CN110988851A - Different-orbit single-satellite time-sharing frequency measurement positioning method based on star position optimization - Google Patents
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Abstract
The invention discloses an off-orbit single-satellite time-sharing frequency measurement positioning method based on star position optimization, which comprises the following steps of: measuring the frequency of a signal transmitted by a ground radiation source reaching an observation satellite; establishing an different-orbit single-satellite time-sharing frequency measurement positioning model, selecting a plurality of satellites with different orbits to respectively carry out frequency measurement at different moments, and establishing a positioning equation set according to a plurality of different measured signal frequencies; deducing geometric dilution precision factors, and analyzing the influence of various factors on positioning precision; and establishing a star position optimization model, and optimizing selection of the orbit and the satellite observation time to improve positioning accuracy. In the invention, in a limited sight range, the single satellite flying through different tracks of the positioning visible area at different moments is used for independently observing the same interference source for multiple times, and due to differences in the aspects of the flying direction, the distribution of the observation positions and the like, compared with a single-track single-satellite time-sharing frequency measurement positioning scheme, the positioning effect is stable, the precision is higher, the inter-satellite distance is larger, and the measurement position selection can be more flexible.
Description
Technical Field
The invention provides an different-orbit single-satellite time-sharing frequency measurement positioning method based on star position optimization.
Background
The passive positioning technology of the radiation target source, especially a passive positioning system depending on modern medium and low orbit satellites, has a large positioning area range, can quickly position the emission signals of the targets on the sea, the land and the air, and has important functions and wide application prospects in the civil and military fields. The radiation source single-star positioning technology has the advantages of high positioning probability, good usability, convenient application and deployment and the like compared with the multi-star positioning technology, particularly, the satellite visible angle of a radio target is limited under the shielding limiting conditions of vegetation, landform, buildings and the like, and the single-star positioning has irreplaceable effect under the condition that a plurality of satellites cannot be used for positioning.
At present, a single-satellite frequency measurement positioning system is manufactured on a traditional single-satellite positioning body, and the single-satellite frequency measurement positioning system has the advantages of low cost, good flexibility, no special requirement on satellite attitude and the like, and becomes a research hotspot. However, the smaller the frequency measurement interval between two adjacent single-satellite frequency measurement positioning technologies is, the poorer the positioning effect is and a positioning blind area exists below a satellite operation trajectory line. If the target source narrows the visible area due to the obstruction, the measurement travel distance of the visible satellite becomes smaller, the frequency measurement interval between two adjacent times by using the single-satellite frequency measurement positioning technology is very short, and the positioning error of the target source under the satellite flight track is further increased. The star-position-based optimal different-orbit single-star time-sharing frequency measurement positioning technology can effectively improve the positioning accuracy in the positioning scene with limited sight lines by optimizing the orbit and the satellite observation position.
Disclosure of Invention
The invention aims to: aiming at the problem that positioning is difficult due to the fact that the probability of a target source visible satellite is reduced in a positioning scene with a limited view field, an different-orbit single-satellite time-sharing frequency measurement positioning method based on satellite position optimization is provided, and the positioning precision is remarkably improved by optimizing an orbit and a satellite observation position.
In order to achieve the above purpose, the method specifically comprises the following steps:
an off-orbit single-satellite time-sharing frequency measurement positioning method based on star position optimization comprises the following steps:
s1: measuring the frequency of a signal transmitted by a ground radiation source reaching an observation satellite;
s2: establishing an different-orbit single-satellite time-sharing frequency measurement positioning model, selecting three satellites with different orbits to respectively perform frequency measurement at different moments, and establishing a positioning equation set according to three different measured signal frequencies;
s3: deducing geometric dilution precision factors (GDOP) of the different-rail single-satellite time-sharing frequency measurement positioning technology, and analyzing the influence of various factors on positioning precision;
s4: and establishing a star position optimization model, and optimizing selection of the orbit and the satellite observation time to further improve the positioning precision.
Preferably: in the step S1, the frequency of the signal sent by the ground radiation source reaching the observation satellite is measured in the different-orbit single-satellite time-division frequency-measurement positioning technology.
The different-orbit single-satellite time-sharing frequency measurement positioning technology is a positioning technology which calculates the position of a target by utilizing the corresponding relation between the Doppler frequency shift generated by the movement of a satellite relative to a radiation source and the position of the radiation source.
As shown in fig. 2, for a radiation source stationary on the ground or in the air, the motion of the satellite will cause the carrier frequency reaching the satellite to generate a doppler shift effect, the satellites in different orbits will have a frequency difference between the frequency of the measurement signal reaching the satellite at different times and the actual signal of the radiation source, the equal frequency plane corresponding to the frequency measured by the satellite is the cone apex at the satellite, the cone surface passes through the cone surface of the radiation source, and the cone angles are different from each other due to the motion of the satellite. Thus, the frequency f of the signal transmitted by the radiation source measured by the satelliteijFor the actual frequency f of the ground radiation source signalcPlus Doppler shift f produced by satellite motiondI.e. by
Wherein v is a radiation source andrelative velocity between satellites, c is the speed of light, fcIs the actual signal frequency of the radiation source, theta is the angle between the relative speed of the radiation source and the satellite and the included angle between the radiation source and the satellite connecting line, i is the orbit number of the observation satellite, and j is the observation time t of the observation satellite of the i orbitj。
Preferably: and in the step S2, establishing a positioning equation set of the different-rail single-satellite time-sharing frequency measurement positioning technology.
The position coordinate of a certain working ground stationary radiation source under a ground fixed rectangular coordinate system is assumed to be s ═ x yz]TWhen the medium and low orbit satellite in different orbits flies over the sky in the visual range, the observation time is t1，t2，t3，…，tMThe position coordinate of the corresponding observation satellite is sij＝[xijyijzij]TAt a speed of
Where i 1, 2., N denotes a track number, j 1, 2., M denotes a corresponding track tjThe satellite number of the time of day.
Assuming a measured Doppler frequency fijThe frequency of the radiation source is known as fcThe available measurement equation is then:
in the formula:
the radial velocity of the satellite and the target;
is the relative position between the satellite and the target, i 1,2, …, N, j 1,2, …, M; and c is the propagation velocity of the electromagnetic wave.
According to a number of measurements, the satellite observation position taken is sijM measured signal frequency f 1,2, …, N, j 1,2ijComprises the following steps:
selecting three measuring frequencies f from the measured signal frequenciesmp，fnq，fkrWherein m, N, k is 1,2, …, N; p, q, r ═ 1,2, …, M subtracting two by two yields the following system of frequency difference equations:
using the WGS-84 earth ellipsoid model during analysis, assuming that the WGS-84 earth reference ellipsoid has a major radius a and a minor radius b, a first eccentricity can be defined as:
take e in general2＝0.00669437999013。
According to the ellipsoid model, if the radiation source is considered to be on the earth surface with an elevation of 0, the radiation source position conforms to the following earth surface equation:
the frequency difference equation and the earth surface equation are combined, and under the condition of considering the constraint of the earth surface, the geodetic coordinate s of the radiation source can be obtained only by knowing the positions and the speeds corresponding to the observation moments of the three satellites and the measured frequency.
Preferably: in the step S3, a formula derivation is performed on a geometric dilution accuracy factor (GDOP) of the different-orbit single-satellite time-sharing frequency measurement positioning technology according to a positioning model of the technology, so as to analyze the positioning accuracy.
The following derivation considers the interference source on the ground, and the satellite observation position s is takenijI 1,2, …, N, j 1,2ijThree measuring frequencies f are selectedmp，fnq，fkrWherein m, N, k is 1,2, …, N; p, q, r ═ 1,2, …, M, the equation for the off-rail single star time-shared frequency location is written as:
the above formula is subdivided into:
let the positioning error covariance matrix be PdX＝E[dXdXT]Wherein dX ═ dX dy dz]T(ii) a The covariance matrix of the frequency difference and the elevation error is RfH＝E[dUdUT]Wherein dU ═ dfmpdfnqdfkrdH]T(ii) a The satellite position error covariance matrix is
Wherein dXij＝[dxijdyijdzij]TI ═ m, j ═ p; i is n, j is q; k, r, j; the covariance matrix of the satellite velocity error is
Wherein
The positioning error covariance matrix is then expressed as:
wherein
Then the geometric dilution precision factor GDOP of the different-rail single-satellite time-sharing frequency difference positioning is:
GDOP(x,y,z)＝tr(PdX)
tr (-) is the trace of the matrix.
Therefore, the conclusion that the positioning accuracy of the different-orbit single-satellite time-sharing frequency measurement positioning technology is related to the elevation error of a radiation source, the frequency measurement error of an observation satellite, the speed error of the observation satellite and the position error of the observation satellite can be obtained, and when the errors are larger, the positioning accuracy is worse, and the positioning accuracy can be effectively improved by improving the errors.
Preferably: in the step S4, the positions of the different orbiting satellites and the observation satellites are optimally selected, so that the positioning error of the interference source can be minimized, and the positioning accuracy can be further improved. The following optimization objective problem can be established:
wherein, JiRepresenting different satellite flight orbits, i 1,2,3, N denoting the orbit number, SijIs on the corresponding track tjThe time of flight through the observed position of the satellite in the visible region, j 1,2,3, M, GDOP (x, y, z) is at the radiation source s [ x, y, z ]]TGeometric dilution accuracy factor of the location of (a). By obtaining the minimum value of the GDOP at the position of the radiation source, the orbit number and the observation time of the corresponding observation satellite are obtained, so that the optimal satellite observation position capable of positioning the radiation source can be obtained.
Has the advantages that: according to the different-orbit single-satellite time-sharing frequency measurement positioning technology based on star position optimization, in a limited sight range, a single satellite flying through different tracks of a positioning visible area at different moments is used for carrying out multiple independent observation on the same interference source, and due to differences in the aspects of the flying direction, the observation position distribution and the like, compared with a single-orbit single-satellite time-sharing frequency measurement positioning scheme, the positioning effect is stable, the accuracy is higher, the inter-satellite distance is larger, and the measurement position selection can be more flexible.
Drawings
FIG. 1: the flow chart of the invention;
FIG. 2: a satellite frequency measurement positioning schematic diagram;
FIG. 3: a different-rail single-star time-sharing frequency measurement positioning model;
FIG. 4: the running track of the visible iridium satellite under the global satellite;
FIG. 5: the running track and running direction of the visible iridium satellite under the satellite within the visible range of the target source;
FIGS. 6 to 8: an error curve diagram of different-rail single-star time-sharing frequency measurement positioning.
Detailed Description
The technical solution of the present invention is further described in detail below with reference to the accompanying drawings, the present invention is implemented on MatlabR2014b and STK11 experimental platforms, fig. 1 is a flow chart of the present invention, and mainly includes the following steps:
firstly, measuring the frequency of a signal transmitted by a ground radiation source reaching an observation satellite
The different-orbit single-satellite time-sharing frequency measurement positioning technology is a positioning technology which calculates the position of a target by utilizing the corresponding relation between the Doppler frequency shift generated by the movement of a satellite relative to a radiation source and the position of the radiation source.
As shown in fig. 2, for a radiation source stationary on the ground or in the air, the motion of the satellite will cause the carrier frequency reaching the satellite to generate a doppler shift effect, the satellites in different orbits will have a frequency difference between the frequency of the measurement signal reaching the satellite at different times and the actual signal of the radiation source, the equal frequency plane corresponding to the frequency measured by the satellite is the cone apex at the satellite, the cone surface passes through the cone surface of the radiation source, and the cone angles are different from each other due to the motion of the satellite. Thus, the frequency f of the signal transmitted by the radiation source measured by the satelliteijFor the actual frequency f of the ground radiation source signalcPlus Doppler shift f produced by satellite motiondI.e. by
Where v is the relative velocity between the radiation source and the satellite, c is the speed of light, fcIs the actual signal frequency of the radiation source, theta is the angle between the relative speed of the radiation source and the satellite and the included angle between the radiation source and the satellite connecting line, i is the orbit number of the observation satellite, and j is the observation time t of the observation satellite of the i orbitj。
Establishing a positioning equation set of the different-rail single-star time-sharing frequency measurement positioning technology
1. Positioning model for different-rail single-star time-sharing frequency measurement positioning
The middle and low orbit satellite is far away from the earth in the process of moving around the earth, the height is generally more than 150km, the satellite and the radiation source can be approximately regarded as particle motion analysis, and fig. 3 is an iso-orbit single-satellite time-sharing frequency measurement positioning model. The position coordinate of a certain working ground stationary radiation source under a ground fixed rectangular coordinate system is assumed to be s ═ x y z]TWhen the medium and low orbit satellite in different orbits flies over the sky in the visual range, the observation time is t1，t2，t3，…，tMThe position coordinate of the corresponding observation satellite is sij＝[xijyijzij]TAt a speed of
Where i 1, 2., N denotes a track number, j 1, 2., M denotes a corresponding track tjThe satellite number of the time of day.
Assuming a measured Doppler frequency fijThe frequency of the radiation source is known as fcThe available measurement equation is then:
in the formula:
the radial velocity of the satellite and the target;
is the relative position between the satellite and the target, i 1,2, …, N, j 1,2, …, M; and c is the propagation velocity of the electromagnetic wave.
2. Establishment of system of positioning equations
According to a number of measurements, the satellite observation position taken is sijM measured signal frequency f 1,2, …, N, j 1,2ijComprises the following steps:
selecting three measuring frequencies f from the measured signal frequenciesmp，fnq，fkrWherein m, N, k is 1,2, …, N; p, q, r ═ 1,2, …, M subtracting two by two yields the following system of frequency difference equations:
using the WGS-84 earth ellipsoid model during analysis, assuming that the WGS-84 earth reference ellipsoid has a major radius a and a minor radius b, a first eccentricity can be defined as:
take e in general2＝0.00669437999013。
According to the ellipsoid model, if the radiation source is considered to be on the earth surface with an elevation of 0, the radiation source position conforms to the following earth surface equation:
equations (4) and (6) are combined, and under the condition of considering the surface constraint of the earth, the geodetic coordinate s of the radiation source can be obtained only by knowing the positions and the speeds corresponding to the observation time of the three satellites and the measured frequency.
Positioning precision analysis of two-different-rail single-star time-sharing frequency measurement positioning technology
The positioning accuracy of the different-orbit single-satellite time-sharing frequency measurement positioning technology is generally described by a geometric dilution accuracy factor (GDOP), which represents the three-dimensional geometric distribution of the positioning error, and the expression is as follows:
in the formula: sigmax,σy,σzIs the standard deviation of the positioning in 3 directions.
The following derivation considers the interference source on the ground, and the satellite observation position s is takenijI 1,2, …, N, j 1,2ijThree measuring frequencies f are selectedmp，fnq，fkrWherein m, N, k is 1,2, …, N; p, q, r ═ 1,2, …, M, the equation for the off-rail single star time-shared frequency location is written as:
the above formula is subdivided into:
let the positioning error covariance matrix be PdX＝E[dXdXT]Wherein dX ═ dX dy dz]T(ii) a The covariance matrix of the frequency difference and the elevation error is RfH＝E[dUdUT]Wherein dU ═ dfmpdfnqdfkrdH]T(ii) a The satellite position error covariance matrix is
Wherein dXij＝[dxijdyijdzij]TI ═ m, j ═ p; i is n, j is q; k, r, j; the covariance matrix of the satellite velocity error is
Wherein
The positioning error covariance matrix is then expressed as:
wherein
Then the geometric dilution precision factor GDOP of the different-rail single-satellite time-sharing frequency difference positioning is:
GDOP(x,y,z)＝tr(PdX) (11)
tr (-) is the trace of the matrix.
The positioning accuracy of the different-orbit single-satellite time-sharing frequency measurement positioning technology is related to the elevation error of a radiation source, the frequency measurement error of an observation satellite, the speed error of the observation satellite and the position error of the observation satellite, and when the errors are larger, the positioning accuracy is worse, and the positioning accuracy can be effectively improved by improving the errors.
Fourthly, establishing a star position optimization model
As shown in fig. 3, there are a plurality of orbiting satellites flying through a cone-shaped visible area, and by optimally selecting the positions of different orbiting satellites and their observation satellites, the positioning error of the interference source can be minimized, and the positioning accuracy can be further improved.
Establishing the following optimization target problem:
wherein, JiRepresenting different satellite flight orbits, i 1,2,3, N denoting the orbit number, SijIs on the corresponding track tjThe time of flight through the observed position of the satellite in the visible region, j 1,2,3, M, GDOP (x, y, z) is at the radiation source s [ x, y, z ]]TGeometric dilution accuracy factor of the location of (a). By obtaining the minimum value of the GDOP at the position of the radiation source, the orbit number and the observation time of the corresponding observation satellite are obtained, so that the optimal satellite observation position capable of positioning the radiation source can be obtained.
Fifth, comparing simulation results
And (3) supposing that an LEO iridium satellite transparent transponder is adopted to carry out earth surface target source positioning, comparing the positioning effects of single-track single-satellite time-sharing frequency measurement positioning and different-track single-satellite time-sharing frequency measurement positioning through the observation position optimization of single-track satellite time-sharing frequency measurement positioning and the optimization of the frequency measurement position of a satellite in different tracks flying into a visible area in a time-sharing manner.
1. Simulation parameters
Selecting 23Oct 201804: 00:00(UTCG) as an initial time and 23Oct 201809: 00:00(UTCG) as an end time, and acquiring ephemeris data of the Iridium system by using STK11 simulation software. Assuming that the target source location is located in Nanjing (119 degrees from east longitude, 32 degrees from north latitude, 0km in elevation), and the lowest elevation angle of the user of the target source is 71.57 degrees, three iridium stars pass through the visible range of the target source in the time period, which are 209 iridium star, 306 iridium star and 404 iridium star respectively, the running tracks of the three iridium stars under the satellites in the global range are shown in FIG. 5, the running tracks and running directions under the satellites in the visible range of the target source are shown in FIG. 4, and the track parameters and the visible time are shown in tables 1 and 2.
TABLE 1 orbit parameters for Iridium satellites across a target Source visibility Range
TABLE 2 visibility times for Iridium satellites past target Source visibility Range
2. Single-track single-star time-sharing frequency-measuring positioning observation star position optimization
If a single-satellite frequency measurement technology is selected for positioning the interference source in the scene, three selection schemes are available, iridium 209, 306 and 404 can be observed at three different times respectively, and the target source is positioned by using the acquired Doppler frequency shift generated by the movement relative to the radiation source. Assuming that the frequency measurement interval is 2s, the two fixed satellite observation times are the starting times t when the satellite enters the visible area0And an end time tMAnd the third satellite observation time is t0And tMAt any time tjJ represents the time interval from the start time, j is 2,4, …, M-2(j is an even number), the signal carrier frequency is 1.620GHz, the frequency measurement error is 1Hz, the elevation error, the satellite velocity error and the position error are ignored, and the minimum positioning error of three options of single-orbit single-satellite time-sharing frequency measurement positioning by using 209, 306 and 404 iridium satellites and the corresponding satellite observation time are shown in table 3.
TABLE 3 Single-track single-star time-sharing frequency-measuring positioning observation star position selection optimization scheme and minimum positioning error thereof
As can be seen from Table 3, when positioning is performed by using the single-track single-satellite frequency measurement positioning technology, the observation time of the third satellite is closer to the starting time t when the satellite enters the visible area0And an end time tMCentral time t in betweenM/2The better the positioning effect. The position of the target source is just near the satellite running track line of 209 iridium satellite in the visual range, so that the single satellite frequency measurement positioning effect by using 209 iridium satellite is the worst, and the single satellite frequency measurement positioning effect by using 306 iridium satellite is the best, compared with the best, the minimum positioning error is 6.4259km, so that the visual field is influenced by the position of the target source in the visual fieldThe positioning precision of single-track single-star frequency measurement positioning is not high under the limited condition. The influence of the different-orbit single-satellite time-division frequency measurement positioning technology on the positioning accuracy in the scene is discussed below by considering the case that the observation position of the third satellite is located on a different orbit.
3. Different-rail single-star time-sharing frequency-measuring positioning observation star position optimization
Assuming that two satellite observation positions are in one orbit and the third satellite observation position is in the other orbit, there are six options, and the minimum positioning error and the corresponding satellite observation time of the six options are shown in table 4. If the frequency measurement interval is 2s, the observation time of the two fixed satellites is the starting time t when the satellites enter the visible area on the same orbit0And an end time tMThe observation time of the third satellite is any time t on another orbitjJ represents the time interval from the start time, j is 0,2, …, M (j is an even number), the signal carrier frequency is 1.620GHz, the frequency measurement error is 1Hz, the elevation error, the satellite velocity error and the position error are ignored, and the positioning error graph compared with the single-orbit single-satellite frequency measurement positioning is shown in fig. 6, 7 and 8.
TABLE 4 optimization scheme for selection of observation star position for different-orbit single-star time-sharing frequency measurement positioning and minimum positioning error thereof
As can be seen from table 4, the minimum positioning error of all schemes using the different-rail single-satellite time-sharing frequency measurement positioning technology is significantly reduced compared with that of the single-rail single-satellite frequency measurement positioning scheme, and the positioning accuracy can reach a hundred meter level; the satellite observation time corresponding to the situation of the minimum positioning error is the initial time, the end time or the central time. It can be seen from fig. 6, 7, and 8 that under the original single track condition, another track is introduced, and the different-track single-satellite time-sharing frequency measurement is used for positioning, so that the positioning accuracy of the original single-track single-satellite frequency measurement positioning can be improved, the positioning error changes stably, and the selection of the satellite observation time is flexible. Simulation results show that the different-orbit single-satellite time-sharing frequency measurement positioning technology can remarkably improve the positioning accuracy under the condition of limited view field, and the optimization of star position selection can enable the positioning accuracy to reach the hundred-meter magnitude.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.
Claims (5)
1. An off-orbit single-satellite time-sharing frequency measurement positioning method based on star position optimization is characterized by comprising the following steps:
s1: measuring the frequency of a signal transmitted by a ground radiation source reaching an observation satellite;
s2: establishing an different-orbit single-satellite time-sharing frequency measurement positioning model, selecting a plurality of satellites with different orbits to respectively carry out frequency measurement at different moments, and establishing a positioning equation set according to a plurality of different measured signal frequencies;
s3: deducing geometric dilution precision factors, and analyzing the influence of various factors on positioning precision;
s4: and establishing a star position optimization model, and optimizing selection of the orbit and the satellite observation time to further improve the positioning precision.
2. The time-sharing and frequency-measuring positioning method for the different-orbit single satellite based on the star position optimization as claimed in claim 1, wherein in step S1, the signal frequency f transmitted by the radiation source measured by the satellite isijFor the actual frequency f of the ground radiation source signalcPlus Doppler shift f produced by satellite motiondI.e. by
Where v is the relative velocity between the radiation source and the satellite, c is the speed of light, fcIs the actual signal frequency of the radiation source, theta is the angle between the relative speed of the radiation source and the satellite and the included angle between the radiation source and the satellite connecting line, i is the orbit number of the observation satellite, and j is the observation time t of the observation satellite of the i orbitj。
3. The time-sharing frequency-measuring positioning method for the different-orbit single satellite based on the star position optimization according to claim 1, wherein the step S2 comprises the following steps:
step S2.1: establishing a different-rail single-star time-sharing frequency measurement positioning model;
the position coordinate of a certain working ground stationary radiation source under a ground fixed rectangular coordinate system is assumed to be s ═ x y z]TWhen the medium and low orbit satellite in different orbits flies over the sky in the visual range, the observation time is t1,t2,t3,…,tMThe position coordinates of the corresponding observation satellite are
At a speed of
Where i 1, 2., N denotes a track number, j 1, 2., M denotes a corresponding track tjA satellite number of a time;
assuming a measured Doppler frequency fijThe frequency of the radiation source is known as fcThen the measurement equation is:
in the formula:
the radial velocity of the satellite and the target;
is the relative position between the satellite and the target; c is the propagation of electromagnetic wavesSpeed;
step S2.2: selecting a plurality of satellites with different orbits to respectively carry out frequency measurement at different moments, and establishing a positioning equation set according to a plurality of different measured signal frequencies;
according to a number of measurements, the satellite observation position taken is sijM measured signal frequency f 1,2, …, N, j 1,2ijComprises the following steps:
selecting three measuring frequencies f from the measured signal frequenciesmp，fnq，fkrWherein m, N, k is 1,2, …, N; p, q, r ═ 1,2, …, M subtracting two by two yields the following system of frequency difference equations:
in the analysis process, a WGS-84 earth ellipsoid model is used, and if the major radius of a WGS-84 earth ellipsoid is a, the minor radius of the earth ellipsoid is b, a first eccentricity is defined as:
according to the ellipsoid model, if the radiation source is considered to be on the earth surface with an elevation of 0, the radiation source position conforms to the following earth surface equation:
the frequency difference equation and the earth surface equation are combined, and under the condition of considering the constraint of the earth surface, the geodetic coordinate s of the radiation source can be obtained only by knowing the positions and the speeds corresponding to the observation moments of the three satellites and the measured frequency.
4. The time-sharing frequency-measuring positioning method for the different orbits and the single stars based on the star optimization as claimed in claim 1, wherein the step of deriving the geometric dilution precision factor in step S3 comprises:
the following derivation considers the interference source on the ground, and the satellite observation position s is takenijI 1,2, …, N, j 1,2ijThree measuring frequencies f are selectedmp，fnq，fkrWherein m, N, k is 1,2, …, N; p, q, r ═ 1,2, …, M, the equation for the off-rail single star time-shared frequency location is written as:
the above formula is subdivided into:
let the positioning error covariance matrix be PdX＝E[dXdXT]Wherein dX ═ dX dy dz]T(ii) a The covariance matrix of the frequency difference and the elevation error is RfH＝E[dUdUT]Wherein dU ═ dfmpdfnqdfkrdH]T(ii) a The satellite position error covariance matrix is
Wherein dXij＝[dxijdyijdzij]TI ═ m, j ═ p; i is n, j is q; k, r, j; the covariance matrix of the satellite velocity error is
Wherein
i ═ m, j ═ p; i is n, j is q; k, r, j; the positioning error covariance matrix is then expressed as:
wherein
Then the geometric dilution precision factor GDOP of the different-rail single-satellite time-sharing frequency difference positioning is:
GDOP(x,y,z)＝tr(PdX)
tr (-) is the trace of the matrix.
5. The off-orbit single-satellite time-sharing frequency measurement positioning method based on the star position optimization as claimed in claim 1, characterized in that: the step of S4 includes the following steps:
establishing the following optimization target problem:
wherein, JiRepresenting different satellite flight orbits, i 1,2,3, N denoting the orbit number, SijIs on the corresponding track tjThe time of flight through the observed position of the satellite in the visible region, j 1,2,3, M, GDOP (x, y, z) is at the radiation source s [ x, y, z ]]TGeometric dilution accuracy factor of the location of (d); by obtaining the minimum value of the GDOP at the position of the radiation source, the orbit number and the observation time of the corresponding observation satellite are obtained, so that the optimal satellite observation position capable of positioning the radiation source can be obtained.
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