JPH07260918A - Measurement of wave refractive index of ionosphere and atmospheric gas layer via follow-up of wave propagation route and measurement of relative position between target and observation point - Google Patents

Abstract

PURPOSE:To accurately measure the cosine of the critical incident angle of a wave to an ionosphere by following up the wave from the position of a satellite assumed on the basis of a wave propagation time therefrom and the approximate value of a vertical distance between horizontal planes across the satellite and an observation point on the ground. CONSTITUTION:The virtual point P1 of a satellite (point P) is set on the basis of the approximate value of the 3D position of the point P obtained from a wave transmitted from the satellite, and a linear distance between the point P1 and an observation point A on the ground is divided by a flux (u), thereby establishing a wave propagation time pi. Then, a virtual point P'1 is set on a wave propagation route P1CA with length P1DA kept equal to P'1CA, so that a wave from the point P1 can reach in the propagation time P1. Also, the virtual point P2 of the satellite is established, so as to keep route length P2EA equal to P'1CA, thereby obtaining a vertical distance Lzi. between horizontal planes across the point P2 and the observation point A. As a result, a critical incident angle alphaio when a wave passing the route P2EA enters the interface of a wave rectilinear propagation layer and an ionosphere, can be detected, thereby improving the measurement accuracy of the 3D position of the satellite.

Description

Detailed Description of the Invention

The three-dimensional position of the target can be determined by measuring the accurate radio wave refractive index of the ionosphere and atmospheric gas layer from the approximate values of the radio wave propagation time and vertical distance between the target and the observation point. Can be obtained within a measurement accuracy of 1 mm. Using this technology, the trajectory of a target flying at high speed in the sky is determined and its shape and size are recognized. Further, guidance control in a specific region of the flying object is performed by taking a delicate interface between the thrust of the flying object and the technology for recognizing the three-dimensional position of the flying object.

2. Description of the Related Art In single positioning in which radio waves from GPS satellites are received by a receiver on the ground to determine a three-dimensional position, satellite orbit information, radio wave propagation paths (ionosphere and atmospheric gas layer), observation points and satellites are used. Due to the error of the clock, the C / A code has a nominal accuracy of 100 meters, and the P code has a nominal accuracy of 16 meters. Further, in relative positioning in which radio waves from GPS satellites are received by a plurality of receivers and the baseline length between receiving points is obtained, the accuracy is significantly improved from a few centimeters to a few meters, compared to single positioning. However, the measurement recording time of about 15 minutes or more and about 2 hours is required, and not only the result cannot be obtained in a short time, but also the receiving point and the three-dimensional position of the satellite cannot be obtained.

[Industrial Application Field and Effect of Invention]

1. Operation management of ships, cars, trains and aircraft. 2. Application to geodetic survey. 3. Application to large-scale civil engineering work. 4. Application to monitoring deformation / movement of structures. 5. Application to scientific observation (earthquake, volcanic eruption prediction, movement of plate technics). 6, Application to ocean observation and space observation. 7. Application to phones that cannot be eavesdropped via geostationary satellites. 8. Application to micro area broadcasting via geostationary satellite. 9. Attitude control and tracking of satellites. 10. Control and tracking of high-speed flying objects. 11. Application of microwave high power to transportation system. 12. Application to hyperopic radar. With the development of this technology, three-dimensional position measurement of a target can be performed at a level with a range-finding accuracy of millimeters or less, and can be measured kinematically.

[Means / actions for solving problems]

1. Virtual point P ₁ where the satellite is located
Accurate follow of the propagation path of microwaves radiated from. (See Fig. 1) At a certain time; T, microwaves radiated from the point P where the satellite is located in the sky enter the point C on the interface between the radio wave rectilinear layer and the ionosphere, and then n with a thickness of hkm. It is assumed that the observation point located at the point A on the ground is reached after passing through the parallel plane layer of the layer. Then, the approximate value of the three-dimensional position of the point P is obtained. Now, the location defined by the approximate value of the three-dimensional position of the point P and the point P _1. It is assumed that the three-dimensional position of the point A is correctly obtained. Thus, the linear distance between the point P ₁ and point A, and the vertical distance between the horizontal plane passing through the point P ₁ and point A; is L _zi obtained. Now, the straight line distance between the points P ₁ and A is divided by the speed of light, and the quotient is defined as the radio wave propagation time between the satellite and the observation point; P _i . If the intersection of the straight line connecting point P ₁ and point A and the interface of the radio wave rectilinear layer and the ionosphere is D, then path length; P ₁ DA <path length; P ₁ CA. Therefore, the microwave radiated from the point P ₁ is
At the propagation time; P _i , the point A cannot be reached. Therefore, the point P ₁ 'is set on the route P ₁ CA so that the route length P ₁ DA = route length P ₁ ' CA. Then, at a certain time; T,
The microwave from the microwave radiation source located at the point P ₁ ′ reaches the observation point located at the point A through the path; P ₁ ′ CA. However, since the vertical distance between the point P ₁ ′ and the horizontal plane passing through the point A cannot be obtained, the incident angle of this microwave at the point C cannot be similarly obtained. Then, at a certain time; T, there is a microwave radiation source at a point P ₂ in the sky, and the microwave from the point P ₂ rushes to the point E on the interface between the radio wave rectilinear layer and the ionosphere, and then on the ground. It is assumed that an observation point located at a certain point A is reached. At this time, the path length; P ₂ EA = path length; P ₁ 'CA The vertical distance between the point P ₂ and the horizontal plane passing through the point A = L _zi , the path; P ₂ EA microwave rectilinear layer Angle of incidence at point E on the interface between the ionosphere and the ionosphere; α _i0
^' Is cosα _i0 ^' = {φ'a ・ L _zi + φ'c ・ L _zi -2φ'c ・ h ・ Int (L _zi / 2h)} / {(φ'a ・ u ± φ'c ・ v ) · P _i } (1) where u; speed of light. v; Earth's rotation speed. h; parallel plane layer thickness. Int (...); The calculation formula in parentheses or the number after the decimal point is omitted. φ′a: The slope of the K _ij -n _ij characteristic curve when the incident angle when entering a point on the interface between the microwave straight traveling layer and the ionosphere of the microwave is changed in units of φ degrees. φ'c: The slope of the K _ij · n _ij −n _ij characteristic curve when the incident angle when entering a point on the interface between the microwave straight layer and the ionosphere of the microwave is changed in units of φ degrees. K _ij ; Radio wave refraction coefficient of each parallel plane layer corresponding to each radio wave path. K _ij = {(1-sin ² α _i0 ) / (n _ij ² -sin ² α _i0 )} ^1/2 n _ij ; The radio wave refractive index of each parallel plane layer corresponding to each radio wave path. i: A symbol representing each radio wave route. j: A symbol indicating the number of parallel plane layers located in the ground surface direction from the interface between the radio wave rectilinear layer and the ionosphere. The microwave path received at the observation point A is the one when h is approached to zero in the formula (1).
Now, in the formula (1), the incident angle when the microwave when h _approaches zero as much as possible enters the interface between the radio wave rectilinear layer and the ionosphere is called the critical incident angle, and is represented by α _i0a ' And from the formula (1), when h → 0, from φ'c · L _zi -2 · φ'c · h · Int (L _zi / 2h) → 0, cos α _i0a '= φ'a · L _zi / {(Φ'a ・ u ± φ'c ・ v) ・ P _i } (2) In equation (2), L _zi , P _i , u and v are fixed, so α _i0a 'is also fixed. . Note that φ'a and φ'c are cos
It is expressed as a quadratic expression of α _i0a '. For details, see Japanese Patent Application No. 361415 of 1991. However, Lzi and P
Even if i is the vertical distance and the propagation time between the satellite and the observation point with no error, α _{i0 a} 'obtained in this way is 10 ⁻⁵ from the characteristics of equation (1) or equation (2). Including an error less than degrees. Therefore, in order to make this error smaller than 10 ^-13 degrees, by the method of obtaining the true value of the critical incident angle described later,
It is necessary to make a correction. Substituting the critical incident angle corrected in this _way into α _i0a 'of equation (2), φ'a and φ'c are c
_osα i0a 'is a quadratic equation but, alpha _I0a' value prior to the correction of, as it is used. Path length; P ₂ EA = path length; P ₁ 'from CA, ∠EP ₂ P ₁ '
≈ π / 2 Therefore, the path from point P ₁ ; if a perpendicular is drawn on the extension line of AEP ₂ beyond point P ₂ and its foot is point P ₃ , ΔP ₁ P
_From 1′P ₂ ≡ΔP ₁ P ₃ P ₂ , P ₁ P ₁ ′ = P ₃ P ₂ Therefore, at a certain time; T, if there is a microwave radiation source at point P ₃ in the sky, The microwave from the point P ₃ passes through the path; P ₃ P ₂ EA and reaches the observation point located at the point A on the ground. The propagation time of the microwave at this time is that the microwave radiated from the point P ₁ has a path; P ₁ CA
It is equal to the propagation time when reaching the observation point A through the.
Now, the point P ₂ and the point P ₃ when connecting the point P ₂ and the point P ₃ in a straight line
If the propagation time of the microwave passing through the path between the _two is ΔP _i , then P ₂ P ₃ = ΔP _i · u Therefore, if the foot of the perpendicular line drawn from the point P ₃ to the horizontal plane passing through the point P ₂ is P _4. , P ₃ P ₄ = ΔP _i · u · cos α _i0 ^′ , so cosα _i0 ^′ = {φ′a · (L _zi + ΔP _i · u · cos α _i0 ^′ ) + φ ^′ c · (L _zi + ΔP _i · u ・ cosα _i0 ^' ) -2φ'c ・ h ・ Int ((L _zi + ΔPi ・ u ・ cosα _i0 ') / 2h)} / {(φ'a ・ u ± φ'c ・ v) ・ (P _i + ΔP _i )} However, the microwaves that we usually observe are those when h _approaches zero as much as possible, and the angle of incidence at this time is known from the equation (2) by α _i0a ' _{cosα i0a} '= φ'a ・ (L _zi + ΔP _i・ u ・ cos _i0a ') / {(φ'a ・ u + φ'c ・ v) ・ (P _i + ΔP _i )} (3) α _i0a ^{Since '} , φ'a, L _zi , u, φ'c, v and P _i are determined, ΔP _i can be obtained from the equation (3). Therefore, let α _i0 be the angle of incidence at point C in the radio wave path P ₁ CA, and cos α _i0 = {φa ・ L _zi + φc ・ L _zi -2φc ・ h ・ Int (L _zi / 2h)} / (φa ・ u ± φc ・ v) ・ (P _i + ΔP _i ) (4) Usually, the microwaves we observe are those in which h is as close to zero as possible, so _{cosα i0a} = φa ・ L _zi / (φa ・ u ± φc ・ v) ・ (P _i + ΔP _i ) (5) Since α _i0a thus obtained includes an error as described above, the true value of the critical incident angle is Correction is made according to the required method. Therefore, the cosine of the incident angle when the microwave radiated from the point P _{1 where the} satellite is located at a certain time T enters the interface between the radio wave rectilinear layer and the ionosphere is determined from the equation (5). Rather than whether actual satellite point P ₁ is located is a problem, as if the satellite to the point P ₁ is located, it is an object to follow a wave path at that time. In fact
The satellite is rarely located exactly at point P ₁ . (Fig. 1
Reference) At a certain time: T, it is assumed that the satellite is actually located at the point P. When the microwave from the satellite at the point P is received at the observation point A, it looks as if the microwave from the satellite at the point P ₁ was received, but the point P ₁ is located near the point P. Is certain. Therefore, the path of the microwave radiated from the point P in the ionosphere and atmospheric gas layer is
It is very close to that from point P ₁ . Therefore, assuming that it is received from the satellite located at the point P ₁ , the path of the microwave assumed to be radiated from the point P ₁ is accurately followed, and the line between the points P ₁ and A is The microwave refraction index of each parallel plane layer is obtained by correctly obtaining the radio wave propagation time, height, and the cosine of the critical incident angle of the radio wave entering the interface between the radio wave straight traveling layer and the ionosphere. (See FIG. 1) In FIG. 1, when the distance between the point P ₃ and the point P ₂ is extremely small compared to the radio wave propagation path distance; P ₂ EA, in other words, P _i >> ΔP _i , The time from point P ₃ ; (T−Δ
The microwave radiated when P _i ) is the path; P ₃ P ₂ E
The observation point A is reached through A, and the equation (6) is established. _{cosα i0a} = φa · (L _zi + u · ΔP _i · cos α _i0a ) / {(φa · u ± _φc · v) · (P _i + ΔP _i )} (6) This is apparent from the table below. That is, it is proved that α _i0a is almost constant even if ΔP _i is changed variously. Therefore, the following can be said. That is, at time; T, the microwave radiated from the radio wave radiation source located at the point P ₂ rushes to a point E on the interface between the radio wave rectilinear layer and the ionosphere, and then to a point A on the ground surface. Assuming that the observation point is located, there is a radio wave radiation source at a point P ₃ on the extension line beyond the point P ₂ of the radio wave path AEP ₂ , and the time from the point P ₃ ; (T−P ₂
The microwave radiated at P ₃ / u) reaches the observation point located at the point A at the time; T through the same radio path as the microwave radiated from the point P ₂ at the same time.
Also, the following equation holds. In addition, if ΔP _i = P ₂ P ₃ / u,
If P _i >> ΔP _i , then _{cosα i0a} = φa ・ (L _zi + u ・ ΔP _i・_{cosα i0a} ) / ((φa ・ u ± _φc・ v) ・ (P _i + ΔP _i )) (7) However, α _i0a ; a point E on the interface between the rectilinear layer and the ionosphere
Critical angle of incidence of microwaves rushing into. P _i : Propagation time of the microwave radiated from the point P ₂ . L _zi ; vertical distance between the point P ₂ and a horizontal plane passing through the point A. φa: slope of the K _ij -n _ij characteristic curve when the incident angle of the microwave entering the interface between the radio wave rectilinear layer and the ionosphere is changed in units of φ degrees. φ c; K _ij · n _ij -n when the incident angle of the microwave entering the interface between the radio wave rectilinear layer and the ionosphere is changed in units of φ degrees
_ij The slope of the characteristic curve. u; speed of light. v; Earth's rotation speed. K _ij : Radio wave refraction coefficient of each parallel plane layer corresponding to each radio wave path. K _ij = cos α _i0a / (n _ij ² -sin ² α _i0a ) ^1/2 n _ij ; Radio wave refractive index of each parallel plane layer corresponding to each radio wave path. i: A symbol representing each radio wave route. j: A symbol indicating the number of parallel plane layers in the ground surface direction from the interface between the radio wave rectilinear layer and the ionosphere. P _i + ΔP _i (ΔP _i ) L _zi + u ・ ΔP _i・_{cosα i0a} α _i0a (u ・ ΔP _i・_{cosα i0a} ) .068001431232363 (0) 16699492.96243313 (0) 34.99999830259679 .068001441232363 (1 ・ 10 ^-7 ) 16699495.41818922 (2.45575610) 34.99999830259697 .068001451232363 ^(2-10-7) 16,699,497.87394533 (4.91151220) 34.99999830259671 .068001461232363 ^(3-10-7) 16,699,500.32970143 (7.36726830) 34.99999830259671 .068001471232363 ^(4-10-7) 16,699,502.78545753 (9.82302440) 34.99999830259685 .068001481232363 (5 · 10 ^-7) 16,699,505.24121363 (12.2787805) 34.99999830259686 .068001531232363 (1 · 10 ^-6) 16,699,517.51999413 (24.5575610) 34.99999830259674 .068001631232363 (2 · 10 ^-6) 16,699,542.07755514 (49.1151220) 34.99999830259676 .068001731232363 (3 · 10 ^-6) 16,699,566.63511614 (73.6726830 ) 34.99999830259691 .068001831232363 (4 ・ 10 ^-6 ) 16699591.19267715 (98.2302440) 34.99999830259691 .068001931242463 (5 ・ 10 ^-6 ) 16699615.75023815 (122.787805) 34.99999830259687

[Method for obtaining the true value of the critical incident angle] However, α _i0a and α _i0a 'obtained in this way include a considerable error. Therefore, α _i0a and α _i0a 'will be called hereafter the calculated values of the critical incident angle, and the difference from the true value will be obtained.
Therefore, we devise a model as shown in FIG. That is, the area from the ground surface to 10 km above the ground is divided into plane layers parallel to the horizontal plane passing through the observation point A having a thickness of h meters, and the area higher than 10 km above the ground surface is a radio wave straight layer, and The area goes straight. And 10k above the ground surface
The region up to m is hereinafter referred to as the ionosphere and atmospheric gas layer.
The radio wave refractive indices of the ionosphere and the atmospheric gas layer are assumed to change linearly and are represented by y = a · x + b. However, b: radio wave refractive index at the observation point A, a: inclination of the radio wave refractive index, x: height from the observation point A, y: radio wave refractive index at a point of height x from the observation point A. Then, the radio wave refractive index of each parallel plane layer is the arithmetic mean of the radio wave refractive index of the upper surface and the lower surface of each parallel plane layer, the radio wave propagation time is constant, and the critical incident angle is changed, The total length of the radio wave path through the ionosphere and atmospheric gas layer when the thickness is changed, the vertical distance between the observation point and the radio wave radiation source, and the radio wave refractive index of each parallel plane layer are obtained. The above operation is performed while changing the gradient of the radio wave refractive index; a at a certain ratio, and Tables 1 to 10 are created. Table 1 to Table 10
As can be seen, the sum of the radio wave refractive indexes of the parallel plane layers changes at a certain fixed rate (0.25 in the case of this model). Description of Table 1 to Table 10. Unit change in true value of critical incident angle

[Table 1] (Unit: degree) P _i : .068001431232363 Δα: 1 a: -2.56D-05 Radio wave propagation time (unit: seconds) b: 1.000301 α _i0a : 35 _Slope of radio wave refractive index of ionosphere and atmospheric gas layer h: 1000 Observation Radio wave refractive index at point A True value of critical incidence angle (unit: degree) Thickness of parallel plane layer in ionosphere and atmospheric gas layer (unit: m) 0 0 12.20671089556446 16699.49345258485 10.00173 0 1 12.20671089628706 16699.49345258426 100.0173 0 2 12.20671089629429 16,699.49345258425 1000.173 0 3 12.20671089629436 16,699.49345258425 10001.73 1 0 12.35955151962885 16,492.87718514699 10.00173 1 1 12.35955152043641 16,492.87718514633 100.0173 1 2 12.35955152044449 16492.87718514633 1000.173 1 3 12.35955152044458 16,492.87718574633 10001.73 '''total observation point a and radio source of ionospheric and in radio refractive index in the atmosphere gas layer Vertical distance (unit: km) 'Path length of radio wave passing through ionosphere and atmospheric gas layer (unit: km)' Ionization It is an index showing the thickness of the layer and the plane-parallel layer in the atmospheric gas layer, and indicates that 1000 * 10 ^-3 = 1 m. 'This value is multiplied by the rate of change of the true value of the critical incident angle to express the amount of change of the true value of the critical angle of incidence. In this case, the true value of the critical incident angle is 36 degrees. As can be seen from Table 11 and Table 11-1, the index representing the thickness of the plane-parallel layer in the ionosphere and atmospheric gas layer is 3 or more, that is,
When the thickness of each parallel plane layer in the ionosphere and the atmospheric gas layer becomes 1 m or less, the radio path length passing through the ionosphere and the atmospheric gas layer hardly changes. This means that it is in perfect agreement with the radio waves that we normally observe when the thickness of each parallel plane layer in the ionosphere and atmospheric gas layer approaches zero as much as possible. Therefore, assuming that the thickness of each parallel plane layer in the ionosphere and atmospheric gas layer is 1 m, from Table 1 to Table 10, (1) From the radio wave propagation time and the vertical distance between the observation point and the radio wave radiation source, the critical incident angle Calculated values, the slope of the K _ij -n _ij characteristic curve: φa and the slope of the K _ij · n _ij -n _ij characteristic curve: φc are obtained. (2) When the sum of the radio refractive index of the parallel planar layers of the ionosphere and the atmosphere gas layer expressed by ^{_{Σ j = 0 n n ij,}} Σ j = 0 n n ij = {u · Lzi ± v · Lzi + φa・ H ・ n ・ u-2 ・ h ・ u ・ Int (Lzi / 2h) ± φc ・ h ・ n ・ v} / (φa ・ u ± φc ・ v) ・ h (8) (Patent application in 1991) No. 36141 page 9 formula (34)) Since h = 1 m, it is equivalent to when h approaches zero as much as possible. That is, h → 0 u · L _zi −2 · h · u · Int (L _zi / 2h) → 0 Therefore, from equation (8), Σ _{j = 0} ⁿ n _ij = (± v · L _zi + φa · h ・ n ・ u ± φc ・ h ・ n ・ v) / (φa ・ u ± φc ・ v) ・ h = ± v ・ L _zi / (φa ・ u ± φc ・ v) + n (9) Previous item (1 Substituting φa and φc obtained in) into equation (9), Σ _{j = 0} ⁿ n _ij (hereinafter referred to as the calculated value of the sum of the radio wave refractive indices of the parallel plane layers in the ionosphere and atmospheric gas layer). Ask). With the above operation, the radio wave propagation time is kept constant, and the true value of the critical incident angle is changed in units of 1 degree, and Tables 12 to 21 are created. (3) Sum of radio wave refractive indices in the ionosphere and atmospheric gas layer: R _i is plotted on the horizontal axis, and the difference between the true value of the critical incident angle and its calculated value is plotted on the vertical axis. Then, different curves are drawn corresponding to the true values of the critical incident angles. When the difference between the true value of the critical incident angle and its calculated value is represented by Y, from Tables 11, 12, ..., 21, the space between X and Y is represented as shown in Table 22-1. It Further, the relationship between X and Y shown in Table 22-1 can be expressed as shown in Table 22-2. Now, the ten formulas in Table 22-2 are combined into one formula and displayed as in formula (10). Y = f (α _i0a ) ・ X ² + g (α _i0a ) ・ X + h (α _i0a ) (10) where α _i0a : True value of critical incident angle X: Radio refraction in ionosphere and atmospheric gas layer Sum of rates:
A portion of R _i that is not related to the number of parallel plane layers. Y: Difference between the true value of the critical incident angle and its calculated value f (α _i0a ), g (α _i0a ), h (α _i0a ): It is a certain function of α _i0a . (4) Calculated value of the sum of the radio wave refractive indices of the parallel plane layers of the ionosphere and atmospheric gas layer obtained in (2) above: Σ _{j = 0} ⁿ n _ij , which is not related to the number of parallel plane layers. Ask. When this part is expressed as Z, Tables 11, 12, ..., 21
Therefore, between X and Z is represented by Table 23-1 and Table 23-2. When the relationship between X and Z shown in Table 23-1 and Table 23-2 is expressed by a mathematical expression, it is shown in Table 23-3. Table 23
-3 is discontinuously displayed for each true value of the critical incident angle. Now, if this is displayed in correspondence with the true values of the continuous critical incident angles, Z = k (α _i0a ) ・ X ² + l (α _i0a ) ・ X + m (α _i0a ) (11) where α _i0a : True value of critical incident angle X: Sum of radio wave refractive indices in ionosphere and atmospheric gas layer: Part of R _i that is not related to the number of parallel plane layers. Z: Calculated value of the sum of the radio wave refractive indices of the parallel plane layers in the ionosphere and the atmospheric gas layer: Σ _{j = 0} ⁿ n _ij , which is not related to the number of parallel plane layers. k (α _i0a ), l (α _i0a ), m (α _i0a ): It is a function of α _i0a . (5) When the calculated value of the critical incident angle obtained in (1) above is expressed as W, from Tables 11, 12, ...
The space between and is shown in Table 24-1. If the relationship between X and W shown in Table 24-1 is represented by a mathematical expression, it is shown in Table 24-2. Table 24-2 is displayed discontinuously for each true value of the critical incident angle. Now, when this is displayed in correspondence with the true values of the continuous critical incident angles, W = p (α _i0a ) ・ X ² + q (α _i0a ) ・ X + r (α _i0a ) (12) where α _i0a : True value of critical incident angle X: Sum of radio wave refractive indices in ionosphere and atmospheric gas layer: Part of R _i that is not related to the number of parallel plane layers. W: Calculated value of the critical incident angle. p (α _i0a ), q (α _i0a ), r (α _i0a ): It is a certain function of α _i0a . W and Z are determined from the previous items (1) and (2).
Therefore, X, Y and α _i0a can be obtained from the equations (2), (3) and (4). Up to now, the true value of the critical incident angle has been performed in the range of 35 degrees to 44 degrees. Therefore, in order to cover most of the sky, the true value of the critical incident angle is 15 ° to 25 ° 25 ° The same applies to ˜35 ° 44 ° to 55 ° 55 ° to 65 ° 65 ° to 75 °. Then, the range of the true value of the critical incident angle is determined from the calculated value of the critical incident angle, and the critical incident angle is obtained. To obtain the true value of the actual critical incident angle, the area from the ground surface up to 1000 km above
Divide into plane layers parallel to the horizontal plane that passes 1 m observation point, and do the same as the previous small model.

2. The area from the ground surface to 1000 km above the ground is divided into n parallel plane layers parallel to the horizontal plane passing through the observation point, and the radio wave refractive index of each parallel plane layer is obtained. (See Fig. 5) True value of radio wave refractive index of layer 1; X ₁ True value of radio wave refractive index of layer 2; X ₂ Initial value of radio wave refractive index of layer 1; X ₁ ^' Initial wave refractive index of layer 2 Value; Error in radio wave refractive index of X ₂ ^' Layer 1; Error in radio wave refractive index of Δ X ₁ ^' Layer 2; ΔX ₂ ^' Incident angle of microwave entering the interface between the radio wave rectilinear layer and the ionosphere; α ₀ Layer 1 Refraction angle of microwaves; α ₁ Refraction angle of microwaves in layer 2; Inclination of two characteristic curves corresponding to cosine of α ₂ α ₀ ; a, c Path length of microwaves passing through layer 1 and α ₀ True cosine of the product of the cosine of the microwave passing through layer 2 and the cosine of α ₀ ; the product of the path length of the microwave passing through layer A and the cosine of α ₀ And the initial value of the sum of products of the path length of the microwave passing through the layer 2 and the cosine of α ₀ ; A ′ The product of the path length of the microwave passing through the layer 1 and the cosine of α ₀ , and the layer 2 through a path length of a microwave and alpha ₀ of Error of the sum of the product of the chord; a .DELTA.A '. c ・ X ₁ + d + c ・ X ₂ + d = A (a ・ X ₁ + b) ・ X ₁ + (a ・ X ₂ + b) ・ X ₂ = A c + d = 1 a + b = 1 X ₁ = X ₁ '+ ΔX ₁ ' X ₂ = X ₂ '+ ΔX ₂ ' A = A '+ ΔA'. See Japanese Patent Application No. 361415 for the details of the establishment of the equations, and. ,
Substitute ,, and. c ・ (X ₁ '+ ΔX ₁ ') + 1-c + c ・ (X ₂ '+ ΔX ₂ ') + 1-c = A '+ ΔA' ∴ ΔX ₁ '+ ΔX ₂ ' = {A '+ From ΔA'-2 ・ (1-c)} / c- (X ₁ '+ X ₂ '), a ・ X ₁ ² + b ・ X ₁ + a ・ X ₂ ² + b ・ X ₂ = A a ・From (X ₁ ² + X ₂ ² ) + b ・ (X ₁ + X ₂ ) = A (8-1), c ・ (X ₁ + X ₂ ) +2 ・ d = A ∴ X ₁ + X ₂ = (A-2 ・ d) / c (8-2) Substituting (8-2) into (8-1), a ・ (X ₁ ² + X ₂ ² ) + b ・ (A-2 ・ d ) / c = A ,,, and are assigned to. (X ₁ '+ ΔX ₁ ') ² + (X ₂ '+ ΔX ₂ ') ² = {A '+ ΔA'-(b / c) ・ (A '+ ΔA') + 2 ・ (b ・ d) / c} / a = {1-b / c) (A '+ ΔA') + 2 ・ (b ・ d) / c} / a X ₁ ' ² +2 ・ X ₁ ' ・ ΔX ₁ '+ ΔX ₁ ' ² + X ₂ ' ² +2 ・ X ₂ '・ ΔX ₂ ' + ΔX ₂ ' ² = {(1- (1-a) / c) ・ (A' + ΔA ') + 2 ・ (1-a ) ・ (1-c) / c} / a 'ΔX ₁ ^{' 2} ≒ 0, ΔX ₂ ^'2 ≒ 0, X ₁ ' ・ ΔX ₁ '+ X ₂ ' ・ ΔX ₂ '= 〔{(a + c -1) ・ (A '+ ΔA') + 2 ・ (1-a-c + a ・ c)} / (a ・ c)-(X ₁ ' ² + X ₂ ' ² )] / 2 (10) Multiply both sides by X ₂ '. X ₂ '・ ΔX ₁ ' + X ₂ '・ ΔX ₂ ' = X ₂ '・ [{A' + ΔA'-2 ・ (1-c)} / c- (X ₁ '+ X ₂ ')] ( 11) From (11)-(10), (X ₂ '-X ₁ ') ・ ΔX ₁ '= X ₂ ' ・ {(A '+ ΔA'-2 ・ (1-c)) / c- (X ₁ '+ X ₂ ')}-(1/2) ・ {((a + c-1) ・ (A '+ ΔA') + 2 ・ (1-a-c + a ・ c)) / (a・ C)-(X ₁ ' ² + X ₂ ' ² )} (12) Now, {A'-2 ・ (1-c)} / c- (X ₁ '+ X ₂ ') = B (13) (1/2) ・ [{(a + c-1) ・ A '+ 2 (1-a-c + a ・ c)} / (a ・ c)-(X ₁ ' ² + X ₂ ' ² ) ] = D (14) From (12), (13) and (14), (X ₂ '-X ₁ ') ・ ΔX ₁ '= X ₂ ' ・ B-D + (X ₂ '/ c) ・ ΔA'-(1/2)・ {(A + c-1) / (a ・ c)} ・ ΔA '= X ₂ ' ・ B-D + {X ₂ '/ c- (1/2) ・ (a + c-1) / (a・ C)} ・ ΔA '(15) is multiplied by X ₁ ' on both sides. X ₁ '・ ΔX ₁ ' + X ₁ '・ ΔX ₂ ' = X ₁ '・ {(A' + ΔA'-2 ・ (1-c)) / c- (X ₁ '+ X ₂ ')} ( 16) From (16)-(10), (X ₁ '-X ₂ ') ・ ΔX ₂ '= X ₁ ' ・ {(A '+ ΔA'-2 ・ (1-c)) / c- (X ₁ '+ X ₂ ')}-(1/2) ・ [{(a + c-1) ・ (A '+ ΔA') + 2 ・ (1-a-c + a ・ c)} / (a・ C)-(X ₁ ' ² + X ₂ ' ² )] (17) Substituting (13) and (14) into (17). (X ₁ '-X ₂ ') ・ ΔX ₂ '= X ₁ ' ・ B-D + (X ₁ '/ c) ・ ΔA'-(1/2) ・ {(a + c-1) / (a ・c)} ・ ΔA '= X ₁ ' ・ B-D + {(X ₁ '/ c)-(1/2) ・ (a + c-1) / (a ・ c)} ・ ΔA' (18) ( From (15), ΔA '= {(X ₂ ' -X ₁ ') ・ (X ₁ -X ₁ ') -X ₂ '・ B + D} / {X ₂ ' / c- (1/2) (( a + c-1) / (a ・ c))} (19) (18), ΔA '= {(X ₁ ' -X ₂ ') ・ (X ₂ -X ₂ ') -X ₁ '・ B + D} / {X ₁ '/ c- (1/2) ((a + c-1) / (a ・ c))} (20) X ₁ ', X ₂ ', B, D, a and c Since (19) is fixed, ΔA '= m · X ₁ + n (21) (20) is expressed as ΔA' = p · X ₂ + q (22). From m · p <0 and n · q <0, (21) and (22) are shown in a graph as shown in FIG. Since the refractive index of the USA standard atmosphere is used as X ₁ 'and X ₂ ', it is usually X ₁ '<X ₁ and X ₂ '<X ₂ , so the initial value of the radio wave refractive index of each layer is the true value. In order to get closer to X, it is necessary to approach X ₁ and X ₂ by increasing X ₁ 'and X ₂ ' while decreasing the absolute value of ΔA '. However, when the absolute value of ΔA 'is reduced from Fig. 4, X ₁ ' and X ₂ '
Has a relationship where one increases and the other decreases. Therefore, (2
Either one of (1) and (22) is converted to a straight line that passes through the intersection of (21) and (22) and has the same absolute value of gradient and different sign. ΔA ′ = − p · X ₂ + q ′ (23) When one of the refractive indices is determined from (21) and (23), ΔA ′ is determined. Therefore, as a result, the refractive index of the other layer is also determined. Then, assuming that X ₁ and X ₂ just determined represent the true value of the radio wave refractive index of each layer, A '+ ΔA' = cos α ₀ / (1-sin ² α ₀ / X ₁ ² ) ^1/2 + cos α ₀ / (1-sin ² α ₀ / X ₂ ² ) ^1/2 = A (24) must hold. A '= cos α ₀ / (1-sin ² α ₀ / X ₁ ' ² ) ^1/2 + cos α ₀ / (1-sin ² α ₀ / X ₂ ' ² ) ^1/2 (24') However, as can be seen from Tables 25, 26, and 27, (24) does not hold because it has an inherent error value based on the combination of the radio wave refractive indexes of the layers. That is, the radio wave refractive index of the parallel plane layers adjacent to each other in the atmospheric gas layer and the ionosphere, the incident angle of the radio wave entering the interface between the radio wave rectilinear layer and the ionosphere, and passing through the parallel plane layers adjacent to each other in the atmospheric gas layer and the ionosphere. There is a relationship of (25) between the radio path lengths to be performed. cos α _i0・ (l _ij + l _{ij + 1} ) = c _i・ X ₁ + d _i + c _i・ X ₂ + d _i (25) α _i0 ; of the microwave rushing into the interface between the rectilinear layer and the ionosphere Angle of incidence. l _ij , l _{ij + 1} ; Microwave path length through the parallel plane layers adjacent to each other in the atmospheric gas layer and the ionosphere. c _i , d _i ; a gradient and a constant representing the K _ij · n _ij -n _ij characteristic curve corresponding to the radio wave path. However, if c _i + d _i = 1 and ΔA '' is the error value peculiar to the combination of the radio wave refractive indices of each layer, ΔA '' = A- (A '+ ΔA') (26) ΔA ' Table 2 using (21), (24) and (26)
5, the tables shown in Tables 26 and 27 are prepared. A-
When (A '+ ΔA') is displayed on the vertical axis and X ₂ is displayed on the horizontal axis, FIG.
Is displayed. That is, ΔA ″ is represented by (27) corresponding to the radio wave refractive index of the other layer; X ₂ . ΔA '' = ζ · X ₂ + η (27) where ζ has a certain value corresponding to the range of the radio wave refractive index of the other layer; X ₂ , but η has the radio wave refractive index of one layer; X ₁
Draw a straight line corresponding to the range. That is, from η = κ ・ X ₁ + ξ (28) (27), (28), ΔA '' = ζ ・ X ₂ + κ ・ X ₁ + ξ (29) (29) represents ΔA '' Since it is an approximate expression, the values on the left and right sides of (29) do not match. Therefore, when this error is represented by a numerical table, it becomes like the right end of Table 25, Table 26, and Table 27. or,
When expressed in a graph, a parabola is drawn as shown in FIG. Therefore, if this is expressed by a mathematical formula, ΔA ''-(ζ ・ X ₂ + κ ・ X ₁ + ξ) = ε ・ (X ₂ -ν) ² + ρ ・ (X ₁ -τ) ² + χ Radio wave refractive index of one layer; based on X ₁ ,
If ΔΛ such that A- (A '+ ΔΛ) = 0 is obtained, ΔΛ = m ・ X ₁ + n + ζ ・ X ₂ + κ ・ X ₁ + ξ + ε ・ (X ₂ -ν) ² + ρ ・(X ₁ -τ) ² + χ (30). Next, with reference to the radio wave refractive index of the other layer; X ₂ , ΔΛ for A- (A ′ + ΔΛ) = 0 is obtained. From Table 28, Table 29, Table 30, and FIG. ΔΛ = -p ・ X ₂ + q '+ ζ' ・ X ₁ + κ '・ X ₂ + ξ' + ε '・ (X ₁ -ν') ² + ρ '・ (X ₂ -τ') ² + From χ '(31) (24), cos α ₀ / (1-sin ² α ₀ / X ₁ ² ) ^1/2 + cos α ₀ / (1-sin ² α ₀ / X ₂ ² ) ^1/2 = A' + ΔΛ (31 ') Also, from (25), c ・ X ₁ + d + c ・ X ₂ + d = A' + ΔΛ (32) cosα _i0 = {φa ・ L _zi + φc ・ L _zi -2 ・φc ・ h ・ Int (L _zi / 2h)} / {(φa ・ u ± φc ・ v) ・ P _i } (33) L _zi = n ・ h + u ・ P _i・ cosα _i0 -hΣ _{j = 0} ⁿ The microwave when K _ij · n _ij (34) h → 0 is received. At this time, φc ・ L _zi -2 ・ φc ・ h ・ Int (L _zi / 2h) → 0 (35) Now, when the microwave received at the observation point enters the interface between the radio wave rectilinear layer and the ionosphere the angle of incidence is called the critical angle of incidence, if indicated as _{α i0a, cosα i0a = φa ·} L zi / {(φa · u ± φc · v) · P i} (36) L zi and P _i are determined From equation (36), α _i0a
Is also confirmed. From equation (34), hΣ _{j = 0} ⁿ K _ij · n _ij = n · h + u · P _i · cos α _i0 -L _zi (37) Substituting equation (36) into equation (37), hΣ _{j = 0} ⁿ K _ij・ n _ij = n ・ h + φa ・ u ・ L _zi / (φa ・ u ± φc ・ v) -L _zi (38) The path length of microwaves passing through the atmospheric gas layer and the ionosphere is l _ia Then, from equation (38), l _ia = (n ・ h + φa ・ u ・ L _zi / (φa ・ u ± _φc・ v) -L _zi ) / _{cosα i0a} (39) Now, the atmospheric gas layer and ionosphere Is divided into parallel plane layers having a thickness h, and the microwave travels straight in each parallel plane layer, the path length of the microwave passing through the atmospheric gas layer and the ionosphere is reduced by Δl _ia . Accordingly, the microwave path length in the radio wave straight-ahead layer increases because the radio wave propagation time is constant. Therefore, the distance between the satellite and the horizontal plane passing between the observation points increases by Δl _{ia ·} cos α _i0a (40). Therefore, from equations (33) and (40), _{cosα i0a} = {φa ・ (L _zi + Δl _ia・_{cosα i0a} ) + _φc・ (L _zi + Δl _ia・_{cosα i0a} ) -2 ・_φc・ h ・ Int ((L _zi + Δl _ia · cos α _i0a ) / 2h)} / {(φa · u ± φc · v) · P _i } (41) Since α _i0a , L _zi and P _i are determined, the formula ( 41) Δl _ia also determined from. Therefore, when the atmospheric gas layer and the ionosphere are divided into parallel plane layers of thickness h, in each parallel plane layer, if the microwave goes straight, (l _ia −Δl _ia ) · cos α _i0a = A _i '+ ΔΛ _i ' (42) However, even if the atmospheric gas layer and the ionosphere are divided into parallel plane layers of a certain thickness so that Δl _ia takes a positive value, such an atmospheric gas layer and There are no microwaves propagating in the ionosphere. The microwave that actually exists is Δl _ia
Is a microwave that propagates through the atmospheric gas layer and the ionosphere so that is zero. In the formula (33), such a microwave has h as close to zero as possible, but a model devised to accurately determine the incident angle of the radio wave entering the interface between the radio wave rectilinear layer and the ionosphere. Simulation Table 1
As can be seen from 1, when the atmospheric gas layer and the ionosphere are divided into parallel plane layers having a thickness of 1 m or less, Δl _ia becomes zero. This means that when the atmospheric gas layer and the ionosphere are divided into parallel plane layers with a thickness of 1 m, the microwave passing therethrough is completely equivalent to the microwave that we normally observe. Therefore, from equations (37) and (42), l _ia · cos α _i0a = A _i '+ ΔΛ _i ' = n · 1 + u · P _i · cos α _i0a -L _zi (43) Equation (31 ') is established between the adjacent parallel plane layers. Therefore, Σ _{j = 1} ^{n / 2} ( _{cosα i0a} / (1-sin ² α _i0a / n _j ² ) ^1/2 + _{cosα i0a} / (1-sin ² α _i0a / n _j ² ) ^1/2 = A _i = Σ _{j = 1} ^{n / 2} (A _j '+ ΔΛ _j ') (44) holds Σ _{j = 1} ^{n / 2} (A _j '+ ΔΛ _j ') = Σ _{j = 1} ^{n / 2} A _j '+ Σ _{j = 1} ^{n / 2} ΔA _j ' = A _i '+ ΔΛ _i ' (45) From equation (30), ΔΛ _j '= m _j · X _j + n _j + ζ · X _{j + 1} + κ _j・ X _j + ξ + ε ・ (X _{j + 1} -ν _j ) ² + ρ _j・ (X _j -τ _j ) ² + χ _j (46) x _j = x _j '+ Δx _j '(47) x _{j + 1} = x _{j + 1} ' + Δx _{j + 1} '(48) Substituting equations (47) and (48) into equation (46), we obtain Δ
If x _j '≈ 0 and Δx _{j + 1} ' ≈ 0, then ΔΛ _j '= m _j · (x _j + Δx _j ') + n _j + ζ · (x _{j + 1} '+ Δx _{j + 1} ' ) + κ ・ (x _j '+ Δx _j ') + ξ + ε _j・ (x _{j + 1} '+ Δx _{j + 1} ' -ν _j ) ² + ρ _j・ (x _j '+ Δx _j ' -τ _j ) ² + χ _j = m _j・ x _j '+ n _j + ζ ・ x _{j + 1} ' + κ ・ x _j '+ ξ + ε _j・ x _{j + 1} ' ² + ε _j・ ν _j ^2- 2 ・ ε _j・ ν _j・ x _{j + 1} '+ ρ _j・ x _j ' ² + ρ _j・ τ _j ² -2 ・ ρ _j・ τ _j・ x _j '+ ρ _j・ χ _j + (m _j + κ + 2 ・ ρ _j・ x _j '-2 ・ ρ _j・ τ _j ) ・ Δx _j ' + (2 ・ ε _j・ x _{j + 1} '-2 ・ ε _j・ ν _j ) ・ Δx _{j + 1} '= ω _j + σ ・ Δx _j ' + ψ ・ Δx _{j + 1} '(49) Therefore, from Equation (45) and Equation (49), Σ _{j = 1} ^{n / 2} A _j ' + Σ _{j = 1} ^{n / 2} ΔΛ _j '= Σ _{j = 1} ^{n / 2} A _j ' + Σ _{j = 1} ^{n / 2} (ω _j + σ _j・ Δx _j '+ ψ ・ Δx _{j + 1} ') (50) Σ _{j = 1} ^{Since n / 2} A _j 'is a constant, formula (44) and formula (5
0), Σ _{j = 1} ⁿ a _ij · Δx _j '= A _i (51) From formula (43) and formula (51), Σ _{j = 1} ⁿ a _ij · Δx _j ' = n + u · P _i Cos α _i0a −L _zi (52) That is, a multidimensional linear simultaneous equation with Δx _j (j = 1 to n) as a variable is established. Therefore, the radio wave refractive index of each parallel plane layer;
x _j is a solution of the multidimensional linear simultaneous equations; (52); Δx _j ′ is obtained and x _j = x _j ′ + Δx _j ′ (j = 1 to n). However, n is an even number.

3. At a certain time; at T, a guard in the sky
Accurately determine the three-dimensional position of the point P where the star is located. (Fig. 8
See) The area from the ground surface to a height of 1000 km
It is divided into parallel plane layers of thickness hm parallel to the horizontal plane passing through the measurement point A.
Divide. Radio wave refractive index of each parallel plane layer; n_ijIs known
It This is a very exact expression, and usually a set of
The radio wave refractive index of each parallel plane layer in the radio wave path is the same
It can be considered that they are the same in the surface layer. That is, each parallel
The refractive index of the plane layer is n_jIt is represented by. There is a satellite
A point P is a position at time T. Located at point P
Radio waves emitted from the satellite
The critical incident angle α at one point M on the interface _i0aThis radio wave
Observation point A on the ground surface propagating through the ionosphere and atmospheric gas layer
Is reached. In the following, this radio wave is called the radio wave PMA.
To call. Similarly, it is emitted from a satellite located at point P.
Generated radio waves are reflected on the interface between the rectilinear layer and the ionosphere.
Critical incident angle β at point N_i0aThis radio wave penetrates into the ionosphere
And another observation point B on the ground surface
Is reached. However, the observation point B passes through the observation point A
A straight line within the same horizontal plane and within a distance of 20km
And In addition, hereinafter, this radio wave is referred to as a radio wave PNB.
Point the foot of the perpendicular drawn from the point P to the horizontal plane passing through the observation point A
Q, and this perpendicular line intersects the interface between the radio wave straight layer and the ionosphere.
A point R is defined as the point where the change occurs. The interface between the radio wave straight layer and the ionosphere
Is parallel to the horizontal plane passing through the observation point A. Point M and point N
From the point K to the foot of the vertical line that goes down to the horizontal plane passing through the observation point A.
And point L, and from observation points A and B through observation point A.
Establish normals AH and BJ on the horizontal plane. Observation points A and B
The incident angle of radio waves PMA and PNB at_inas well as
β_in, Elevation angle γ_inAnd δ_inAnd Also, ∠ABQ =
θ_B, ∠MNR = θ_NAnd Radio wave PMA and radio wave PNB
Of the radio wave path through the ionosphere and atmospheric gas layer of_AMOver
And l_BNThen l_AM= h ・ f (cosα_i0a) * L_BN= h ・ f (cosβ_i0a) * Therefore, the radio wave radiated from a certain satellite located at point P is
P is the time to reach observation points A and B_iAnd Q_iTosu
Then, the radio waves pass through the radio wave straight layers of the radio waves PMA and PNB.
Radio path length_PMAnd l_PNWhere, and from l_PM= u ・ P_i-l_AM= u ・ P_i-h ・ f (cosα_i0a) l_PN= u ・ Q_i-l_BN= u ・ Q_i-h ・ f (cosβ_i0a) It is assumed that the distance between the observation point A and the observation point B is r.
And r ・ cosν_B= u ・ (Q_i-P_i) Where ν_BIs the angle between the radio wave PNB and the straight line AB.
And u is the speed of light. l_AMAnd l_BNThe horizontal component of l
_AKAnd l_BLThen l_AK= h ・ sinα_i0a・ G (cos α_i0a) * L_BL= h ・ sinβ_i0a ・ g (cos β_i0a) * PR = PM ・ cosα_i0a = l_PM・ Cos α_i0a = {u ・ P_i-h ・ f (cosα_i0a)} ・ Cos α_i0a  Also, PR = PN ・ cosβ_i0a = l_PN・ Cos β_i0a = {u ・ Q_i-h ・ f (cosβ_i0a)} ・ Cos β_i0a  From the expression and, {u · P_i-h ・ f (cosα_i0a)} ・ Cos α_i0a = {u ・ Q_i-h ・ f (cosβ_i0a)} ・ Cos β_i0a ∴ {u ・ P_i-h ・ f (cosα_i0a)} / {u ・ Q_i-h ・ f (cosβ_i0a)} = cos β_i0a/ cos α_i0a (10) In ABAB, from AB | KL, KQ / AQ = LQ / BQ (11) AQ = AK + KQ = l_AK+ MR = l_AK+ PM ・ sinα_i0a= l_AK+ l_PM・ Sinα_i0a = h ・ sinα_i0a・ G (cos α_i0a) + (u ・ P_i-h ・ f (cosα_i0a)} ・ Sinα_i0a (12) BQ = BL + LQ = l_BL+ NR = l_BL+ PN ・ sinβ_i0a= l_BL+ l_PN・ Sinβ_i0a = h ・ sinβ_i0a・ G (cos β_i0a) + {u ・ Q_i-h ・ f (cosβ_i0a)} ・ Sinβ_i0a (13) KQ = MR = PM ・ sinα_i0a= l_PM・ Sinα_i0a= {u ・ P_i-h ・ f (cosα_i0a)} ・ Sinα_i0a (14) LQ = NR = PN ・ sinβ_i0a= l_PN・ Sinβ_i0a= {u ・ Q_i-h ・ f (cosβ_i0a)} ・ Sinβ_i0a (15) Substituting equations (12), (13), (14) and (15) into equation (11). [{U ・ P_i-h ・ f (cosα_i0a)} ・ Sinα_i0a] / [H ・ sinα_i0a・ G (cos α_i0a) + (u ・ P_i-h ・ f (cosα_i0a)} ・ Sinα_i0a] = [{U ・ Q_i-h ・ f (cosβ_i0a)} ・ Sinβ_i0a] / [H ・ sinβ_i0a・ G (cos β_i0a) + {u ・ Q_i-h ・ f (cosβ_i0a)} ・ Sinβ_i0a] ∴ {u ・ P_i-h ・ f (cosα_i0a)} / {u ・ P_i+ h ・ g (cos α_i0a) -h ・ f (cosα_i0a)} = {u ・ Q_i-h ・ f (cosβ_i0a)} / {u ・ Q_i+ h ・ g (sin β_i0a) -h ・ f (cos β_i0a)} (16) At a certain time; Is it the point P at which the satellite in the sky is located at T?
Received these radio waves at point A, which is located on the ground at the observation point.
And measure the position of the satellite from the orbital information of the satellite
And as if the satellite were at point P₁Observed as if
It Point P₁The position of 1 is as described above. Accurately determined by
You can Therefore, the point P₁Radio waves emitted from
Is the critical incident angle at which the electromagnetic wave enters the interface between the rectilinear layer and the ionosphere.
Δ_i0aThen the critical incident angle δ_i0aCan be stopped accurately
You can Point P is point P₁Exists in the vicinity of_i0a
And β_i0aIs the size of δ_i0aIs approximately equal to the size of
You can think of it. Draw a parallel line from the point L to the straight line AQ and draw the straight line AB
Let S be the point of intersection with. △ In ABQ, is AQ | SL?
BS / AB = SL / AQ ∴ BS = (SL / AQ) ・ AB = (AK / AQ) ・ AB (SL = AK) AQ = AK + KQ = AK + MR = AK + MP ・ sinα_i0a= l_AK+ l_PM・ Sinα_i0a = h ・ sinα_i0a・ G (cos α_i0a) + (u ・ P_i-h ・ f (cosα_i0a)} ・ Sinα_i0a ∴BS = h ・ sinα_i0a・ G (cos α_i0a) ・ R / (h ・ sinα_i0a・ G (cos α_i0a) + (u ・ P_i-h ・ f (cosα_i0a)} ・ Sinα_i0a] = H ・ g (cosα_i0a) ・ R / {u ・ P_i+ h ・ g (cos α_i0a) -h ・ f (cosα_i0a)} (29) △ BS, BS²+ BL²-2 ・ BS ・ BL ・ cos θ_B= SL² ∴ cos θ_B= (BS²+ BL²-SL²) / (2 ・ BS ・ BL) (30) BS²+ BL²-SL²= 〔(H ・ g (cosα_i0a) ・ R} / {u ・ P_i+ h ・ g (cos α_i0a) -h ・ f (cosα_i0a)}]² + {h ・ sinβ_i0a-g (cosβ_i0a)}²-{h ・ sinα_i0a・ G (cos α_i0a)}² (31) 2 ・ BS ・ BL = 2 ・ (h ・ g (cos α_i0a) ・ R / {u ・ P_i+ h ・ g (cos α_i0a) -h ・ f (cosα_i0a)}] ・ {H ・ sinβ_i0a・ G (cos β_i0a)} = 2 ・ h²・ R ・ sinβ_i0a・ G (cos α_i0a) ・ G (cosβ_i0a) / (u ・ P_i + h ・ g (cos α_i0a) -h ・ f (cosα_i0a)} (32) Substituting Eqs. (31) and (32) into Eq. (30) and putting them in order, cos θ_B= 〔G²(cos α_i0a) ・ R²+ {u ・ P_i+ h ・ g (cos α_i0a) -h ・ f (cosα_i0a)}² ・ (Sin²β_i0a・ G²(cos β_i0a) -sin²α_i0a・ G²(cos α_i0a)}] / [2 ・ r ・ sinβ_i0a・ G (cos α_i0a) ・ G (cosβ_i0a) ・ (U ・ P_i+ h ・ g (cos α_i0a) -h ・ f (cosα_i0a)}] (33) Also, cosν_B= sinβ_in・ Cos θ_B = (sin β_i0a/ n_in) ・ Cos θ_B (34) In ABAB, from AB | KL, KL / AB = KQ / AQ KQ = MR = MP ・ sinα_i0a= l_PM・ Sinα_i0a= {u ・ P_i-h ・ f (cosα_i0a)} ・ Sinα_i0a ∴ MN = KL = (KQ / AQ) ・ AB = [{u ・ P_i-h ・ f (cosα_i0a)} ・ Sinα_i0a/ 〔H ・ sinα_i0a・ G (cos α_i0a) + (u ・ P_i-h ・ f (cosα_i0a)} ・ Sinα_i0a]] ・ R = {u ・ P_i-h ・ f (cosα_i0a)} ・ R / {u ・ P_i+ h ・ g (cos α_i0a) -h ・ f (cosα_i0a)} (34 ') PN-PM = MN · cosν_n From the expression, and (3
4 '), therefore, (u ・ Q_i-h ・ f (cosβ_i0a)}-{u ・ P_i-h ・ f (cosα_i0a)} = [{u ・ P_i-h ・ f (cosα_i0a)} ・ R / {u ・ P_i+ h ・ g (cos α_i0a) -h ・ f (cosα_i0a)}] ・ Cosν_N (35) cosν_N= sinβ_i0a・ Cos θ_N cosν_B= sinβ_in・ Cos θ_B From AB‖MN, BQ‖NR, θ_N= θ_B cosν_N/ cosν_B= cosν_B/ sinβ_in ∴ cosν_N/ cosν_B= sinβ_i0/ sinβ_in= n_in Arrange the left side of equation (35) so that u ・ (Q_i-P_i) -h ・ f (cos β_i0a) + h ・ f (cos α_i0a) = r ・ cosν_B-h ・ f (cosβ_i0a) + h ・ f (cos α_i0a) = [{u ・ P_i-h ・ f (cosα_i0a)} ・ R / {u ・ P_i+ h ・ g (cos α_i0a) -h ・ f (cosα_i0a)}] ・ N_in・ Cosν_B (36) By rearranging equation (36), r ・ cosν_B・ [1-nin ・ {u ・ P_i-h ・ f (cosα_i0a)} / {u ・ P_i + h ・ g (cos α_i0a) -h ・ f (cosα_i0a)}] = H ・ f (cosβ_i0a₎-h ・ f (cosα_i0a) (37) From formulas (33), (34) and (37), [(g²(cos α_i0a) ・ R²+ {u ・ P_i+ h ・ g (cos α_i0a) -h ・ f (cosα_i0a)}² ・ (Sin²β_i0a・ G²(cos β_i0a) -sin²α_i0a・ G²(cos α_i0a)}] / [2 ・ n_in・ G (cos α_i0a) ・ G (cosβ_i0a) ・ (U ・ P_i+ h ・ g (cos α_i0a) -h ・ f (cosα_i0a)}] ・ [1-n_in・ {U ・ P_i-h ・ f (cosα_i0a)} / {u ・ P_i + h ・ g (cos α_i0a) -h ・ f (cosα_i0a)}] = H ・ f (cosβ_i0a) -h ・ f (cosα_i0a) (38) Equation (38) can be rearranged as a higher-order equation of Pi.³・ (1-n_in) ・ (Sin²β_i0a・ G²(cos β_i0a) -sin²α_i0a・ G²(cos α_i0a)} ・ Pi³ + u²・ H ・ g (cos α_i0a) ・ (Sin²β_i0a・ G²(cos β_i0a) -sin²α_i0a・ G²(cos α_i0a)} ・ Pi² -u²・ H ・ f (cos α_i0a) ・ (Sin²β_i0a・ G²(cos β_i0a) -sin²α_i0a・ G²(cos α_i0a)} ・ Pi² + u²・ H ・ n_in・ F (cosα_i0a) ・ (Sin²β_i0a・ G²(cos β_i0a) -sin²α_i0a・ G²(cos α_i0a)} ・ Pi² +2 ・ u²・ H ・ (1-n_in) ・ (G (cosα_i0a) -f (cosα_i0a)} ・ {Sin²β_i0a・ G²(cos β_i0a) -sin²α_i0a・ G²(cos α_i0a)} ・ Pi² +2 ・ u²・ H ・ n_in・ G (cos α_i0a) ・ G (cosβ_i0a) ・ (F (cosβ_i0a) -f (cosα_i0a)} ・ Pi² + u ・ (1-n_in) ・ R²・ G²(cos α_i0a) ・ P_i +2 ・ u ・ h²・ (G (cosα_i0a) -f (cosα_i0a)} ・ {Sin²β_i0a・ G²(cos β_i0a) -sin²α_i0a・ G²(cos α_i0a)} ・ {G (cosα_i0a) -f (cosα_i0a) + n_in・ F (cosα_i0a)} ・ P_i + u ・ h²・ (1-n_in) ・ (G²(cos α_i0a) -2 ・ g (cos α_i0a) ・ F (cos α_i0a) + f²(cos α_i0a)} ・ {Sin²β_i0a・ G²(cos β_i0a) -sin²α_i0a・ G²(cos α_i0a)} ・ P_i +4 ・ u ・ h²・ N_in・ G (cos α_i0a) ・ G (cosβ_i0a) ・ (G (cosα_i0a) -f (cosα_i0a)} ・ {F (cosβ_i0a) -f (cosα_i0a)} ・ P_i + h ・ r²・ G³(cos α_i0a) -h ・ r²・ G²(cos α_i0a) ・ F (cos α_i0a) + h ・ n_in・ R²・ G²(cos α_i0a) ・ F (cos α_i0a) + h³・ (G²(cos α_i0a) -2 ・ g (cos α_i0a) ・ F (cos α_i0a) + f²(cos α_i0a)} ・ {Sin²β_i0a・ G²(cos β_i0a) -sin²α_i0a・ G²(cos α_i0a)} ・ {G (cosα_i0a) -f (cosα_i0a) + n_in・ F (cosα_i0a)} +2 ・ h³・ N_in・ G (cos α_i0a) ・ G (cosβ_i0a) ・ (G²(cos α_i0a) -2 ・ g (cos α_i0a) ・ F (cos α_i0a) + f²(cos α_i0a)} ・ {F (cosβ_i0a) -f (cosα_i0a)} = 0 (39) u ・ (Q_i-P_i) = r ・ cosν_B (40) cos α_i0a= φaα ・ L_zi/ {(Φaα ・ u ± φcα ・ v) ・ P_i} (41) cos β_i0a= φaβ ・ L_zi/ {(Φaβ ・ u ± φcβ ・ v) ・ Q_i} (42) L_zi= n ・ h + u ・ P_i・ Cos α_i0a-h ・ f (cosα_i0a) ・ Cos α_i0a (43) L_zi= n ・ h + u ・ Q_i・ Cos β_i0a-h ・ f (cosβ_i0a) ・ Cos β_i0a (44) Substituting equation (43) into equation (41). cosα_i0a= φaα ・ {n ・ h + u ・ P_i・ Cos α_i0a-h ・ f (cosα_i0a) ・
cosα_i0a} / {(Φaα ・ u ± φcα ・ v) ・ P_i} Keep in order ± φcα ・ v ・ P_i・ Cos α_i0a= φaα ・ n ・ h-φaα ・ h ・ f (cosα_i0a) ・ Cos α_i0a (45) ∴P_i= {Φaα ・ n ・ h-φaα ・ h ・ f (cosα_i0a) ・ Cos α_i0a} / (± φcα ・ v ・ cosα_i0a) (46) Substituting equation (44) into equation (42). As before, Q_i= {Φaβ ・ n ・ h-φaβ ・ h ・ f (cosβ_i0a) ・ Cos β_i0a} / (± φcβ ・ v ・ cosβ_i0a) (47) Substituting equation (46) and equation (47) into equation (40). u ・ [{φaβ ・ n ・ h-φaβ ・ h ・ cosβ_i0a) ・ Cos β_i0a} / (± φcβ ・ v ・ cosβ_i0a)-{Φaα ・ n ・ h-φaα ・ h ・ cosα_i0a) ・ Cos α_i0a} / (± φcα ・ v ・ cosα_i0a)] = R ・ cosν_B (48) Substituting equation (46) into equation (43). L_zi= n ・ h + u ・ [{φaα ・ n ・ h-φaα ・ h ・ f (cosα_i0a) ・ Cos α_i0a} / (± φcα ・ v ・ cosα_i0a)] ・ Cos α_i0a-h ・ f (cosα_i0a) ・ Cos α_i0a = n ・ h + (u / v) ・ {φaα ・ n ・ h-φaα ・ h ・ f (cosα_i0a) ・ Cos α_i0a} / ± φcα -h ・ f (cosα_i0a) ・ Cos α_i0a (49) Substituting equation (47) into equation (44). L_zi= n ・ h + u ・ ({φaβ ・ n ・ h-φaβ ・ h ・ cosβ_i0a) ・ Cos β_i0a} / (± φcβ ・ v ・ cosβ_i0a)] ・ Cos β_i0a-h ・ cos β_i0a) ・ Cos β_i0a = n ・ h + (u / v) ・ {± (φaβ ・ n ・ h-φaβ ・ h ・ f (cosβ_i0a) ・ Cos β_i0a} / ± φcβ -h ・ f (cosβ_i0a) ・ Cos β_i0a (50) From equation (49) and equation (50), (u / v) ・ {φaα ・ n ・ h-φaα ・ h ・ f (cosα_i0a) ・ Cos α_i0a} / ± φaα -h ・ f (cosα_i0a) ・ Cos α_i0a = (u / v) ・ {φaβ ・ n ・ h-φaβ ・ h ・ f (cosβ_i0a) ・ Cos β_i0a} / ± φaβ -h ・ f (cosβ_i0a) ・ Cos β_i0a (51) From equation (48) and equation (34), (u / v) ・ [{φaβ ・ n ・ h-φaβ ・ h ・ cosβ_i0a) ・ Cos β_i0a} / (± φcβ ・ cosβ_i0a)-{Φaα ・ n ・ h-φaα ・ h ・ cosα_i0a) ・ Cos α_i0a} / (± φcα ・ cosα_i0a)) = (G²(cos α_i0a) ・ R²+ {u ・ P_i+ h ・ g (cos α_i0a) -h ・ f (cosα_i0a)}² ・ (Sin²β_i0a・ G²(cos β_i0a) -sin²α_i0a・ G²(cos α_i0a)}] / [2 ・ n_in・ G (cos α_i0a) ・ G (cosβ_i0a) ・ (U ・ P_i+ h ・ g (cos α_i0a) -h ・ f (cosα_i0a)}] (52) Substituting equation (46) into equation (52). (u / v) ・ ({φaβ ・ n ・ h-φaβh ・ (cosβ_i0a) ・ Cos β_i0a} / (± φcβ ・ cosβ_i0a)-{Φaα ・ n ・ h-φaα ・ h ・ f (cosα_i0a) ・ Cos α_i0a} / (± φcα ・ cosα_i0a)) = (G²(cos α_i0a) ・ R²+ {u ・ {φaα ・ n ・ h-φaα ・ h ・ f (cosα_i0a) ・ Cos α_i0a} / (± φcα ・ v ・ cosα_i0a) + h ・ g (cos α_i0a) -h ・ f (cosα_i0a)}² ・ (Sin²β_i0a・ G²(cos β_i0a) -sin²α_i0a・ G²(cos α_i0a)}] / [2 ・ n_in・ G (cos α_i0a) ・ G (cosβ_i0a) ・ (U ・ {φaα ・ n ・ h-φaα ・ f (cosα_i0a) ・ Cos α_i0a} / (± φcα ・ v ・ cosα_i0a) + h ・ g (cos α_i0a) -h ・ f (cosα_i0a)}) (53) α_i0aAnd β_i0aApproximate value of δ_i0aIs required correctly
From φaα, φaβ, φcα and φcβ,
The number is fixed. Therefore, both equations (13) and (14) are c
osα_i0aAnd cosβ_i0aThe formula is Therefore, the formula (5
From 1) and equation (53), α_i0aAnd β_i0aSeeking
You can Α obtained in this way_i0aAnd β_i0aYes
It is a calculated value of the critical incident angle and includes an error. This place
The refractive index of the ionosphere and atmospheric gas layer near the radio path
Is determined, the radio refraction of the ionosphere and atmospheric gas layer
Sum of rates: X is also determined. Now of the calculated value of the critical incidence angle
The true value is α_i0atAnd β_i0atIf so, the above 1
Et al_i0a= p (α_i0at) ・ X²+ q (α_i0at) ・ X + r (α_i0at) (54) β_i0a= p (β_i0at) ・ X²+ q (β_i0at) ・ X + r (β_i0at) (55) Therefore, the calculated value of the critical angle of incidence α_i0aAnd β_i0aas well as
Sum of radio wave refractive indices in the ionosphere and atmospheric gas layer: X is confirmed
Therefore, α_i0aAnd β_i0aTrue of the critical angle of incidence corresponding to
The value α_i0atAnd β_i0atIs equation (54) or (55)?
Can be obtained from Α obtained in this way_i0atAnd β_i0atThe formula
Α of (39)_i0aAnd β_i0aTo P,_iAsk for.
Therefore, P_iIf is determined, then from equation (43), L_ziWanted
It Therefore, the three-dimensional position of the point P is obtained. * L_AMAnd l_BNIs 1. Virtual when the satellite is located
The exact path of the microwave propagation path radiated from point P1
In the same way as described in
Of the radio wave refractive index and the collision between the radio wave straight layer and the ionosphere
It is displayed as a function of the true value of the incident angle of the incoming radio wave.
In addition, Table 31 of simulation by a small model,
See 32 and 33. That is, l_AM= h ・ f (cosα_i0a) = p '(cosα_i0a) ・ X²+ q '(cos α_i0a) ・ X + r '(cos α_i0a) (56) l_BN= h ・ f (cosβ_i0a) = p '(cosβ_i0a) ・ X²+ q '(cosβ_i0a) ・ X + r '(cos β_i0a) (57) Similarly, l_AK= h ・ sinα_i0a・ G (cos α_i0a) = k '(cos α_i0a) ・ X²+ l '(cosα_i0a) ・ X + m '(cos α_i0a) (58) l_BL= h ・ sinβ_i0a・ G (cos β_i0a) = k '(cos β_i0a) ・ X²+ l '(cosβ_i0a) ・ X + m '(cos β_i0a) (59) X is the sum of the radio wave refractive indices in the ionosphere and atmospheric gas layer.
Since it has already been decided, equations (56), (57),
From (58) and (59), l_AM, L_BN, L_AkAnd l _BL
Is α_i0aAnd β_i0aIt is a function of the cosine of.

[Brief description of drawings]

FIG. 1 is a reference diagram for accurately following a propagation path of a microwave radiated from a point P ₁ which is supposed to be located when a satellite is located.

[Fig. 2] An area from the ground surface to 10 km above the ground is divided into some parallel plane layers, and the characteristics of microwaves propagating in this area are analyzed while changing the radio wave refractive index of the parallel plane layers variously. Represents a small model for a simulation.

[Fig.3] Sum of radio wave refractive indices of the ionosphere and atmospheric gas layer and the entry into the interface between the radio wave rectilinear layer and the ionosphere at a height of 10 km above the ground surface when simulating using a small model. The relationship between the true value of the critical incident angle of the microwave and the calculated value is shown.

FIG. 4 is a path length of microwaves passing through the layer 1 and an incident angle α _{0 of} microwaves entering the interface between the radio wave rectilinear layer and the ionosphere.
The relationship between X ₁ and X _2; between the product of the cosine, the product sum of errors of the cosine of the path length and alpha ₀ of the microwave passing through the layer 2; .DELTA.A 'a radio refractive index of the layer 1 and 2 Represent

FIG. 5 shows a relationship between a radio wave refractive index of one of adjacent parallel plane layers and an inherent error based on a combination of radio wave refractive indexes of the layers with the radio wave refractive index of the other layer as a parameter. It was done.

FIG. 6 shows a difference between a specific error based on a combination of radio wave refractive indices of adjacent parallel plane layers and a value of a linear equation having each radio wave refractive index of adjacent parallel plane layers as a variable. The radio wave refractive index of one of the adjacent parallel plane layers is expressed as a variable.

FIG. 7 shows that the minimum value of the quadratic curve in FIG. 6 is displayed as a quadratic equation having the radio wave refractive index of the other adjacent parallel plane layer as a variable.

FIG. 8: When the radio wave refractive indices of the ionosphere and atmospheric gas layer are known, the paths of radio waves emitted from satellites in the sky are determined. Therefore, two observation points are set up on the ground, radio waves from satellites in the sky are simultaneously received, and these two radio wave paths are geometrically analyzed to obtain the three-dimensional position of the satellite in the sky. It is a figure.

[Table 2]

[Table 3]

[Table 4]

[Table 5]

[Table 6]

[Table 7]

[Table 8]

[Table 9]

[Table 10]

[Table 11]

[Table 11-1]

[Table 12]

[Table 13]

[Table 14]

[Table 15]

[Table 16]

[Table 17]

[Table 18]

[Table 19]

[Table 20]

[Table 21]

[Table 22]

[Table 22-1]

[Table 22-2]

[Table 23-1]

[Table 23-2]

[Table 23-3]

[Table 24-1]

[Table 24-2]

[Table 25]

[Table 26]

[Table 27]

[Table 28]

[Table 29]

[Table 30]

[Table 31]

[Table 32]

[Table 33]

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

[Procedure amendment]

[Submission date] July 8, 1994

[Procedure Amendment 1]

[Document name to be corrected] Drawing

[Name of item to be corrected] Figure 3

[Correction method] Change

[Correction content]

[Figure 3]

[Procedure Amendment 2]

[Document name to be corrected] Drawing

[Name of item to be corrected] Figure 5

[Correction method] Change

[Correction content]

[Figure 5]

[Procedure 3]

[Document name to be corrected] Drawing

[Name of item to be corrected] Figure 6

[Correction method] Change

[Correction content]

[Figure 6]

[Procedure amendment 4]

[Document name to be corrected] Drawing

[Name of item to be corrected] Figure 7

[Correction method] Change

[Correction content]

[Figure 7]

Claims (5)

[Claims] 1. At a certain time: T, a microwave from a radio wave radiation source: P in the sky is received at an observation point: A on the ground, and a microwave propagation time from the radio wave radiation source: P is received. And, the approximate value of the vertical distance between the radio wave radiation source: P and the observation point: A passing through the horizontal plane is obtained. Then, assuming that the point: P ₁ defined by these two approximate values has a radio wave radiation source, the propagation of the microwave from the point: P ₁ is faithfully followed, and the microwave from the point: P ₁ is Propagation time, a vertical distance between the point P ₁ and the observation point: horizontal plane passing through A, and a method of correctly obtaining the cosine of the critical incident angle when the microwave from the point P ₁ enters the interface between the radio wave rectilinear layer and the ionosphere. 2. At time: T, the microwave radiated from the radio wave radiation source located at the point P ₂ is on the ground surface after entering a point E on the interface between the radio wave rectilinear layer and the ionosphere. When reaching the observation point located at point a, Telecommunications path: There are radio source to P ₃ points on the extended line beyond the point P ₂ of the AEP _2, the time from point _{P 3: (T-P 2} P ₃ / u), the microwave radiated at the time: T simultaneously reaches the observation point located at the point A through the same radio wave path as the microwave radiated from the point P _{2 at} the time T. Also, the following equation holds. In addition, ΔP
_{Let i} = P ₂ P ₃ / u and P _i >> ΔP _i . _{cosα i0a} = φa ・ (L _zi + u ・ ΔP _i・_{cosα i0a} ) / {(φa ・ u ± φ
c) · (P _i + ΔP _i )} where α _i0a : a point E on the interface between the radio wave rectilinear layer and the ionosphere
The critical angle of incidence of the microwave entering the. P _i : Propagation time of the microwave radiated from the point P ₂ . L _zi : vertical distance between the point P ₂ and a horizontal plane passing through the point A. φa: The slope of the K _ij -n _ij characteristic curve when the incident angle of the microwave entering the interface between the radio wave rectilinear layer and the ionosphere is changed in units of φ degrees. φc: K _ij · n _ij -n when the incident angle of the microwave entering the interface between the radio wave rectilinear layer and the ionosphere is changed in units of φ degrees.
_ij The slope of the characteristic curve. u: speed of light. v: Earth's rotation speed. K _ij : Radio wave refraction coefficient of each parallel plane layer corresponding to each radio wave path. K _ij = cos α _i0a / (n _ij ² -sin ² α _i0a ) ^1/2 n _ij : Radio wave refractive index of each parallel plane layer corresponding to each radio wave path. i: A symbol representing each radio wave route. j: A symbol indicating the number of parallel plane layers that are located in the direction from the interface between the radio wave straight layer and the ionosphere toward the ground surface. 3. A microwave straight-ahead layer obtained from a microwave propagation time from a radio wave radiation source (or a radio wave reflection source) and a vertical distance between the radio wave radiation source (or a radio wave reflection source) and a horizontal plane passing through an observation point. There is an error between the critical incident angle at the interface between the ionosphere and the ionosphere (hereinafter referred to as the calculated value of the critical incident angle), and the error, the calculated value of the critical incident angle, and the ionosphere and the atmosphere. The calculated value of the sum of the radio wave refractive index of the gas layer is
It is uniquely determined by the sum of the radio wave refractive indices of the ionosphere and atmospheric gas layer and the true value of the critical incident angle. Now, the calculated value of the critical incident angle is W, the true value of the critical incident angle is α _i0a , the difference between the true value of the critical incident angle and the calculated value is Y, and the sum of the radio wave refractive indices of the ionosphere and atmospheric gas layer is included. , X is the part that is not related to the number of parallel plane layers, and Z is the part that is not related to the number of parallel plane layers in the calculated sum of the radio wave refractive indices of the ionosphere and the atmospheric gas layer, and W + Y = α _i0a Y = f (α _i0a ) ・ X ² + g (α _i0a ) ・ X + h (α _i0a ) Z = k (α _i0a ) ・ X ² + l (α _i0a ) ・ X + m (α _i0a ) W = p (α _ioa ) _× X ² + q (α _i0a ) _× X + r (α _i0a ) holds. Further, in this case, X is not affected by the order of the radio wave refractive indices of the parallel plane layers of the ionosphere and the atmospheric gas layer. 4. At a certain time: T, by accurately following the path of the microwave radiated from the point P ₁ where the satellite is assumed to be located by the method of claims 1, 2 and 3, The true value of the radio wave propagation time: P _i and the vertical distance: L _zi between the point P ₁ and the observation point A is obtained. Also, the difference between the cosine of the critical incident angle when the microwave enters the interface between the radio wave rectilinear layer and the ionosphere, assumed to be radiated from the point P _1, and α _i0a is 10 ⁻¹³ degrees. Ask to be smaller.
Then, using the three data thus obtained, the difference between the radio path length: k _i passing through the area from the ground surface to 1000 km above the sky: k _i is smaller than 10 ^-07 , Accurately seek. Then, the product of the radio wave path length and the critical incident angle in the ionosphere and atmospheric gas layer from the ground surface to 1000 km above the radio wave path is n · h + u · P _i · _{cosα i0a} -L _zi = It is displayed as k _i . However, n: 1000 km above the ground surface
The number of parallel plane layers in the area up to h: the thickness of the parallel plane layer u: the speed of light Next, the area from the ground surface to 1000 km above the ground is divided into parallel plane layers with a thickness of 1 m and adjacent to each other. The length of the radio wave path that passes through the parallel plane layer includes a unique error due to the combination of the radio wave refractive indices of the adjacent layers as well as the external propagation path. If the product of the cosine of the incident angle is A _j '+ ΔΛ _j ', then A _j '+ ΔΛ _j ' = A _j '+ m _j · x _j + n _j + ζ · x _{j + 1} + κ _j · x _j + ξ + ε ・ (x _{j + 1} -ν _j ) ² + ρ _j・ (x _j -τ _j ) ² + χ _j A _j '= cos α _i0a / (1-sin ² α _i0a / x _j ' ² ) ¹ It is displayed as ^{/ 2} + cos α _i0a / (1-sin ² α _i0a / x _{j + 1} ' ² ) ^1/2 , and this is totaled for one radio wave path. That is, Σ _{j = 1} ^{n / 2} (A _j '+ ΔΛ _j ') = Σ _{j = 1} ^{n / 2} {A _j '+ m _j・ x _j + n _j + ζ ・ x _{j + 1} + κ _j・x _j + ξ + ε · (x _{j + 1} −ν _j ) ² + ρ _j · (x _j −τ _j ) ² + χ _j } where X _j , X _{j + 1} : of adjacent parallel plane layers True value of radio wave refractive index X _j ', X _{j + 1} ': initial value of radio wave refractive index of parallel plane layers adjacent to each other. give. Since the radio wave refractive index of the USA standard atmosphere is the radio wave refractive index of a parallel plane layer having a thickness of 1 km, it is assumed that the radio wave refractive index changes linearly in the same layer as the upper surface of a layer having a thickness of 1 m. The radio wave refractive index with the lower surface is obtained, and the arithmetic mean is taken. That is, from x _j = x _j '+ Δx _j (j = 1,2, ・ ・ ・ ・ ・ ・ ・ ・, 1000000), the formula is Σ _{j = 1} ^{n / 2} (A _j ' + ΔA _j ') = Σ _{j = 1} ⁿ a _j · Δ x _j This is performed for 1,000,000 radio wave paths. That is, while changing the time: T, Σ _{i = 1} ⁿ Σ _{j = 1} ^{n / 2} (A _ij '+ ΔΛ _ij ') = Σ _i, j _{= 1} ⁿ a _ij · Δx _j Do this for each radio path. Since n, h, u, P _i , α _i0a, and L _zi are fixed, k _i becomes a constant, and Σ _{i = 1} ⁿ (n · h + u · P _i · cos α _i0a −L _zi ) = Σ _{i ^{= 1 n k i Σ i =}} 1 n k i = Σ a _{(a ij '+ ΔΛ ij'} ), Σ i, j = 1 n a ij · Δx j = Σ i = 1 n k i becomes [Delta] x _j variables The following n-dimensional simultaneous equations are established.
Solve this and find x _j from the equation. 5. If the radio wave refractive index in the ionosphere and atmospheric gas layer is known, the path of the radio wave radiated from the satellite in the sky at a certain time: T is determined. Therefore, two observation points are set up on the ground to simultaneously receive radio waves from satellites. However, one of these two observation points is an ideal observation point, and only one observation point is actually set. At this time, the critical incident angle of the radio wave entering the interface between the radio wave rectilinear layer and the ionosphere at a height of 1000 km above the ground surface is α
_{Given i0a} and β _i0a , the following relationship holds between α _i0a and β _i0a . (u / v) ・ {φaα ・ n ・ h-φaα ・ h ・ f ( _{cosα i0a} ) ・_{cosα i0a} } / ± φaα -h ・ f ( _{cosα i0a} ) ・_{cosα i0a} = (u / v) ・ {φaβ ・n ・ h-φaβ ・ h ・ f ( _{cosβ i0a} ) ・_{cosβ i0a} } / ± φaβ -h ・ f ( _{cosβ i0a} ) ・_{cosβ i0a} (51) Therefore, by solving this equation (51), α _i0a and β _i0a is fixed. Furthermore, the critical incident angles α _i0a and β _i0a and the radio wave propagation time: P are _obtained by geometrical analysis of the two radio wave paths from the satellite which are simultaneously received at the two observation points on the ground.
_The following relation holds with _i . u ³・ (1-n _in ) ・ {sin ² β _i0a・ g ² ( _{cosβ i0a} ) -sin ² α _i0a・ g ² ( _{cosα i0a} )} ・ Pi ³ + u ²・ h ・ g ( _{cosα i0a} ) ・{sin ² β _i0a・ g ² ( _{cosβ i0a} ) -sin ² α _i0a・ g ² ( _{cosα i0a} )} ・ Pi ² -u ²・ h ・ f ( _{cosα i0a} ) ・ {sin ² β _i0a・ g ² ( _{cosβ i0a} ) -sin ² α _i0a・ g ² ( _{cosα i0a} )} ・ Pi ² + u ²・ h ・ n _in・ f ( _{cosα i0a} ) ・ {sin ² β _i0a・ g ² ( _{cosβ i0a} ) -sin ² α _i0a・ G ² ( _{cosα i0a} )} ・ Pi ² +2 ・ u ²・ h ・ (1-n _in ) ・ {g ( _{cosα i0a} ) -f ( _{cosα i0a} )} ・ {sin ² β _i0a・ g ² ( _{cosβ i0a} ) -sin ² α _i0a・ g ² ( _{cosα i0a} )} ・ Pi ² +2 ・ u ²・ h ・ n _in・ g ( _{cosα i0a} ) ・ g ( _{cosβ i0a} ) ・ {f ( _{cosβ i0a} ) -f ( _{cosα i0a} )} ・ Pi ² + u ・ (1-n _in ) ・ r ²・ g ² ( _{cosα i0a} ) ・ P _i +2 ・ u ・ h ²・ {g ( _{cosα i0a} ) -f ( _{cosα i0a} )}・ {Sin ² β _i0a・ g ² ( _{cosβ i0a} ) -sin ² α _i0a・ g ² ( _{cosα i0a} )} ・ {g ( _{cosα i0a} ) -f ( _{cosα i0a} ) + n _in・ f ( _{cosα i0a} )} ・P _i + u ・ h ²・ (1-n _in ) ・ {g ² ( _{cosα i0a} ) -2 ・ g ( _{cosα i0a} ) ・ f ( _{cosα i0a} ) + f ² ( _{cosα i0a} )} ・ {sin ² β _i0a・ G ² (cos β _i0a ) -sin ² α _{i0 a}・ g ² ( _{cosα i0a} )} ・ P _i +4 ・ u ・ h ²・ n _in・ g ( _{cosα i0a} ) ・ g ( _{cosβ i0a} ) ・ {g ( _{cosα i0a} ) -f ( _{cosα i0a} )} ・ { f ( _{cosβ i0a} ) -f ( _{cosα i0a} )} ・ P _i + h ・ r ²・ g ³ ( _{cosα i0a} ) -h ・ r ²・ g ² ( _{cosα i0a} ) ・ f ( _{cosα i0a} ) + h ・ n _in・ R ²・ g ² ( _{cosα i0a} ) ・ f ( _{cosα i0a} ) + h ³・ {g ² ( _{cosα i0a} ) -2 ・ g ( _{cosα i0a} ) ・ f ( _{cosα i0a} ) + f ² ( _{cosα i0a} )} ・{sin ² β _i0a・ g ² ( _{cosβ i0a} ) -sin ² α _i0a・ g ² ( _{cosα i0a} )} ・ {g ( _{cosα i0a} ) -f ( _{cosα i0a} ) + n _in・ f ( _{cosα i0a} )} +2・ H ³・ n _in・ g ( _{cosα i0a} ) ・ g ( _{cosβ i0a} ) ・ {g ² ( _{cosα i0a} ) -2 ・ g ( _{cosα i0a} ) ・ f ( _{cosα i0a} ) + f ² ( _{cosα i0a} )} ・ { f ( _{cosβ i0a} ) -f ( _{cosα i0a} )} = 0 (39) _{cosα i0a} and _{cosβ i0a} are already determined,
The radio wave propagation time: Pi is also determined from the equation (39). Therefore, since the vertical distance between the satellite and the observation point is also determined, the relative position between the satellite and the observation point is determined, and if the absolute position of either the satellite or the observation point is determined, the absolute position of the other is determined. Is also determined. Where u: speed of light v: rotation speed of the earth n: number of plane layers parallel to the horizontal plane passing through the observation points in the ionosphere and atmospheric gas layer h: thickness of parallel plane layers in the ionosphere and atmospheric gas layer Φaα, φaβ: slope of the characteristic curve k _ij -n _ij k _ij : parallel plane layer corresponding to each radio wave path: i: radio wave refraction coefficient of j K _ij = cos α _i0a / (n _ij ² -sin ² α _i0a ) ^1/2 _nij : Radio wave index of each parallel plane layer: j corresponding to each radio path: i r: Distance between two observation points n _in : Observation actually set among the two observation points Telecommunications refraction coefficient of a point located at point _{f (cosα i0a), g (} cosα i0a): propagation path of radio wave rectilinear layer and Telecommunications ionospheric and atmospheric gas layer to rush at a critical angle of incidence alpha _I0a to interface with the ionosphere the length and the horizontal component _{f (cosβ i0a), g (} cosβ i0a): Telecommunications straight layer and the interface to the beta _I0a critical input of the ionosphere Propagation path lengths of radio waves entering at an angle in the ionosphere and atmospheric gas layer and their horizontal components The y-coordinates of the xyz coordinates, which are the criteria for determining the positions of the satellite and the observation point, should be set so as to always match the rotation direction of the earth. Has been. Also, φaα and φaβ are _{cosα i0a} and co
It is expressed _by the quadratic formula of sβ _i0a , and its coefficient is fixed.