From position M _{11 of the} ground station, a radio wave is radiated toward a radio relay device mounted on the satellite at time T _M11 . It is assumed that the radio wave propagates and reaches the position P ₁₂ of the radio repeater at time T _P12 . At this time T _P12 , there is a radio wave emitted from the position P ₁₂ of the radio repeater toward the ground station. That is, it is a radio wave radiated from the position M _{01 of the} ground station toward the radio relay device mounted on the satellite at time T _M01 . Times when the radio waves radiated from the position P ₁₂ of the radio repeater at time T _P12 reach the positions M ₀₄ and M ₀₄ ′ of the ground station are _defined as T _M04 and T _M04 ′, respectively. (Note: Times T _M04 and T _M04 ′ are extremely close to each other, and it seems that actual measurement is impossible, but they theoretically exist. Because radio path length P ₁₂ M ₀₄ ≠ P
₁₂ M ₀₄ '. The radio wave radiated from the position M _{11 of the} ground station reaches the position W ₁₄ of the fixed ground station via the radio relay device at time T _W14 and is stored in the computer connected to this fixed ground station. That is, the radio path M ₁₁
-P ₁₂ -P ₁₃ waves passing through the -W ₁₄ is an electronic computing machine which is connected to a fixed earth station _T M11 _{· T P12}
· _T are stored as data consisting of P13 _{· T W14.} The radio waves arriving at the positions M ₀₄ and M ₀₄ ′ of the ground station at the times T _M04 and T _M04 ′ are _{stored in} the transmitter buffer of the ground station as T _M01 , T _P02 , T _P03 , T
_M04 and T _M01 , T _P02 , T _P03 , T _M04 '
Is stored as data. Then, at time T _M21 , the data held in the transmitter buffer in the ground station is radiated from the position M _{21 of} the ground station toward the radio relay, and at time T _W24 , the position W _{24 of the} fixed ground station is transmitted. To reach. (▲ Note ▼ The time until the ground station enters the next reception mode is called the ground station data retention time, and the ground station reception data is guaranteed only for this ground station data retention time.)
Then, it is stored in the electronic computer connected to this fixed ground station. That is, the radio path M ₀₁ -P ₀₂ -P _03-
M ₀₄ (or _{M 04 ') -M 21 -P 22} -P 23 -W
_The radio wave that has passed through ₂₄ is stored in the computer connected to the fixed ground station as T _M01 , T _P02 , T _M04 (or T
_M04 '), T _M21 , T _P22, and T _W24 are stored as data. 2. Measurement of the radio path length between the ground station and the radio repeater The atmosphere is set as the range from the ground surface to Hkm (500) above, and the shortest distance corrected for the error of the radio path length due to the influence of the refractive index of gas in this atmosphere is the satellite. Find between the onboard radio repeater and the ground station. From the time and distance thus obtained, the elevation angle of the radio wave received and transmitted by the ground station is obtained. (1) The satellite is always located on the right side of the ground station, and the timekeeping mechanism of the radio repeater mounted on the ground station and the satellite is completely synchronized with the timekeeping mechanism equipped with the fixed ground station. . (2) The time when the radio wave is radiated from the ground station to the radio wave repeater mounted on the satellite and the time when the radio wave propagates and reaches the radio wave repeater are measured by the timekeeping mechanism mounted on each of them.
Using this time difference and the refraction angle and incident angle of the radio waves radiated from the ground station toward the radio repeater in each parallel plane layer as a variable, the radio path length error due to the refraction of the radio waves caused by the atmospheric gas is corrected to Find the shortest distance between the position of the onboard radio repeater and the position of the ground station. (3) At the same time when the radio wave radiated from the ground station reaches the radio relay station, the radio wave radiated from the radio relay station to this ground station is selected. There are two types of radio waves that propagate and reach the ground station, and the arrival time of each radio wave is measured by a timekeeping mechanism mounted on the ground station. For these two types of radio waves, the time difference between the time radiated from the radio repeater and the time received by the ground station and the refraction angle and incident angle of the radio waves received by the ground station in each parallel plane layer are used as variables. Find the shortest distance between the position of the radio repeater and the position of the ground station. (4) The rotation direction of the earth is selected as the Y-axis, and the coordinates of the three positions of the ground station and the position of the radio repeater in the XYZ-space are determined with one point on the Y-axis as the origin. However, it is assumed that the three coordinate positions of the ground station are on the Y axis. From this, the elevation angle of the radio waves transmitted and received from the ground station is obtained. That is, from the distances obtained from the terms (b) and (c), the radio wave propagation time, the radio wave velocity, the rotation speed of the earth, the ground station parallel to the ground surface, the refractive index of the parallel plane layer of thickness h, and the ground The following relational expression holds with the cosine of the incident angle (or refraction angle) of the radio wave on the interface parallel to the ground surface 500 km above the station. cos α ₀ = kh Σ _{i = 1} ⁿ (1 + n _i ) / (c ± V) p where c is the speed of the radio wave, V is the rotation speed of the earth, p is the radio wave propagation time between the ground station and the satellite, h the refractive index of the thickness of the parallel plane layers parallel to the ground surface, n _i is parallel to the surface plane parallel layer and k is a proportional constant 5. Improving the position accuracy of the object Up to now, the method of measuring the position of the object and the radio repeater has been described. Next, the method of improving the accuracy of the measuring position of the object will be described. From the method of measuring the position of the object, it is necessary to improve the position accuracy of the satellite in order to improve the position accuracy of the object. Therefore, in order to improve the satellite position accuracy, the following is done. 1. The circumference of the earth is divided into a horizontal layer, a spherical layer, and a radio wave straight layer. Then, the medium through which the radio wave passes is divided into parallel plane layers having a thickness h parallel to the horizontal plane passing through the observation point. And
The refractive index of the radio wave in each of the parallel plane layers of the horizontal layer and the spherical layer is measured. Further, the refractive index of radio waves in the radio wave straight traveling layer is 1. 2. If the angle (incident angle or refraction angle) formed by the normal line of the radio wave entry point at the interface between the radio wave straight layer and the spherical layer and the traveling direction of the radio wave is determined, the horizontal layer and the spherical layer are parallel to each other. Since the refractive index of the radio wave in the plane layer is known from the previous item, the refraction angle (or incident angle) of the radio wave to each parallel plane layer is determined. Therefore,
Each path length of the radio wave passing through each parallel plane layer is obtained. Therefore, the only horizontal layer area and spherical layer that correspond to the angle (incident angle or refraction angle) formed by the normal line at the entry point of the radio wave to the interface between the radio wave rectilinear layer and the spherical layer and the traveling direction of the radio wave. The radio path length through the area is determined. 3. The cosine of the angle (incident angle or refraction angle) formed by the normal line of the radio wave entry point at the interface between the radio wave rectilinear layer and the spherical layer and the traveling direction of the radio wave is used as a parameter to determine the horizontal area and The length of the radio wave path that passes through the spherical area is calculated and shown in a graph. In this case, the cosine of the angle (incident angle or refraction angle) formed by the normal line at the entry point of the radio wave to the interface between the radio wave rectilinear layer and the spherical layer region and the traveling direction of the radio wave is taken as the X axis,
The Y-axis is the length of the radio wave path passing through the horizontal layer region and the spherical layer region, which is obtained by the above item 3. 4. Two points A and B are set on the curve obtained in the previous item 3. The coordinates of these two points A and B are (AX, AY), (BX,
BY), the straight line passing through the two points A and B is (Y-AY) / (X-AX) = (AY-BY) / (AX
-AX) However, the part surrounded by | AX | <| BX | curve AB and straight line AB is the normal line at the point of entry of radio waves into the interface between the radio wave rectilinear layer and the spherical layer and the propagation of this radio wave. It is represented by a quadratic curve AB whose variable is the cosine of the angle (incident angle or refraction angle) formed with the direction. Therefore, the curve AB
Is represented by a straight line AB and a quadratic curve AB. 5. The distance between the satellite and the horizontal plane passing through the observation point is the number of parallel plane layers with thickness h (this number is n), the radio wave propagation speed, and the distance from the horizontal plane passing through the observation point to the height nh. It is represented by the radio wave path length, and is also represented by the number (n) of parallel plane layers having a thickness h and a proportional constant k. The angle formed by the normal line at the point of entry of the radio wave to the interface between the radio wave rectilinear layer and the spherical layer and the direction of travel of this radio wave (incident angle or refraction angle is the cosine of the parallel plane layer of thickness h). It is expressed by the number (n), the velocity of the radio wave, the radio wave propagation time, the rotation speed of the earth, and the proportional constant k. Therefore, from the previous item, it was set as the entry point of the radio wave to the interface between the radio wave rectilinear layer and the spherical layer. A cubic equation with the cosine of the angle (incident angle or refraction angle) between the normal and the traveling direction of this radio wave is established, and the solution of this cubic equation is The angle (incident angle or refraction angle) formed by the normal line at the entry point and the traveling direction of this radio wave is calculated from the number (n) of parallel plane layers of thickness h. The horizontal and vertical distances between the point and the observation point are obtained 6. Radio wave rectilinear layer and sphere obtained in the previous section The accuracy is measured from item 3 with the cosine of the angle (incident angle or refraction angle) formed by the normal line at the entry point of the radio wave to the interface of the radio wave and the traveling direction of the radio wave as the center, and the values around it. Raise it by 10 times to find the length of the radio wave path that passes through the horizontal layer region and the spherical layer region, and show this on a graph 7. Take two points C and D on the curve obtained in the previous section.
Coordinates of points C and D are (CX, CY), (DX, D
Y) as | CX |> | AX |, | DX | << | BX
If |, a straight line passing through the two points C and D is expressed by the following equation. (Y-CY) / (X-CX) = (CY-DY) / (CX
-DX) However, | CX | <| DX | The portion enclosed by the curved line CD and the straight line CD is the normal line at the point where the radio wave enters the interface between the radio wave rectilinear layer and the spherical layer and this normal line. Angle (incident angle or refraction angle) with the traveling direction of the radio wave
It is represented by a quadratic curve CD whose variable is the cosine of. Therefore,
The curve CD is represented by a straight line CD and a quadratic curve CD. Then, the process returns to item 5. If it cannot be expressed by a quadratic curve, go to item 7. 8. Take two points on the curve obtained in the previous section, and if the part surrounded by the straight line passing through these two points and the curve is not represented by a quadratic curve, the interface to the wave rectilinear layer and spherical layer obtained immediately before this Take two points on the curve around the intersection of the cosine and the curve of the angle (incident angle or refraction angle) formed by the normal line at the entry point of the radio wave and the traveling direction of this radio wave, and these two points Select two points so that the passing straight line almost overlaps the curved line. As a result, the angle (incident angle or refraction angle) formed by the normal line at the entry point of the radio wave to the interface between the radio wave rectilinear layer and the spherical layer and the traveling direction of this radio wave.
A quadratic equation with the cosine of as a variable holds. The solution of this quadratic equation is what you want. Centering on the intersection of the solution and the curve obtained in this way, two points are taken on the curve and
Repeat until the straight lines passing through the points overlap. 6. Determination of azimuth angle A radio wave is emitted from a ground station toward a radio repeater. At the same time when this radio wave propagates and reaches the radio repeater, the radio wave radiated from the radio repeater toward the ground station is selected. Radio waves radiated from this radio repeater are received by the above ground station.
At this time, the azimuth angle is measured from the time when the radio wave is emitted from the ground station, the time when the radio wave reaches the radio wave repeater, and the time when the radio wave emitted from the radio wave repeater reaches the ground station. γ and δ are azimuth angles to be obtained. (See Figure 2)