CN113708874A - Doppler frequency shift estimation method for return link of low-orbit satellite TDMA communication-in-motion system - Google Patents

Doppler frequency shift estimation method for return link of low-orbit satellite TDMA communication-in-motion system Download PDF

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CN113708874A
CN113708874A CN202110973081.3A CN202110973081A CN113708874A CN 113708874 A CN113708874 A CN 113708874A CN 202110973081 A CN202110973081 A CN 202110973081A CN 113708874 A CN113708874 A CN 113708874A
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贺俊文
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Sichuan Andi Technology Industrial Co Ltd
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Abstract

A method for estimating the Doppler frequency shift of a return link of a transparent forwarding low-orbit satellite TDMA communication-in-motion system comprises the following steps: pre-calculating a function of satellite/master station transmission delay and ephemeris time, a function of satellite linear velocity and ephemeris time and a function of satellite-to-master station radial velocity and ephemeris time; estimating ephemeris time for the return burst to reach the satellite; estimating ephemeris time for sending a return burst; respectively estimating the radial speed of the satellite to the main station and the radial speed of the satellite to the end station; estimating a return uplink Doppler frequency shift according to the radial velocity of the satellite to the end station; estimating the Doppler frequency shift of a return downlink according to the radial velocity of the satellite to the main station; and adding the Doppler frequency shifts of the return uplink and the return downlink to obtain the Doppler frequency shift of the whole return link. The method adopts an extrapolation estimation method based on linear approximation, and is simple and convenient to calculate; under the condition that the satellite ephemeris information is accurate, good estimation performance can be obtained.

Description

Doppler frequency shift estimation method for return link of low-orbit satellite TDMA communication-in-motion system
Technical Field
The invention belongs to the technical field of digital communication, relates to a frequency synchronization technology of a TDMA satellite communication system, and particularly relates to a return link Doppler frequency shift estimation method of a transparent forwarding low-orbit satellite TDMA communication-in-motion system.
Background
In wireless communication, when the source isWhen the signal sink moves relatively in the radial direction, the frequency of the signal received by the signal sink is not consistent with the frequency of the signal transmitted by the signal source, namely the frequency of the signal received by the signal sink is shifted, the phenomenon is called Doppler effect, and the deviation of the frequency of the signals at the transmitting end and the receiving end is called Doppler shift. As shown in fig. 1, the source is stationary, the sink moves in the direction of the arrow at velocity v, and communicates with the source while moving. The frequency of the source transmission signal being fc. When the sink moves from position A to position A' within Δ t, the Doppler shift produced by its received signal is
Figure BDA0003226630700000011
Where θ is an angle between the moving direction of the signal sink and the connecting line of the signal source/signal sink at the position a ', c is the propagation velocity of the electromagnetic wave, and v · cos (θ) represents the radial velocity of the signal sink to the signal source at the position a'.
As shown in fig. 2, in a transparent transponded low earth orbit satellite TDMA communication system, the return link is a transmission link from the end station to the satellite and then to the master station, and consists of two parts, a return uplink and a return downlink. Wherein, the return uplink refers to a transmission link from the end station to the satellite, and the return downlink refers to a transmission link from the satellite to the main station. For a communication-in-motion scene, the position of the master station is fixed, and the satellite and the end station are in motion. This is equivalent to that in the return uplink, both the source and the sink move; in the return downlink, the source moves and the sink is stationary. Therefore, there is a relative movement of the source and the sink in the radial direction in both the return uplink and the return downlink, i.e. there is a doppler shift in both the return uplink and the return downlink.
In a low earth orbit satellite communication system, the return link is not a fixed, constant transmission link, but it varies with time, since the position of the satellite varies with time. The first prerequisite for accurate estimation of the doppler shift of the return link is to correctly find which return link is to be estimated. For communication-in-motion scene, the bit of the master stationThe position of the satellite and the end station is fixed and the position of the satellite and the end station changes with time, so the return link is uniquely determined by the positions of the satellite and the end station. The positions of the satellite and the end station are functions of time, so that the position of the end station and the position of the satellite at a corresponding moment can be determined as long as the time when the return burst is sent by the end station and the time when the return burst arrives at the satellite are determined, and further a return link for transmitting the return burst is uniquely determined. For example, as shown in FIG. 2, a backward burst BF [ n ]]At t ″)nTime of day is sent from the end station, at t'nThe time of arrival at the satellite, which is then forwarded by the satellite to the Master station, at tnThe moment arrives at the master station. At t ″)nAt the moment, the position of the end station is R (t ″)n) (ii) a At t'nAt time, the position of the satellite is P (t'n). Thus, BF [ n ] is transmitted]The return link of (a) is R (t ″)n)→P(t′n) → H. In summary, determining the time at which the end station transmits the return burst and the time at which the return burst arrives at the satellite is key to accurately estimate the return link doppler shift.
Disclosure of Invention
Aiming at the current situation, the invention provides a method for estimating the Doppler frequency shift of a return link of a transparent forwarding low-orbit satellite TDMA communication-in-motion system, which adopts an extrapolation estimation method based on linear approximation and has simple and convenient calculation; under the condition that the satellite ephemeris information is accurate, good estimation performance can be obtained.
In order to achieve the purpose of the invention, the invention is realized by the following technical scheme:
a method for estimating the Doppler frequency shift of a return link of a transparent forwarding low-orbit satellite TDMA communication-in-motion system comprises the following specific steps:
s1, establishing a rectangular coordinate system
Figure BDA0003226630700000021
Ephemeris time t is used as abscissa and a backward burst BF [ n ] is used]Expected ephemeris time t to reach the primary station target slotnIs the origin of the abscissa; by transmission time delay tau 'between satellite/master station'SAT/HUB(t) is ordinate, and 0 is the origin of the ordinate.
S2, rectangular coordinate system
Figure BDA0003226630700000022
In (1), two linear equations are established: one is an inverse-identity linear equation l1:τ′SAT/HUB(t) t, the other being a function τ of satellite/master station transmission delay and ephemeris timeSAT/HUB(t)＝g1Coordinate-translated version of (t) 'τ'SAT/HUB(t)＝τSAT/HUB(t+tn)＝g1(t+tn) In the interval [ -T,0 [)]Equation of local approximate straight line segment l2:
Figure BDA0003226630700000035
t∈[-T,0]. The establishment method of the latter is as follows: first, at curve τ'SAT/HUB(t)＝g1(t+tn),t∈[-T,0]Two adjacent points (0, g) are selected1(tn) And (-T, g)1(tμ) Wherein t) isμ＝tnT, T is a time increment, and
Figure BDA0003226630700000031
representing the maximum value of the return downlink free-space transmission delay. Then, establishing a straight-line equation according to the coordinates of the two points to obtain
Figure BDA0003226630700000032
S3 solving straight line l1And straight line segment l2Coordinates of the intersection point of
Figure BDA0003226630700000033
S4, estimating the ephemeris time of the arrival of the return burst BF [ n ] at the satellite to obtain
t′n＝tn+tintersect.
S5, establishing a rectangular coordinate system
Figure BDA0003226630700000036
Ephemeris time t is used as abscissa and a backward burst BF [ n ] is used]Ephemeris time t 'to satellite'nIs the origin of the abscissa; by transmission delay tau 'between satellite/terminal stations'SAT/RCST(t|t′n) Is ordinate and has 0 as origin of ordinate.
S6, rectangular coordinate system
Figure BDA0003226630700000037
In (1), two linear equations are established: one is an inverse-identity linear equation l3:τ′SAT/RCST(t|t′n) The other is a function τ of satellite/end station transmission delay and ephemeris timeSAT/RCST(t|t′n)＝g2Coordinate-translated version of (t) 'τ'SAT/RCST(t|t′n)＝τSAT/RCST(t+t′n|t′n)＝g2(t+t′n) In the interval [ -T ]α,0]Equation of local approximate straight line segment l4:
Figure BDA0003226630700000034
t∈[-Tα,0]. The establishment method of the latter is as follows: first, at curve τ'SAT/RCST(t|t′n)＝g2(t+t′n),t∈[-Tα,0]Two points (-T) are selectedα,g2(tα) And (-T)β,g2(tβ) Wherein t) isα＝t′n-Tα，tβ＝t′n-Tβ，TαAnd TβIs two time increments, and
Figure BDA0003226630700000041
representing the maximum value of the return uplink free space transmission delay. Then, establishing a straight-line equation according to the coordinates of the two points to obtain
Figure BDA0003226630700000042
S7 solving straight line l3And straight line segment l4Coordinates of the intersection point of
Figure BDA0003226630700000043
S8, estimating the ephemeris time of the return burst BF [ n ] sent by the end station to obtain
t″n＝t′n+t′intersect.
S9, establishing a rectangular coordinate system
Figure BDA00032266307000000410
: ephemeris time t is used as abscissa and a backward burst BF [ n ] is used]Ephemeris time t 'to satellite'nIs the origin of the abscissa; at satellite line speed v (t'n) Is connected with the satellite/terminal station
Figure BDA0003226630700000044
Angle of (d)'SAT/RCST(t|t′n) Is ordinate and has 0 as origin of ordinate.
S10, rectangular coordinate system
Figure BDA00032266307000000411
In (c), establishing a satellite linear velocity v (t'n) Is connected with the satellite/terminal station
Figure BDA0003226630700000045
Angle of (theta)SAT/RCST(t|t′n) Function of ephemeris time thetaSAT/RCST(t|t′n)＝s2(t) coordinate-translated version θ'SAT/RCST(t|t′n)＝θSAT/RCST(t+t′n|t′n)＝s2(t+t′n) In the interval [ -T ]α,0]Equation of local approximate straight line segment l5:
Figure BDA0003226630700000049
t∈[-Tα,0]. The specific method comprises the following steps:first, at curve θ'SAT/RCST(t|t′n)＝s2(t+t′n),t∈[-Tα,0]Two points (-T) are selectedα,s2(tα) And (-T)β,s2(tβ) Wherein t) isα＝t′n-Tα，tβ＝t′n-Tβ，TαAnd TβIs two time increments, and
Figure BDA0003226630700000046
representing the maximum value of the return uplink free space transmission delay. Then, establishing a straight-line equation according to the coordinates of the two points to obtain
Figure BDA0003226630700000047
S11, estimating satellite linear velocity v (t'n) Is connected with the satellite/terminal station
Figure BDA0003226630700000048
Is at an angle of
Figure BDA0003226630700000051
S12, according to two groups of pre-calculated parameters: a function v (t) q (t) of the linear velocity and the ephemeris time of the satellite in an earth-centered earth-fixed (ECEF) coordinate system and a function v (t) of the radial velocity and the ephemeris time of the satellite to the primary stationSAT/HUB(t)＝h1(t), and a backward burst BF [ n ]]Ephemeris time t 'to satellite'nAnd satellite line speed v (t'n) Is connected with the satellite/terminal station
Figure BDA0003226630700000052
Angle of (theta)SAT/RCST(t″n|t′n) Separately estimating the radial velocity v of the satellite to the master stationSAT/HUB(t′n) And radial velocity v of the satellite to the end stationSAT/RCST(t′n,t″n)：
Figure BDA0003226630700000057
S13, estimating the Doppler shift of the return uplink and the Doppler shift of the return downlink to obtain
Figure BDA0003226630700000053
Wherein the content of the first and second substances,
Figure BDA0003226630700000054
is the frequency of the return uplink carrier,
Figure BDA0003226630700000055
is the frequency of the return downlink carrier and c is the propagation velocity of the electromagnetic wave.
S14, the Doppler frequency shifts of the return uplink and the return downlink are added to obtain the Doppler frequency shift of the return link, namely the Doppler frequency shift of the return link
Figure BDA0003226630700000056
The invention has the beneficial effects that:
the method adopts an extrapolation estimation method based on linear approximation, and is simple and convenient to calculate; under the condition that the satellite ephemeris information is accurate, good estimation performance can be obtained.
Drawings
Fig. 1 is a schematic diagram of analyzing the doppler effect mechanism and calculating the doppler shift.
Fig. 2 is a schematic diagram of a return link of a transparent transponded low earth orbit satellite TDMA communication system.
FIG. 3 shows an embodiment of the present application for estimating the backward burst BF n]Ephemeris time t 'to satellite'nSchematic diagram of the method of (1).
FIG. 4 is a geometric diagram of steps S1-S3 in the embodiment of the present application.
FIG. 5 is a diagram of an embodiment of the present application for estimating the transmission of a backward burst BF [ n ]]Ephemeris time t ″nSchematic diagram of the method of (1).
FIG. 6 is a geometric diagram of steps S5-S7 in the embodiment of the present application.
FIG. 7 is a geometric diagram of steps S9-S11 in the embodiment of the present application.
Detailed Description
In order to make the purpose, technical scheme and specific implementation method of the application clearer, the application is further described in detail by combining with an example of the attached drawings.
The embodiment of the application provides a method for estimating the Doppler frequency shift of a return link of a transparent forwarding low-orbit satellite TDMA communication-in-motion system, which has the following design thought:
firstly, a function v (t) of a linear velocity and an ephemeris time of the satellite in an earth-centered earth-fixed (ECEF) coordinate system, and a function tau of a satellite/master station transmission delay and the ephemeris time are calculated in advance according to ephemeris information of the satellite and GNSS position information of the master stationSAT/HUB(t)＝g1(t) and a function v of the radial velocity of the satellite with respect to the primary station and the ephemeris timeSAT/HUB(t)＝h1(t)。
Then, BF [ n ] is determined according to the backward burst]Expected ephemeris time t to reach the primary station target slotn(known quantity) and the functional relation τSAT/HUB(t)＝g1(t) estimating the backward burst BF [ n ]]Ephemeris time t 'to satellite'n。
Then, the terminal station in the time period t ∈ [ t'n-Tα,t′n]During the movement, the uplink R (t) → P (t'n) Is a function tau of the transmission delay and the ephemeris timeSAT/RCST(t|t′n)＝g2(t) linear approximation function
Figure BDA0003226630700000061
And satellite line speed v (t'n) Is connected with the satellite/terminal station
Figure BDA0003226630700000062
Angle of (theta)SAT/RCST(t|t′n) Function of ephemeris time thetaSAT/RCST(t|t′n)＝s2(t) linear approximation function
Figure BDA0003226630700000073
Wherein T isα> 0 is a time increment like f (t'n) Is with respect to t'nCondition function of (2) is represented by a parameter t'nUnder certain conditions, a function is established with respect to the variable t.
Then, BF [ n ] is determined according to the backward burst]Ephemeris time t 'to satellite'nAnd functional relation
Figure BDA0003226630700000071
t∈[t′n-Tα,t′n]Estimating a transmission backward burst BF [ n ]]Ephemeris time t ″n。
Then, BF [ n ] is determined according to the backward burst]Ephemeris time t 'to satellite'nAnd functional relation vSAT/HUB(t)＝h1(t) estimating the radial velocity v of the satellite to the Master stationSAT/HUB(t′n) (ii) a Sending a backward burst BF [ n ] from an end station]Ephemeris time t ″nBackward burst BF [ n ]]Ephemeris time t 'to satellite'nAnd the functional relationships v (t) ═ q (t) and
Figure BDA0003226630700000072
t∈[t′n-Tα,t′n]estimating radial velocity v of a satellite terminalSAT/RCST(t′n,t″n)。
Then, estimating the Doppler frequency shift of the return uplink according to the radial velocity of the satellite to the end station; the doppler shift back to the downlink is estimated from the radial velocity of the satellite to the primary station.
And finally, adding the Doppler frequency shifts of the return uplink and the return downlink to obtain the Doppler frequency shift of the whole return link.
To use the method described in this example, three preconditions were prepared:
1. and establishing a mapping relation between the NCR time and the ephemeris time at the primary station side.
2. The end station completes the forward link time synchronization, i.e., NCR synchronization.
3. The end station can acquire GNSS position information of the end station in real time.
Under the precondition, in order to simplify the calculation complexity of the doppler shift estimation of the return link, three sets of parameters are prepared in advance: function v (t) q (t) of linear velocity and ephemeris time of satellite in ECEF coordinate system, function tau of satellite/main station transmission delay and ephemeris timeSAT/HUB(t)＝g1(t) and a function v of the radial velocity of the satellite with respect to the primary station and the ephemeris timeSAT/HUB(t)＝h1(t)。
The method for calculating the function of the satellite/main station transmission time delay and the ephemeris time is as follows:
1) a function of the position of the satellite in an earth-centered-earth-fixed (ECEF) coordinate system and ephemeris time within a satellite view window is calculated from the ephemeris information of the satellite.
2) And converting the GNSS position of the master station to obtain the position of the master station in the ECEF coordinate system.
3) Under an ECEF coordinate system, according to the position information of the satellite and the master station, calculating a function d of the distance between the satellite and the master station and the ephemeris timeSAT/HUB(t)＝f1(t)。
4) By dSAT/HUB(t)＝f1(t) dividing by the propagation velocity c of the electromagnetic wave to obtain a function tau of the satellite/master station transmission delay and ephemeris timeSAT/HUB(t)＝dSAT/HUB(t)/c。
Calculating a function v of the radial velocity of the satellite to the primary station and the ephemeris timeSAT/HUB(t)＝h1The method of (t) is as follows:
1) and (c) calculating a function v (t) q (t) of the linear velocity and the ephemeris time of the satellite in the ECEF coordinate system in a satellite view window according to the ephemeris information of the satellite.
2) And converting the GNSS position of the master station to obtain the position of the master station in the ECEF coordinate system.
3) In the ECEF coordinate system according toCalculating the included angle theta between the linear velocity direction of the satellite and the satellite/main station connecting line in the satellite view window and the ephemeris information of the satellite and the position information of the main stationSAT/HUB(t) function of ephemeris time θSAT/HUB(t)＝s1(t)。
4) According to the functions v (t) q (t) and θSAT/HUB(t)＝s1(t) calculating the radial velocity of the satellite relative to the primary station as a function of ephemeris time, i.e. vSAT/HUB(t)＝v(t)·cos(θSAT/HUB(t))。
Under the above conditions, the doppler shift estimation of the return link is performed:
s1, establishing a rectangular coordinate system
Figure BDA0003226630700000081
Ephemeris time t is used as abscissa and a backward burst BF [ n ] is used]Expected ephemeris time t to reach the primary station target slotnIs the origin of the abscissa; by transmission time delay tau 'between satellite/master station'SAT/HUB(t) is ordinate, and 0 is the origin of the ordinate.
S2, rectangular coordinate system
Figure BDA0003226630700000094
In (1), two linear equations are established: one is an inverse-identity linear equation l1:τ′SAT/HUB(t) t, the other being a function τ of satellite/master station transmission delay and ephemeris timeSAT/HUB(t)＝g1Coordinate-translated version of (t) 'τ'SAT/HUB(t)＝τSAT/HUB(t+tn)＝g1(t+tn) In the interval [ -T,0 [)]Equation of local approximate straight line segment l2:
Figure BDA0003226630700000095
t∈[-T,0]. The establishment method of the latter is as follows: first, at curve τ'SAT/HUB(t)＝g1(t+tn),t∈[-T,0]Two adjacent points (0, g) are selected1(tn) And (-T, g)1(tμ) Wherein t) isμ＝tnT, T is a time increment, and
Figure BDA0003226630700000091
representing the maximum value of the return downlink free-space transmission delay. Then, establishing a straight-line equation according to the coordinates of the two points to obtain
Figure BDA0003226630700000092
S3 solving straight line l1And straight line segment l2Coordinates of the intersection point of
Figure BDA0003226630700000093
The geometrical diagrams of S1 to S3 are shown in fig. 4, and represent a scenario in which the distance between the satellite and the master station gradually decreases, and therefore the transmission delay to the return downlink also gradually decreases.
S4, estimating the ephemeris time of the arrival of the return burst BF [ n ] at the satellite to obtain
t′n＝tn+tintersect.
In particular, a backward burst BF n is estimated]Ephemeris time t 'to satellite'nThe method comprises the following steps:
as shown in fig. 2, at t ″nTime of day, backward burst BF [ n ]]From the end station and at t'nThe time of day arrives at the satellite. At this time, the position of the satellite is P (t'n). Subsequently, BF [ n ]]Is forwarded to the master station by the satellite and at tnThe moment arrives at the master station. And at tn-t′nFrom position P (t'n) Has moved to a new position P (t)n). Satellite in orbit P (t'n)→P(tn) Time of up movement and BF [ n ]]In the return downlink P (t'n) The propagation delays on the → H are exactly equal, i.e. the straight line τSAT/HUB(t)＝-t+tnAnd curve τSAT/HUB(t)＝g1(t) at tnMust have crossed before, and the crossing point is t'n(As shown in FIG. 3, this represents a scenario in which the satellite is in communication with a Master stationThe distance is gradually reduced, so that the transmission delay of the return downlink is also gradually reduced; in FIG. 3, g1(t′n)＝tn-t′n). Therefore, solving a system of non-linear equations
Figure BDA0003226630700000101
A backward burst BF n can be obtained]Ephemeris time t 'to satellite'n。
In general, in a low-earth orbit satellite communication system, the free space transmission delay of a return downlink is small, the moving distance of a satellite in the time is short, and the motion track of the satellite can be approximate to a straight line segment.
Thus, curve τSAT/HUB(t)＝g1(t) at tnThe nearby area may also be approximated by straight line segments. Let the equation for this straight line segment be
Figure BDA0003226630700000106
t∈[tn-T,tn]Where T is a time increment. Furthermore, the above problem can be simplified to the straight line τSAT/HUB(t)＝-t+tnAnd straight line segment
Figure BDA0003226630700000102
t∈[tn-T,tn]The intersection problem of (a). In summary, solving a system of linear equations is described
Figure BDA0003226630700000103
A backward burst BF n can be obtained]Ephemeris time t 'to satellite'n。
Estimating terminal station in time period t epsilon [ t'n-Tα,t′n]During the movement, the uplink R (t) → P (t'n) Is a function tau of the transmission delay and the ephemeris timeSAT/RCST(t|t′n)＝g2(t) linear approximation function
Figure BDA0003226630700000104
The method comprises the following steps:
1) calculating the t 'of the satellite according to the ephemeris information of the satellite'nPosition of time P (t'n)。
2) In a time period of t'n-Tα,t′n]In the method, two times t are respectively selectedα＝t′n-TαAnd tβ＝t′n-Tβ(
Figure BDA0003226630700000105
Maximum value representing return uplink free-space transmission delay), the GNSS position R of the end station at these two times is acquiredGNSS(tα) And RGNSS(tβ) And converting them into their corresponding ECEF coordinates R (t)α) And R (t)β)。
3) In the ECEF coordinate system, satellite positions P (t 'are respectively calculated'n) To end station position R (t)α) And R (t)β) The transmission distance therebetween.
4) The propagation velocity of the electromagnetic wave is divided by the transmission distance to obtain a satellite position P (t'n) To end station position R (t)α) And R (t)β) Inter-transmission delay g2(tα) And g2(tβ)。
5) Calculating an interval [ t'n-Tα,t′n]Upper passing point (t)α,g2(tα) Are a and (t)β,g2(tβ) Equation for the straight line segment of (c), which is the function τSAT/RCST(t|t′n)＝g2(t) is in the interval [ t'n-Tα,t′n]Linear approximation function of (c).
S5, establishing a rectangular coordinate system
Figure BDA0003226630700000116
Ephemeris time t is used as abscissa and a backward burst BF [ n ] is used]Ephemeris time t 'to satellite'nIs the origin of the abscissa; by transmission between satellites/stationsTime delay of τ'SAT/RCST(t|t′n) Is ordinate and has 0 as origin of ordinate.
S6, rectangular coordinate system
Figure BDA0003226630700000115
In (1), two linear equations are established: one is an inverse-identity linear equation l3:τ′SAT/RCST(t|t′n) The other is a function τ of satellite/end station transmission delay and ephemeris timeSAT/RCST(t|t′n) Coordinate-translated version τ 'of g2 (t)'SAT/RCST(t|t′n)＝τSAT/RCST(t+t′n|t′n)＝g2(t+t′n) In the interval [ -T ]α,0]Equation of local approximate straight line segment l4:
Figure BDA0003226630700000111
t∈[-Tα,0]. The establishment method of the latter is as follows: first, at curve τ'SAT/RCST(t|t′n)＝g2(t+t′n),t∈[-Tα,0]Two points (-T) are selectedα,g2(tα) And (-T)β,g2(tβ) Wherein t) isα＝t′n-Tα，tβ＝t′n-Tβ，TαAnd TβIs the maximum value of the input delay. Then, establishing a straight-line equation according to the coordinates of the two points to obtain
Figure BDA0003226630700000112
S7 solving straight line l3And straight line segment l4Coordinates of the intersection point of
Figure BDA0003226630700000113
The geometrical diagrams of S5 to S7 are shown in fig. 6, and represent a scenario in which the distance between the satellite and the satellite moving end station gradually decreases, and therefore the transmission delay to return to the uplink gradually decreases.
S8, estimating the ephemeris time of the sent back burst BF [ n ] to obtain
t″n＝t′n+t′intersect.
In particular, a transmit backward burst BF [ n ] is estimated]Ephemeris time t ″nThe method comprises the following steps: as shown in fig. 2, at t ″nAt that moment, the end station sends a backward burst BF [ n ]]At this time, the satellite is located at P (t ″)n) The position of (a). Then BF [ n ]]In the return uplink, the satellite continues to move on the orbit in the direction pointed by the arrow. At t'nAt time, the satellite moves to a new position P (t'n) And then, at this time, BF [ n ]]Also just to the satellite, i.e. with a time delay t'n-t″nBack BF [ n ]]Encounter a satellite. In the encounter problem described above, the satellite is in orbit P (t ″)n)→P(t′n) Time of up movement and BF [ n ]]In the return uplink R (t ″)n)→P(t′n) Exactly equal in transmission delay, i.e. straight line τSAT/RCST(t|t′n)＝-t+t′nAnd curve τSAT/RCST(t|t′n)＝g2(t) at t'nMust intersect before, and the intersection point is t ″n(as shown in FIG. 5, this represents a scenario where the satellite is gradually less distant from the moving end station, and therefore the transmission delay back to the uplink is also gradually reduced2(t″n)＝t′n-t″n). Therefore, solving a system of non-linear equations
Figure BDA0003226630700000121
A send backward burst BF n may be obtained]Ephemeris time t ″n。
Usually, at t'nIn a small time period, the moving distance of the end station is short, and the motion track can be approximate to a straight line segment. Thus, curve τSAT/RCST(t|t′n)＝g2(t)At t'nThe nearby area may also be approximated by straight line segments. Let the equation for this straight line segment be
Figure BDA0003226630700000122
t∈[t′n-Tα,t′n]Wherein, TαIs an increment of time. Furthermore, the above problem can be simplified to the straight line τSAT/RCST(t|t′n)＝-t+t′nAnd straight line segment
Figure BDA0003226630700000123
t∈[t′n-Tα,t′n]The intersection problem of (a). In summary, solving a system of linear equations is described
Figure BDA0003226630700000131
A send backward burst BF n may be obtained]Ephemeris time t ″n。
Estimating terminal station in time period t epsilon [ t'n-Tα,t′n]In the process of moving, the linear velocity v (t ') of the satellite'n) Direction and satellite-
Terminal station connecting line
Figure BDA0003226630700000132
Angle of (theta)SAT/RCST(t|t′n) Function of ephemeris time thetaSAT/RCST(t|t′n)＝s2(t) linear approximation function
Figure BDA0003226630700000133
The method comprises the following steps:
1) in a time period of t'n-Tα,t′n]In the method, two times t are respectively selectedα＝t′n-TαAnd tβ＝t′n-Tβ
Figure BDA0003226630700000134
The acquisition end station at both timesOf GNSS position RGNSS(tα) And RGNSS(tβ) And converting them into their corresponding ECEF coordinates R (t)α) And R (t)β)。
2) In an ECEF coordinate system, the linear velocity v (t ') of the satellite is respectively calculated according to the ephemeris information of the satellite and the position information of the terminal station'n) Is connected with the satellite/terminal station
Figure BDA0003226630700000135
And
Figure BDA0003226630700000136
angle s of2(tα) And s2(tβ)。
3) Calculating an interval [ t'n-Tα,t′n]Upper passing point (t)α,s2(tα) Are a and (t)β,s2(tβ) Equation of the straight line segment), which is the function θSAT/RCST(t|t′n)＝s2(t) is in the interval [ t'n-Tα,t′n]Linear approximation function of (c).
S9, establishing a rectangular coordinate system
Figure BDA00032266307000001310
Ephemeris time t is used as abscissa and a backward burst BF [ n ] is used]Ephemeris time t 'to satellite'nIs the origin of the abscissa; at satellite line speed v (t'n) Is connected with the satellite/terminal station
Figure BDA0003226630700000137
Angle of (d)'SAT/RCST(t|t′n) Is ordinate and has 0 as origin of ordinate.
S10, rectangular coordinate system
Figure BDA00032266307000001311
In (c), establishing a satellite linear velocity v (t'n) Is connected with the satellite/terminal station
Figure BDA0003226630700000138
Angle of (theta)SAT/RCST(t|t′n) Function of ephemeris time thetaSAT/RCST(t|t′n)＝s2(t) coordinate-translated version θ'SAT/RCST(t|t′n)＝θSAT/RCST(t+t′n|t′n)＝s2(t+t′n) In the interval [ -T ]α,0]Equation of local approximate straight line segment l5:
Figure BDA0003226630700000139
t∈[-Tα,0]. The specific method comprises the following steps: first, at curve θ'SAT/RCST(t|t′n)＝s2(t+t′n),t∈[-Tα,0]Two points (-T) are selectedα,s2(tα) And (-T)β,s2(tβ) Wherein t) isα＝t′n-Tα，tβ＝t′n-Tβ，TαAnd TβIs two time increments, and
Figure BDA0003226630700000141
representing the maximum value of the return uplink free space transmission delay. Then, establishing a straight-line equation according to the coordinates of the two points to obtain
Figure BDA0003226630700000142
S11, estimating satellite linear velocity v (t'n) Is connected with the satellite/terminal station
Figure BDA0003226630700000143
Is at an angle of
Figure BDA0003226630700000144
FIG. 7 shows the geometrical diagrams of S9-S11, which represent the linear velocities v (t'n) Is connected with the satellite/terminal station
Figure BDA0003226630700000145
Angle of (theta)SAT/RCST(t|t′n) Becoming progressively larger.
S12, estimating the radial speed of the satellite to the main station and the radial speed of the satellite to the end station when the backward burst BF [ n ] reaches the satellite
Figure BDA00032266307000001410
S13, estimating the Doppler shift of the return uplink and the Doppler shift of the return downlink to obtain
Figure BDA0003226630700000146
Wherein the content of the first and second substances,
Figure BDA0003226630700000147
is the frequency of the return uplink carrier,
Figure BDA0003226630700000148
is the frequency of the return downlink carrier and c is the propagation velocity of the electromagnetic wave.
S14, the Doppler frequency shifts of the return uplink and the return downlink are added to obtain the Doppler frequency shift of the whole return link, namely the Doppler frequency shift of the whole return link
Figure BDA0003226630700000149

Claims (9)

1. A method for estimating Doppler frequency shift of a return link of a transparent forwarding low-orbit satellite TDMA communication-in-motion system is characterized by comprising the following steps:
s1, establishing a rectangular coordinate system
Figure FDA0003226630690000011
Ephemeris time t is used as abscissa and a backward burst BF [ n ] is used]Expected ephemeris time t to reach the primary station target slotnIs the origin of the abscissa; by transmission time delay tau 'between satellite/master station'SAT/HUB(t) is a vertical coordinate, and 0 is taken as an origin of the vertical coordinate;
s2, rectangular coordinate system
Figure FDA0003226630690000012
In (1), two linear equations are established: one is an inverse-identity linear equation l1:τ′SAT/HUB(t) t, the other being a function τ of satellite/master station transmission delay and ephemeris timeSAT/HUB(t)＝g1Coordinate-translated version of (t) 'τ'SAT/HUB(t)＝τSAT/HUB(t+tn)＝g1(t+tn) In the interval [ -T,0 [)]Equation of local approximate straight line segment l2:
Figure FDA0003226630690000013
T is a time increment, and
Figure FDA0003226630690000014
Figure FDA0003226630690000015
a maximum value representing the return downlink free-space transmission delay;
s3 solving straight line l1And straight line segment l2Coordinate t of intersection pointintersect；
S4, estimating the ephemeris time of the arrival of the return burst BF [ n ] at the satellite to obtain
t′n＝tn+tintersect；
S5, establishing a rectangular coordinate system
Figure FDA0003226630690000016
Ephemeris time t is used as abscissa and a backward burst BF [ n ] is used]Ephemeris time t 'to satellite'nAs the origin of the abscissa(ii) a By transmission delay tau 'between satellite/terminal stations'SAT/RCST(t|t′n) Is a vertical coordinate, and 0 is taken as the origin of the vertical coordinate;
s6, rectangular coordinate system
Figure FDA0003226630690000017
In (1), two linear equations are established: one is an inverse-identity linear equation l3:τ′SAT/RCST(t|t′n) The other is a function τ of satellite/end station transmission delay and ephemeris timeSAT/RCST(t|t′n)＝g2Coordinate-translated version of (t) 'τ'SAT/RCST(t|t′n)＝τSAT/RCST(t+t′n|t′n)＝g2(t+t′n) In the interval [ -T ]α,0]Equation of local approximate straight line segment l4:
Figure FDA0003226630690000018
TαIs an increment of time that is greater than the maximum time,
Figure FDA0003226630690000019
Figure FDA00032266306900000110
represents the maximum value of the return-to-uplink free-space propagation delay, shaped as f (t | t'n) Is with respect to t'nCondition function of (2) is represented by a parameter t'nEstablishing a function related to a variable t under the determined condition;
s7 solving straight line l3And straight line segment l4Of intersection coordinate t'intersect；
S8, estimating the ephemeris time of the sent back burst BF [ n ] to obtain
t″n＝t′n+t′intersect；
S9, establishing a rectangular coordinate system
Figure FDA0003226630690000021
Using the duration of a starWith time t as abscissa and with a backward burst BF [ n ]]Ephemeris time t 'to satellite'nIs the origin of the abscissa; at satellite line speed v (t'n) Is connected with the satellite/terminal station
Figure FDA0003226630690000022
Angle of (d)'SAT/RCST(t|t′n) Is a vertical coordinate, and 0 is taken as the origin of the vertical coordinate;
s10, rectangular coordinate system
Figure FDA0003226630690000023
In (c), establishing a satellite linear velocity v (t'n) Is connected with the satellite/terminal station
Figure FDA0003226630690000024
Angle of (theta)SAT/RCST(t|t′n) Function of ephemeris time thetaSAT/RCST(t|t′n)＝s2(t) coordinate-translated version θ'SAT/RCST(t|t′n)＝θSAT/RCST(t+t′n|t′n)＝s2(t+t′n) In the interval [ -T ]α,0]Equation of local approximate straight line segment l5:
Figure FDA0003226630690000025
S11, estimating satellite linear velocity v (t'n) Is connected with the satellite/terminal station
Figure FDA0003226630690000026
Angle of (theta)SAT/RCST(t″n|t'n)；
S12, according to two groups of pre-calculated parameters: a function v (t) q (t) of the linear velocity and the ephemeris time of the satellite in an earth-centered earth-fixed (ECEF) coordinate system and a function v (t) of the radial velocity and the ephemeris time of the satellite to the primary stationSAT/HUB(t)＝h1(t), and a backward burst BF [ n ]]Ephemeris time t 'to satellite'nAnd satellite line speed v (t'n) Is/are as followsDirection line with satellite/terminal station
Figure FDA0003226630690000027
Angle of (theta)SAT/RCST(t″n|t′n) Separately estimating the radial velocity v of the satellite to the master stationSAT/HUB(t′n) And radial velocity v of the satellite to the end stationSAT/RCST(t′n,t″n)：
vSAT/HUB(t′n)＝h1(t′n)
vSAT/RCST(t′n,t″n)＝v(t′n)·cos(θSAT/RCST(t″n|t′n))；
S13, estimating Doppler frequency shift of the return uplink and the return downlink
Figure FDA0003226630690000031
Wherein the content of the first and second substances,
Figure FDA0003226630690000032
is the frequency of the return uplink carrier,
Figure FDA0003226630690000033
is the frequency of the return downlink carrier, c is the propagation velocity of the electromagnetic wave;
s14, the Doppler frequency shifts of the return uplink and the return downlink are added to obtain the Doppler frequency shift of the return link, namely the Doppler frequency shift of the return link
Figure FDA0003226630690000034
2. The method for Doppler shift estimation of the return link in a transparent transponded low-earth-orbit satellite TDMA mobile communication system according to claim 1, wherein the equation of the straight line l2The establishment method comprises the following steps:
at curve τ'SAT/HUB(t)＝g1(t+tn),t∈[-T,0]Two adjacent points (0, g) are selected1(tn) And (-T, g)1(tμ) Wherein t) isμ＝tn-T；
According to (0, g)1(tn) And (-T, g)1(tμ) Equation of straight line segment is established to obtain the coordinates of
Figure FDA0003226630690000035
3. The method of claim 2, wherein the Doppler shift estimation of the return link of the transparent transponded low-earth satellite TDMA communication-in-motion system,
Figure FDA0003226630690000036
4. the method for Doppler shift estimation of the return link of a transparent transponding low-earth-orbit satellite TDMA communication-in-motion system according to claim 1, equation I4The establishment method comprises the following steps:
at curve τ'SAT/RCST(t|tn′)＝g2(t+t′n),t∈[-Tα,0]Two points (-T) are selectedα,g2(tα) And (-T)β,g2(tβ) Wherein t) isα＝t′n-Tα，tβ＝t′n-Tβ，TαAnd TβIs two time increments, and
Figure FDA0003226630690000037
according to the point (-T)α,g2(tα) And (-T)β,g2(tβ) Equation of straight line segment is established to obtain the coordinates of
Figure FDA0003226630690000041
5. The method of claim 4, wherein the Doppler shift estimation of the return link of the transparent transponded low-earth satellite TDMA communication-in-motion system,
Figure FDA0003226630690000042
6. the method of claim 4, wherein g is the Doppler shift estimation of the return link of the transparent retransmission low-earth orbit satellite TDMA communication-in-motion system2(tα) And g2(tβ) The calculation method of (2) is as follows:
based on ephemeris information and a backward burst BF n of the satellite]Ephemeris time t 'to satellite'nEstimating the position P (t ') of the satellite under the ECEF coordinate system at the moment'n)；
In a time period of t'n-Tα,t′n]In the method, two times t are respectively selectedα＝t′n-TαAnd tβ＝t′n-Tβ，
Figure FDA0003226630690000043
Figure FDA0003226630690000044
A maximum value representing a return uplink free space transmission delay;
obtaining the GNSS position R of the end station at the two momentsGNSS(tα) And RGNSS(tβ) And converting the corresponding ECEF coordinate R (t)α) And R (t)β)；
In the ECEF coordinate system, satellite positions P (t 'are respectively calculated'n) To end station position R (t)α) And R (t)β) The transmission distance therebetween;
dividing the transmission distance by the propagation velocity of the electromagnetic wave to obtainTo satellite position P (t'n) To end station position R (t)α) And R (t)β) Inter-transmission delay g2(tα) And g2(tβ)。
7. The method for Doppler shift estimation of the return link in a transparent transponded low-earth-orbit satellite TDMA mobile communication system according to claim 1, wherein the equation of the straight line l5The establishment method comprises the following steps:
at curve θ'SAT/RCST(t|t′n)＝s2(t+t′n),t∈[-Tα,0]Two points (-T) are selectedα,s2(tα) And (-T)β,s2(tβ) Wherein t) isα＝t′n-Tα，tβ＝t′n-Tβ；
According to the point (-T)α,s2(tα) And (-T)β,s2(tβ) Equation of straight line segment is established to obtain the coordinates of
Figure FDA0003226630690000051
8. The method of claim 7, wherein s is a Doppler shift estimation method for a return link of a transparent transponded low-earth-orbit satellite TDMA communication-in-motion system2(tα) And s2(tβ) The calculation method of (2) is as follows:
in a time period of t'n-Tα,t′n]In the method, two times t are respectively selectedα＝t′n-TαAnd tβ＝t′n-Tβ，
Figure FDA0003226630690000052
Obtaining the GNSS position R of the end station at the two momentsGNSS(tα) And RGNSS(tβ) And convert to the corresponding ECEF seatLabel R (t)α) And R (t)β)；
In an ECEF coordinate system, the linear velocity v (t ') of the satellite is calculated according to the ephemeris information of the satellite and the position information of the end station'n) Is connected with the satellite/terminal station
Figure FDA0003226630690000053
And
Figure FDA0003226630690000054
angle s of2(tα) And s2(tβ)。
9. The method of claim 7, wherein the Doppler shift estimation of the return link of the transparent transponded low-earth satellite TDMA communication-in-motion system,
Figure FDA0003226630690000055
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