A method, system, terminal and medium for precise orbit determination of low-orbit satellites in GNSS denial conditions

Abstract

The present invention discloses a method, system, terminal and medium for precise orbit determination of low-orbit satellites under GNSS denial conditions, wherein the method comprises: obtaining GNSS data received by a satellite receiver of an anchoring satellite, and using a dynamic orbit determination method to solve the precise orbit of the anchoring satellite and its dynamic parameters; wherein the anchoring satellite is a low-orbit satellite in the same constellation that is linked with a GNSS denial satellite and is not subject to co-frequency interference; obtaining inter-satellite link ranging data between the anchoring satellite and the GNSS denial satellite; and using a dynamic orbit determination method to solve the orbit of the GNSS denial satellite based on the precise orbit of the anchoring satellite and the inter-satellite link ranging data between the anchoring satellite and the GNSS denial satellite. The orbit of the GNSS denial satellite is solved based on the precise orbit of the anchoring satellite and the inter-satellite ranging data, thereby suppressing the orbit error divergence problem caused by orbit prediction. The precise orbit determination of low-orbit satellites that does not directly rely on GNSS satellites and ground monitoring stations is achieved under GNSS denial conditions.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite precise orbit determination, and in particular to a method, system, terminal and medium for precise orbit determination of a low-orbit satellite under GNSS denial conditions. Background Art

[0002] Low-orbit constellations have become the forefront and hotspot of the development of the international aerospace field, and are mainly used in communications, navigation and remote sensing services. High-precision orbit products of low-orbit satellites are the key prerequisite for low-orbit constellations to provide communications, navigation and remote sensing and other tasks. Onboard GNSS orbit determination technology can achieve centimeter-level orbit determination of low-orbit satellites and is currently the most commonly used means of precise orbit determination of low-orbit satellites. Previous studies have shown that the premise for achieving high-precision orbit determination of low-orbit satellites based on onboard GNSS data is that the onboard receiver can normally receive GNSS signals.

[0003] In the prior art, there are several low-orbit satellite orbit determination schemes that are highly relevant to this method:

[0004] Solution 1: A method and system for autonomous orbit determination of a low-orbit satellite constellation

[0005] The scheme discloses a method and system for autonomous orbit determination of a low-orbit satellite constellation, including obtaining inter-satellite link ranging data and on-board GNSS receiver observation data; using the observation data to build an observation model and pre-process the observation data; using the pre-processed observation data to perform on-board PPP solution to obtain the rough spatial position of each low-orbit satellite on orbit; selecting an orbit determination perturbation correction mechanical model to establish a low-orbit satellite dynamics differential equation; establishing an orbit determination function model by combining the observation model; constructing a random model, fusing the orbit determination function model and the random model to establish a joint adjustment model to obtain the low-orbit satellite orbit determination result; using the inter-satellite link ranging data to build a low-orbit satellite constellation space network, combining the joint adjustment model to obtain the low-orbit satellite constellation autonomous orbit determination result, and directly using the inter-satellite link ranging data and GNSS receiver observation data to achieve high-precision, safe and autonomous orbit determination on board the low-orbit satellite.

[0006] Solution 2: A method, device and system for determining the orbit of a low-orbit satellite

[0007] The scheme discloses a method and device for determining the orbit of a low-orbit satellite. First, the broadcast ephemeris sent by the navigation satellite is received, and the orbit and clock error of the navigation satellite are calculated based on the broadcast ephemeris. Then, the correction information of the positioning information sent by the ground system is received to correct the positioning information and obtain the corrected positioning information. The corrected positioning information and observation data are then used to determine the orbit of the low-orbit satellite. That is, the invention introduces the correction information of the positioning information, and uses the accurate corrected positioning information to determine the orbit of the low-orbit satellite, thereby improving the orbit determination accuracy of the low-orbit satellite.

[0008] Solution 3: A multi-station local sensing joint orbit determination method for large low-orbit satellite constellations

[0009] This scheme proposes a multi-station local sensing joint orbit determination method for large low-orbit star clusters. It uses the local sensing data of a single station to perform least squares filtering processing, and generates a normal equation system to integrate into the data center joint orbit determination. This method disperses various types of data processing processes at each station, and the data center can obtain the global optimal orbit state estimate only through the joint station normal equation system. Compared with traditional orbit determination schemes, the joint processing at the tracking and control station and the data center avoids the transmission of a large amount of measurement data, significantly reduces the overhead of data transmission and central calculation, enhances the flexibility and robustness of data center processing, and meets the tracking and control management needs of large star clusters. In addition, this scheme is suitable for the orbit determination problem of large star clusters supported by multiple stations and intersatellite links.

[0010] However, none of the above solutions can solve the problem of precise orbit determination of low-orbit satellites under GNSS denial. Large low-orbit constellations are service systems built from a large number of low-orbit satellites with communication, navigation and remote sensing functions. However, when large low-orbit constellations are performing communication, navigation and remote sensing operations, the downlink signals broadcast by some low-orbit satellites have co-frequency interference with the onboard GNSS signals. The interfered low-orbit satellites are called GNSS denied satellites. Co-frequency interference makes it impossible for low-orbit satellites to determine their orbits based on GNSS data. How to achieve precise orbit determination of low-orbit satellites in this scenario becomes a problem. At this time, the orbit of the low-orbit satellite can be obtained through orbit prediction, but the orbit accuracy diverges rapidly with the increase of the predicted arc length, which obviously cannot meet the PNT service needs of the low-orbit constellation. To date, research on precise orbit determination of low-orbit satellites under co-frequency interference has not been proposed. Summary of the invention

[0011] In view of the above-mentioned deficiencies in the prior art, the purpose of the present invention is to provide a method, system, terminal and medium for precise orbit determination of low-orbit satellites under GNSS denial conditions, and proposes to use a low-orbit satellite in the constellation that is linked to a GNSS denied satellite and is not subject to co-frequency interference as an anchor satellite, so as to provide a high-precision space reference for the GNSS denied satellite. The precise orbit of the anchor satellite can be solved based on the onboard GNSS data, and the orbit of the GNSS denied satellite can be solved by combining the inter-satellite ranging data between the two.

[0012] In a first aspect, a method for precise orbit determination of a low-orbit satellite in a GNSS denial situation is provided, comprising the following steps:

[0013] The GNSS data received by the onboard receiver of the anchor satellite is obtained, and the precise orbit and dynamic parameters of the anchor satellite are solved by the dynamic orbit determination method; the anchor satellite is a low-orbit satellite in the same constellation that is linked with the GNSS rejection satellite and is not subject to co-frequency interference;

[0014] Obtain inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite;

[0015] Based on the precise orbit of the anchor satellite and the inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite, the orbit of the GNSS denial satellite is solved by the dynamic orbit determination method.

[0016] Furthermore, the inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite is obtained by the following method:

[0017] S21: Obtaining the original inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite;

[0018] S22: The following model is used to calculate the inter-satellite link ranging data error:

[0019] Assume that the original pseudo-range measurement received by star j from star i at time t1 is ρ ij (t1), the original pseudo-range measurement received by star i from star j at time t2 is ρ ji (t2), the observation equation is expressed as follows:

[0020]

[0021]

[0022] In the formula, R i , R j are the three-dimensional positions of star i and star j respectively; clk i 、clk j are the satellite clock errors of star i and star j respectively; c is the speed of light; Δt1 is the light time of the measurement signal from star i to star j, and Δt2 is the light time of the measurement signal from star j to star i; τ ij is the link equipment delay between the transmission of satellite i and the reception of satellite j; τ ji is the link equipment delay of the j-star transmission and the i-star reception; is the error correction term that can be accurately modeled in the one-way ranging from star i to star j; are the error correction terms that can be accurately modeled in the one-way ranging from the j-star to the i-star; the i-star and the j-star represent the anchor satellite and the GNSS rejection satellite respectively;

[0023] The two-way observations at different times are converted to the same time. Assuming that the pseudo-range measurements at times t1 and t2 are converted to the target time t0, we can obtain ρ ij (t0) and ρ ji (t0), then the corrected inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite can be expressed as follows:

[0024]

[0025] Among them, ρ(t0) is the corrected inter-satellite link ranging data between the anchor satellite and the GNSS denied satellite at time t0.

[0026] Furthermore, in the process of solving the GNSS rejection satellite orbit using the dynamic orbit determination method, the prior constraints of the initial orbit parameters are set and expressed as follows:

[0027]

[0028] In the formula, x p , σ p represent the a priori initial orbit parameters and a priori initial orbit accuracy at the start time of the pth day respectively; They represent the orbit parameters and orbit accuracy at 24 o'clock one day before the interference, which are calculated using the GNSS data before the interference of the GNSS denial satellite; They represent the orbit parameters and orbit accuracy of 24 points on the p-1th day calculated based on the precise orbit of the anchor satellite and the inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite.

[0029] Furthermore, in the process of solving the GNSS rejection satellite orbit using the dynamic orbit determination method, the prior constraints of the dynamic parameters are set and expressed as follows:

[0030]

[0031] In the formula, y q , R q represent the a priori dynamic parameters and a priori dynamic parameter accuracy of the GNSS rejection satellite in period q respectively; Represent the dynamic parameters and dynamic parameter accuracy of the anchor star during period q respectively; the dynamic parameters include the atmospheric drag coefficient, the tangential sine and cosine empirical acceleration coefficients, and the normal sine and cosine empirical acceleration coefficients; among them, the dynamic parameter accuracy Obtained by the following method:

[0032] Collect GNSS data of the anchor satellite and GNSS denial satellite before interference occurs, and then solve the dynamic parameters of the anchor satellite and GNSS denial satellite in the same period respectively;

[0033] The dynamic parameters of the anchor satellite and the GNSS rejection satellite in the same period are subtracted and the root mean square value is calculated, and the root mean square value or its magnitude is used as the accuracy of the dynamic parameters.

[0034] In the second aspect, a low-orbit satellite precise orbit determination system under GNSS denial conditions is provided, comprising:

[0035] The anchor satellite orbit determination module is used to obtain the GNSS data received by the onboard receiver of the anchor satellite, and use the dynamic orbit determination method to solve the precise orbit and dynamic parameters of the anchor satellite; the anchor satellite is a low-orbit satellite in the same constellation that is linked with the GNSS rejection satellite and is not subject to co-frequency interference;

[0036] The inter-satellite link ranging data acquisition module is used to obtain the inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite;

[0037] The GNSS denial satellite orbit determination module is used to solve the GNSS denial satellite orbit using the dynamic orbit determination method based on the precise orbit of the anchor satellite and the inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite.

[0038] Furthermore, the inter-satellite link ranging data of the GNSS denied satellite is obtained by the following method:

[0039] S21: Obtaining the original inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite;

[0040] S22: The following model is used to calculate the inter-satellite link ranging data error:

[0041] Assume that the original pseudo-range measurement received by star j from star i at time t1 is ρ ij (t1), the original pseudo-range measurement received by star i from star j at time t2 is ρ ji (t2), the observation equation is expressed as follows:

[0042]

[0043]

[0044] In the formula, R i , R j are the three-dimensional positions of star i and star j respectively; clk i 、clk j are the satellite clock errors of star i and star j respectively; c is the speed of light; Δt1 is the light time of the measurement signal from star i to star j, and Δt2 is the light time of the measurement signal from star j to star i; τ ij is the link equipment delay between the transmission of satellite i and the reception of satellite j; τ ji is the link equipment delay of the j-star transmission and the i-star reception; is the error correction term that can be accurately modeled in the one-way ranging from star i to star j; are the error correction terms that can be accurately modeled in the one-way ranging from the j-star to the i-star; the i-star and the j-star represent the anchor satellite and the GNSS rejection satellite respectively;

[0045] The two-way observations at different times are converted to the same time. Assuming that the pseudo-range measurements at times t1 and t2 are converted to the target time t0, we can obtain ρ ij (t0) and ρ ji (t0), then the corrected inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite can be expressed as follows:

[0046]

[0047] Among them, ρ(t0) is the corrected inter-satellite link ranging data between the anchor satellite and the GNSS denied satellite at time t0.

[0048] Furthermore, the GNSS rejection satellite orbit determination module sets a priori constraints on initial orbit parameters in the process of solving the GNSS rejection satellite orbit using the dynamic orbit determination method, and is expressed as follows:

[0049]

[0050] In the formula, x p , σ p represent the a priori initial orbit parameters and a priori initial orbit accuracy at the start time of the pth day respectively; They represent the orbit parameters and orbit accuracy at 24 o'clock one day before the interference, which are calculated using the GNSS data before the interference of the GNSS denial satellite; They represent the orbit parameters and orbit accuracy of 24 points on the p-1th day calculated based on the precise orbit of the anchor satellite and the inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite.

[0051] Furthermore, the GNSS rejection satellite orbit determination module sets a priori constraints on dynamic parameters in the process of solving the GNSS rejection satellite orbit using the dynamic orbit determination method, and is expressed as follows:

[0052]

[0053] In the formula, y q , R q represent the a priori dynamic parameters and a priori dynamic parameter accuracy of the GNSS rejection satellite in period q respectively; Represent the dynamic parameters and dynamic parameter accuracy of the anchor star during period q respectively; the dynamic parameters include the atmospheric drag coefficient, the tangential sine and cosine empirical acceleration coefficients, and the normal sine and cosine empirical acceleration coefficients; among them, the dynamic parameter accuracy Obtained by the following method:

[0054] Collect GNSS data of the anchor satellite and GNSS denial satellite before interference occurs, and then solve the dynamic parameters of the anchor satellite and GNSS denial satellite in the same period respectively;

[0055] The dynamic parameters of the anchor satellite and the GNSS rejection satellite in the same period are subtracted and the root mean square value is calculated, and the root mean square value or its magnitude is used as the accuracy of the dynamic parameters.

[0056] In a third aspect, an electronic terminal is provided, comprising:

[0057] a memory having a computer program stored thereon;

[0058] A processor is used to load and execute the computer program to implement the method for precise orbit determination of low-orbit satellites in GNSS denial conditions as described above.

[0059] In a fourth aspect, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the method for precise orbit determination of low-orbit satellites under GNSS denial conditions as described above is implemented.

[0060] The present invention proposes a method, system, terminal and medium for precise orbit determination of low-orbit satellites under GNSS denial conditions, which has the following beneficial effects:

[0061] (1) It is proposed to use low-orbit satellites in the low-orbit constellation that are not subject to co-frequency interference as anchor satellites to provide accurate space references for GNSS denial satellites. The orbit of the GNSS denial satellite is solved based on the precise orbit of the anchor satellite and the inter-satellite ranging data, thereby suppressing the orbit error divergence problem caused by orbit prediction. In the case of GNSS denial, precise orbit determination of low-orbit satellites that does not directly rely on GNSS satellites and ground monitoring stations is achieved. The data used only include the onboard GNSS data of a single anchor satellite and the data of a single inter-satellite link. Only the dynamic orbit determination method is used, and the implementation process is simple and the calculation amount is small.

[0062] (2) A method for a priori constraining the initial orbital parameters of the GNSS rejection satellite is proposed to reduce the correlation between the initial orbital parameters and the dynamic parameters and improve the estimation accuracy of the parameters to be estimated.

[0063] (3) Taking into account the similarities of structural materials and environment of adjacent satellites in the same batch, it is proposed to use the precise dynamic parameters of the anchor satellite as the prior dynamic parameters of the GNSS rejection satellite and impose reasonable constraints to achieve the short-term centimeter-level and long-term decimeter-level orbit determination of the GNSS rejection satellite under the condition of a single intersatellite link. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0065] Figure 1 This is a flow chart of a method for precise orbit determination of a low-orbit satellite in a GNSS denial situation provided by an embodiment of the present invention;

[0066] Figure 2 is a flow chart of a method for precise orbit determination of a low-orbit satellite in a GNSS denial situation provided by another embodiment of the present invention;

[0067] Figure 3 is a flow chart of a method for precise orbit determination of a low-orbit satellite in a GNSS denial situation provided by another embodiment of the present invention;

[0068] Figure 4 It is a flow chart of a method for precise orbit determination of a low-orbit satellite under GNSS denial conditions provided by another embodiment of the present invention. DETAILED DESCRIPTION

[0069] To make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be described in detail below. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other implementation methods obtained by ordinary technicians in this field without creative work belong to the scope of protection of the present invention.

[0070] When a large low-orbit constellation is performing communication, navigation and remote sensing and other operational tasks, the downlink signals broadcast by some low-orbit satellites have co-frequency interference with the onboard GNSS signals. The interfered low-orbit satellites are called GNSS denied satellites. Co-frequency interference makes it impossible for GNSS denied satellites to determine their orbits based on GNSS data. How to achieve precise orbit determination of GNSS denied satellites in this scenario becomes a problem. The unavailability of onboard GNSS data makes it impossible for GNSS denied satellites to use GNSS satellites as a reference. However, a relatively high-precision spatial reference and observation data are still required to achieve precise orbit determination of GNSS denied satellites. The present invention proposes to use low-orbit satellites in the constellation that are linked to GNSS denied satellites and are not subject to co-frequency interference as anchor satellites, providing a high-precision spatial reference for GNSS denied satellites. The precise orbit of the anchor satellite can be solved based on the onboard GNSS data, and the orbit of the GNSS denied satellite can be solved by combining the inter-satellite ranging data between the two.

[0071] Considering the intersatellite link load cost and power consumption, the low-orbit satellite orbit determination method proposed in the present invention is only based on a single intersatellite link. However, the geometric configuration of a single intersatellite link is single, and the estimated parameters directly calculated using the precise orbit of the anchor satellite and the intersatellite link data have a high correlation. The present invention proposes to constrain the priori initial orbit parameters and their accuracy to reduce the correlation between the initial orbit and the dynamic parameters. For the initial orbit parameters of the GNSS rejection satellite, the precise orbit (first day) and the solved orbit (subsequent arc segment) can be used as prior values ​​and constraints are imposed, but the constraints on its dynamic parameters also need to provide more accurate prior values. The low-orbit satellites manufactured and launched in the same batch have basically the same structure and materials, and the adjacent low-orbit satellites in the chain have the characteristics of comparable height and close distance, so the dynamic parameters of adjacent satellites in the chain are similar in theory. The present invention proposes that when the GNSS rejection satellite cannot accurately calculate the dynamic parameters, the precise dynamic parameters of the adjacent satellite in the chain, i.e., the anchor satellite, are used as its prior values ​​and constraints are imposed. The technical solution of the present invention is described in detail below in conjunction with specific embodiments.

[0072] Example 1

[0073] like Figure 1 As shown, this embodiment provides a method for precise orbit determination of a low-orbit satellite in a GNSS denial situation, comprising the following steps:

[0074] S1: Obtain the GNSS data received by the onboard receiver of the anchor satellite, and use the dynamic orbit determination method to solve the precise orbit and dynamic parameters of the anchor satellite; the anchor satellite is a low-orbit satellite in the same constellation that has established a link with the GNSS rejection satellite and is not subject to co-frequency interference.

[0075] For low-orbit satellite receivers that can receive dual-frequency data, the dual-frequency data are generally combined to eliminate the influence of ionospheric delay. For low-orbit satellites, the pseudorange and phase observation equations of the dual-frequency ionospheric-free combination (Ionospheric-Free, IF) can be expressed as:

[0076]

[0077] In the formula, s, r, and i represent GNSS satellites, LEO satellites, and frequencies, respectively. and Represent pseudorange and carrier phase observation values ​​respectively; is the geometric distance between the GNSS satellite and the LEO satellite, δt r and δt s are the LEO onboard receiver clock error and the GNSS satellite clock error, c is the speed of light in vacuum, b is the speed of light in vacuum, r,if , They represent the differential code bias (DCB) of the LEO receiver and GNSS satellite under the IF combination, are the phase deviations of the LEO receiver and the GNSS satellite under the IF combination, λ if , represents the phase wavelength and phase ambiguity under IF combination, represent the measurement noise of pseudorange and phase IF combined observations respectively.

[0078] From the low-orbit satellite dynamics model, it can be seen that the satellite acceleration is mainly related to the satellite position, velocity and dynamic parameters, so the satellite motion equation can be expressed as:

[0079]

[0080]

[0081] In the formula, X(t) represents the state of the satellite at time t, including position r(t), speed Dynamic parameters p(t). Based on the above formula, the satellite position and velocity at any time can be obtained by numerical integration when the initial state of the satellite is known. The essence of precise orbit determination of low-orbit satellites is to use observation data to calculate the satellite state at the initial time (that is, the initial orbit parameters and the accuracy of the corresponding parameters, the orbit parameters include position and velocity) and dynamic parameters.

[0082] Combining the motion equation and observation equation, batch least squares processing can be used to solve the satellite state and dynamic parameters at the initial moment. Then numerical integration can be performed to obtain the satellite state and corresponding dynamic parameters of the entire arc of orbit determination.

[0083] S2: Obtain the inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite. Specifically include:

[0084] S21: Obtaining the original inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite;

[0085] S22: The following model is used to calculate the inter-satellite link ranging data error:

[0086] Assume that the original pseudo-range measurement received by star j from star i at time t1 is ρ ij (t1), the original pseudo-range measurement received by star i from star j at time t2 is ρ ji (t2), the observation equation is expressed as follows:

[0087]

[0088]

[0089] In the formula, R i , R j are the three-dimensional positions of star i and star j respectively; clk i 、clk j are the satellite clock errors of star i and star j respectively; c is the speed of light; Δt1 is the light time of the measurement signal from star i to star j, and Δt2 is the light time of the measurement signal from star j to star i; τ ij is the link equipment delay between the transmission of satellite i and the reception of satellite j; τ ji is the link equipment delay of the j-star transmission and the i-star reception; is the error correction term that can be accurately modeled in the one-way ranging from star i to star j; are the error correction terms that can be accurately modeled in the one-way ranging from the j-star to the i-star; the i-star and the j-star represent the anchor satellite and the GNSS rejection satellite respectively;

[0090] The two-way observations at different times are converted to the same time. Assuming that the pseudo-range measurements at times t1 and t2 are converted to the target time t0, we can obtain ρ ij (t0) and ρ ji (t0), then the corrected inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite can be expressed as follows:

[0091]

[0092] Among them, ρ(t0) is the corrected inter-satellite link ranging data between the anchor satellite and the GNSS rejection satellite at time t0. The above formula also includes the error correction term, where and can be accurately modeled, τ ij and τ ji It is the link equipment delay, which is a constant in the short term and needs to be calibrated separately in the service processing algorithm.

[0093] S3: Based on the precise orbit of the anchor satellite and the inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite, the dynamic orbit determination method is used to solve the GNSS denial satellite orbit.

[0094] Assume that satellite i is an anchor satellite and satellite j is a GNSS denial satellite, t k The intersatellite link observation equation at time can be simply expressed as:

[0095] Y(t k )=G(X i，k , P i，k , X j，k , P j，k )+ε k

[0096] Among them, Y(t k ) is t kThe intersatellite link ranging value at time, G(·) is the nonlinear function expression in the observation equation; X i,k , and X j,k are the orbital parameters of the anchor satellite and the GNSS denial satellite, including t k The three-dimensional position and velocity of the satellite at each moment, P i,k and P j,k They represent the dynamic parameters of the anchor satellite and the GNSS rejection satellite, including the atmospheric drag coefficient, empirical acceleration coefficient, etc.; ε k The noise of the intersatellite link is measured. The orbital parameters and dynamic parameters of the anchor satellite have been obtained by the onboard GNSS orbit determination method.

[0097] Assume that the state transfer matrix of the low-orbit satellite is ψ(t k ,t0), then the corresponding strain equation is

[0098]

[0099] in, They are respectively the GNSS denial satellites at t k The position, velocity and acceleration at the moment, I is the unit matrix.

[0100] According to the motion equation and variational equation of low-orbit satellites, their state transfer matrix ψ(t k ,t0), satisfies the following formula:

[0101] x' j,k =Ψ(t k ,t0)x' j,0

[0102] Among them, x' j,k t for GNSS denial satellite k Orbital parameter correction at the moment, x' j,0 is the correction of the initial orbital parameters of the satellite. Based on the above formula and the intersatellite link observation equation, the orbital and dynamic parameters of the GNSS rejection satellite can be solved based on the least squares estimation method. The parameter plus the corresponding correction is equal to the solved parameter. The least squares solution is the parameter correction. Satellite orbit determination is an iterative process of orbit improvement. When the correction is less than the threshold, the iteration stops.

[0103] This embodiment proposes a method for precise orbit determination of low-orbit satellites in GNSS denial conditions, and proposes to use a low-orbit satellite in the low-orbit constellation that is not subject to co-frequency interference as an anchor satellite to provide an accurate space reference for the GNSS denied satellite. The orbit of the GNSS denied satellite is solved based on the precise orbit of the anchor satellite and the inter-satellite ranging data, thereby suppressing the orbit error divergence problem caused by orbit prediction. In GNSS denial conditions, precise orbit determination of low-orbit satellites that does not directly rely on GNSS satellites and ground monitoring stations is achieved. The data used only include the onboard GNSS data of a single anchor satellite and the data of a single inter-satellite link, and only the dynamic orbit determination method is used. The implementation process is simple and the amount of calculation is small.

[0104] Example 2

[0105] like Figure 2 As shown, this embodiment provides a method for precise orbit determination of a low-orbit satellite under GNSS denial conditions. The difference between this embodiment and embodiment 1 is that, based on embodiment 1, in the process of solving the orbit of the GNSS denied satellite by using the dynamic orbit determination method based on the precise orbit of the anchor satellite and the inter-satellite link ranging data between the anchor satellite and the GNSS denied satellite, a priori constraints on the initial orbit parameters are set and expressed as follows:

[0106]

[0107] In the formula, x p , σ p represent the a priori initial orbit parameters and a priori initial orbit accuracy at the start time of the pth day respectively; They represent the orbit parameters and orbit accuracy at 24 o'clock one day before the interference, which are calculated using the GNSS data before the interference of the GNSS denial satellite; They represent the orbit parameters and orbit accuracy of 24 points on the p-1th day calculated based on the precise orbit of the anchor satellite and the inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite.

[0108] Taking into account the intersatellite link payload cost and power consumption reasons, the low-orbit satellite orbit determination method proposed in the present invention is only based on a single intersatellite link. However, the geometric configuration of a single intersatellite link is single, and the estimated parameters directly calculated using the precise orbit of the anchor satellite and the intersatellite link ranging data have a high correlation. This embodiment proposes to constrain the a priori initial orbit parameters and their accuracy. For the initial orbit parameters of the GNSS rejection satellite, the precise orbit (first day) and the solved orbit (subsequent arc segment) are used as a priori values ​​and constraints are imposed to reduce the correlation between the initial orbit and the dynamic parameters and improve the accuracy of parameter estimation.

[0109] Example 3

[0110] like Figure 3As shown, this embodiment provides a method for precise orbit determination of a low-orbit satellite under GNSS denial conditions. The difference between this embodiment and embodiment 1 is that, based on embodiment 1, in the process of solving the orbit of the GNSS denied satellite by using the dynamic orbit determination method based on the precise orbit of the anchor satellite and the inter-satellite link ranging data between the anchor satellite and the GNSS denied satellite, a priori constraints on the dynamic parameters are set and expressed as follows:

[0111]

[0112] In the formula, y q , R q represent the a priori dynamic parameters and a priori dynamic parameter accuracy of the GNSS rejection satellite in period q respectively; They represent the dynamic parameters and dynamic parameter accuracy of the anchor star in time period q respectively; the dynamic parameters include the atmospheric drag coefficient, the tangential sine and cosine empirical acceleration coefficients, and the normal sine and cosine empirical acceleration coefficients.

[0113] The dynamic parameters of adjacent low-orbit satellites in the same batch are highly consistent. Therefore, this embodiment considers using the precise dynamic parameters of adjacent satellites, i.e., anchor satellites, as the prior dynamic parameters of the GNSS rejection satellites and imposes constraints.

[0114] Among them, the accuracy of dynamic parameters The determination is made by quantitatively analyzing the differences in dynamic parameters between the anchor satellite and the GNSS rejection satellite, and the specific method is as follows:

[0115] Collect GNSS data of the anchor satellite and the GNSS rejection satellite before interference occurs, and then use the method described in the above step S1 to respectively calculate the dynamic parameters of the anchor satellite and the GNSS rejection satellite in the same period;

[0116] The dynamic parameters of the anchor satellite and the GNSS rejection satellite in the same period are subtracted and the root mean square value (RMS value) is calculated, and the root mean square value or its magnitude is used as the accuracy of the dynamic parameters.

[0117] Table 1 shows the differences in dynamic parameters between the anchor satellite and the GNSS rejection satellite in an example, where Cd represents the atmospheric drag coefficient, EMPSIT, EMPCOT, EMPSIN and EMPCON represent the empirical sine and cosine acceleration coefficients in the tangential and normal directions, respectively.

[0118] Table 1

[0119]

[0120]

[0121] In this embodiment, the RMS value is used as an example to illustrate the accuracy of dynamic parameters. Therefore, the prior constraint error of the atmospheric drag coefficient in this scheme is 0.1, and the prior constraint error of the empirical acceleration coefficient is 1e-9m / s 2 .

[0122] Taking into account the similarities of structural materials and environment of adjacent satellites in the same batch, it is proposed to use the precise dynamic parameters of the anchor satellite as the prior dynamic parameters of the GNSS rejection satellite and impose reasonable constraints to achieve short-term centimeter-level and long-term decimeter-level orbit determination of the GNSS rejection satellite under the condition of a single intersatellite link.

[0123] Example 4

[0124] like Figure 4 As shown, this embodiment provides a method for precise orbit determination of low-orbit satellites under GNSS denial conditions, which differs from Embodiment 1 in that, based on Embodiment 1, in the process of solving the orbit of the GNSS denied satellite by using the dynamic orbit determination method based on the precise orbit of the anchor satellite and the inter-satellite link ranging data between the anchor satellite and the GNSS denied satellite, a priori constraints on the initial orbit parameters and a priori constraints on the dynamic parameters are set at the same time to achieve precise orbit determination of the GNSS denied satellite.

[0125] The method for setting the a priori constraints of the initial orbital parameters is as described in the above-mentioned embodiment 2, and the method for setting the a priori constraints of the dynamic parameters is as described in the above-mentioned embodiment 3. The initial orbital parameters and the dynamic parameters are constrained a priori at the same time, which significantly reduces the correlation between the parameters, improves the separability of the parameters and the estimation accuracy, and realizes the short-term centimeter-level and long-term decimeter-level orbit determination of the GNSS rejection satellite under the condition of a single inter-satellite link, which is equivalent to the accuracy of orbit determination based on satellite-borne GNSS data.

[0126] Example 5

[0127] This embodiment provides a low-orbit satellite precise orbit determination system in a GNSS denial situation, including:

[0128] The anchor satellite orbit determination module is used to obtain the GNSS data received by the onboard receiver of the anchor satellite, and use the dynamic orbit determination method to solve the precise orbit and dynamic parameters of the anchor satellite; the anchor satellite is a low-orbit satellite in the same constellation that is linked with the GNSS rejection satellite and is not subject to co-frequency interference;

[0129] The inter-satellite link ranging data acquisition module is used to obtain the inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite;

[0130] The GNSS denial satellite orbit determination module is used to solve the GNSS denial satellite orbit using the dynamic orbit determination method based on the precise orbit of the anchor satellite and the inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite.

[0131] Specifically, the inter-satellite link ranging data of the GNSS denied satellite is obtained by the following method:

[0132] S21: Obtaining the original inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite;

[0133] S22: The following model is used to calculate the inter-satellite link ranging data error:

[0134] Assume that the original pseudo-range measurement received by star j from star i at time t1 is ρ ij (t1), the original pseudo-range measurement received by star i from star j at time t2 is ρ ji (t2), the observation equation is expressed as follows:

[0135]

[0136]

[0137] In the formula, R i , R j are the three-dimensional positions of star i and star j respectively; clk i 、clk j are the satellite clock errors of star i and star j respectively; c is the speed of light; Δt1 is the light time of the measurement signal from star i to star j, and Δt2 is the light time of the measurement signal from star j to star i; τ ij is the link equipment delay between the transmission of satellite i and the reception of satellite j; τ ji is the link equipment delay of the j-star transmission and the i-star reception; is the error correction term that can be accurately modeled in the one-way ranging from star i to star j; are the error correction terms that can be accurately modeled in the one-way ranging from the j-star to the i-star; the i-star and the j-star represent the anchor satellite and the GNSS rejection satellite respectively;

[0138] The two-way observations at different times are converted to the same time. Assuming that the pseudo-range measurements at times t1 and t2 are converted to the target time t0, we can obtain ρ ij (t0) and ρ ji (t0), then the corrected inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite can be expressed as follows:

[0139]

[0140] Among them, ρ(t0) is the corrected inter-satellite link ranging data between the anchor satellite and the GNSS denied satellite at time t0.

[0141] In some preferred embodiments, the GNSS rejection satellite orbit determination module sets a priori constraints on initial orbit parameters when solving the GNSS rejection satellite orbit using the dynamic orbit determination method, and is expressed as follows:

[0142]

[0143] In the formula, x p , σ p represent the a priori initial orbit parameters and a priori initial orbit accuracy at the start time of the pth day respectively; They represent the orbit parameters and orbit accuracy at 24 o'clock one day before the interference, which are calculated using the GNSS data before the interference of the GNSS denial satellite; They represent the orbit parameters and orbit accuracy of 24 points on the p-1th day calculated based on the precise orbit of the anchor satellite and the inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite.

[0144] In some preferred embodiments, the GNSS rejection satellite orbit determination module sets a priori constraints on dynamic parameters when solving the GNSS rejection satellite orbit using the dynamic orbit determination method, and is expressed as follows:

[0145]

[0146] In the formula, y q , R q represent the a priori dynamic parameters and a priori dynamic parameter accuracy of the GNSS rejection satellite in period q respectively; Represent the dynamic parameters and dynamic parameter accuracy of the anchor star during period q respectively; the dynamic parameters include the atmospheric drag coefficient, the tangential sine and cosine empirical acceleration coefficients, and the normal sine and cosine empirical acceleration coefficients; among them, the dynamic parameter accuracy Obtained by the following method:

[0147] Collect GNSS data of the anchor satellite and GNSS denial satellite before interference occurs, and then solve the dynamic parameters of the anchor satellite and GNSS denial satellite in the same period respectively;

[0148] The dynamic parameters of the anchor satellite and the GNSS rejection satellite in the same period are subtracted and the root mean square value is calculated, and the root mean square value or its magnitude is used as the accuracy of the dynamic parameters.

[0149] Example 6

[0150] This embodiment provides an electronic terminal, including:

[0151] a memory having a computer program stored thereon;

[0152] A processor is used to load and execute the computer program to implement the method for precise orbit determination of low-orbit satellites under GNSS denial conditions as described in any one of the aforementioned embodiments 1 to 4.

[0153] Example 7

[0154] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the method for precise orbit determination of low-orbit satellites in a GNSS denial situation as described in any one of the aforementioned embodiments 1 to 4 is implemented.

[0155] It can be understood that the same or similar parts of the above embodiments can be referenced to each other, and the contents not described in detail in some embodiments can refer to the same or similar contents in other embodiments.

[0156] It should be understood that the functional unit modules in various embodiments of the present invention may be concentrated in one processing unit, or each unit module may exist physically separately, or two or more unit modules may be integrated in one unit module, and may be implemented in the form of hardware or software.

[0157] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0158] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0159] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0160] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0161] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, segment or portion of code that includes one or more executable instructions for implementing steps of a specific logical function or process, and the scope of the preferred embodiments of the present invention includes alternative implementations in which functions may not be performed in the order shown or discussed, which should be understood by those skilled in the art to which the embodiments of the present invention belong.

[0162] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A method for precise orbit determination of low-orbit satellites in GNSS denial conditions, characterized in that: The steps include: The GNSS data received by the onboard receiver of the anchor satellite is obtained, and the precise orbit and dynamic parameters of the anchor satellite are solved by the dynamic orbit determination method; the anchor satellite is a low-orbit satellite in the same constellation that is linked with the GNSS rejection satellite and is not subject to co-frequency interference; Obtain inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite; Based on the precise orbit of the anchor satellite and the inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite, the orbit of the GNSS denial satellite is solved by the dynamic orbit determination method.

2. The method for precise orbit determination of low-orbit satellites in GNSS denial conditions according to claim 1, characterized in that: The inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite is obtained by the following method: S21: Obtaining the original inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite; S22: The following model is used to calculate the inter-satellite link ranging data error: Assume that the original pseudo-range measurement received by star j from star i at time t1 is ρ ij (t1), the original pseudo-range measurement received by star i from star j at time t2 is ρ ji (t2), the observation equation is expressed as follows: In the formula, R i , R j are the three-dimensional positions of star i and star j respectively; clk i 、clk j are the satellite clock errors of star i and star j respectively; c is the speed of light; Δt1 is the light time of the measured signal from star i to star j, and Δt2 is the light time of the measured signal from star j to star i; τ ij is the link equipment delay between the transmission of satellite i and the reception of satellite j; τ ji is the link equipment delay of the j-star transmission and the i-star reception; is the error correction term that can be accurately modeled in the one-way ranging from star i to star j; are the error correction terms that can be accurately modeled in the one-way ranging from the j-star to the i-star; the i-star and the j-star represent the anchor satellite and the GNSS rejection satellite respectively; The two-way observations at different times are converted to the same time. Assuming that the pseudo-range measurements at times t1 and t2 are converted to the target time t0, we can obtain ρ ij (t0) and ρ ji (t0), then the corrected inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite can be expressed as follows: Among them, ρ(t0) is the corrected inter-satellite link ranging data between the anchor satellite and the GNSS denied satellite at time t0.

3. The method for precise orbit determination of low-orbit satellites in GNSS denial conditions according to claim 1, characterized in that: In the process of solving the GNSS rejection satellite orbit using the dynamic orbit determination method, the prior constraints of the initial orbit parameters are set and expressed as follows: In the formula, x p , σ p represent the a priori initial orbit parameters and a priori initial orbit accuracy at the start time of the pth day respectively; They represent the orbit parameters and orbit accuracy at 24 o'clock one day before the interference, which are calculated using the GNSS data before the interference of the GNSS denial satellite; They represent the orbit parameters and orbit accuracy of 24 points on the p-1th day calculated based on the precise orbit of the anchor satellite and the inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite.

4. The method for precise orbit determination of low-orbit satellites in GNSS denial conditions according to any one of claims 1 to 3, characterized in that: In the process of solving the orbit of the GNSS rejection satellite using the dynamic orbit determination method, the prior constraints of the dynamic parameters are set and expressed as follows: In the formula, y q , R q represent the a priori dynamic parameters and a priori dynamic parameter accuracy of the GNSS rejection satellite in period q respectively; represent the dynamic parameters and dynamic parameter accuracy of the anchor star in time period q respectively; among which, the dynamic parameter accuracy Obtained by the following method: Collect GNSS data of the anchor satellite and GNSS denial satellite before interference occurs, and then solve the dynamic parameters of the anchor satellite and GNSS denial satellite in the same period respectively; The dynamic parameters of the anchor satellite and the GNSS rejection satellite in the same period are subtracted and the root mean square value is calculated, and the root mean square value or its magnitude is used as the accuracy of the dynamic parameters.

5. A low-orbit satellite precise orbit determination system under GNSS denial conditions, characterized in that: include: The anchor satellite orbit determination module is used to obtain the GNSS data received by the onboard receiver of the anchor satellite, and use the dynamic orbit determination method to solve the precise orbit and dynamic parameters of the anchor satellite; the anchor satellite is a low-orbit satellite in the same constellation that is linked with the GNSS rejection satellite and is not subject to co-frequency interference; The inter-satellite link ranging data acquisition module is used to obtain the inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite; The GNSS denial satellite orbit determination module is used to solve the GNSS denial satellite orbit using the dynamic orbit determination method based on the precise orbit of the anchor satellite and the inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite.

6. The low-orbit satellite precise orbit determination system in GNSS denial conditions according to claim 5, characterized in that: The inter-satellite link ranging data of the GNSS denial satellite is obtained by the following method: S21: Obtaining the original inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite; S22: The following model is used to calculate the inter-satellite link ranging data error: Assume that the original pseudo-range measurement received by star j from star i at time t1 is ρ ij (t1), the original pseudo-range measurement received by star i from star j at time t2 is ρ ji (t2), the observation equation is expressed as follows: In the formula, R i , R j are the three-dimensional positions of star i and star j respectively; clk i 、clk j are the satellite clock errors of star i and star j respectively; c is the speed of light; Δt1 is the light time of the measurement signal from star i to star j, and Δt2 is the light time of the measurement signal from star j to star i; τ ij is the link equipment delay between the transmission of satellite i and the reception of satellite j; τ ji is the link equipment delay of the j-star transmission and the i-star reception; is the error correction term that can be accurately modeled in the one-way ranging from star i to star j; are the error correction terms that can be accurately modeled in the one-way ranging from the j-star to the i-star; the i-star and the j-star represent the anchor satellite and the GNSS rejection satellite respectively; The two-way observations at different times are converted to the same time. Assuming that the pseudo-range measurements at times t1 and t2 are converted to the target time t0, we can obtain ρ ij (t0) and ρ ji (t0), then the corrected inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite can be expressed as follows: Among them, ρ(t0) is the corrected inter-satellite link ranging data between the anchor satellite and the GNSS denied satellite at time t0.

7. The low-orbit satellite precise orbit determination system in GNSS denial conditions according to claim 5, characterized in that: The GNSS rejection satellite orbit determination module sets a priori constraints on the initial orbit parameters when solving the GNSS rejection satellite orbit using the dynamic orbit determination method, and is expressed as follows: In the formula, x p , σ p represent the a priori initial orbit parameters and a priori initial orbit accuracy at the start time of the pth day respectively; They represent the orbit parameters and orbit accuracy at 24 o'clock one day before the interference, which are calculated using the GNSS data before the interference of the GNSS denial satellite; They represent the orbit parameters and orbit accuracy of 24 points on the p-1th day calculated based on the precise orbit of the anchor satellite and the inter-satellite link ranging data between the anchor satellite and the GNSS denial satellite.

8. The low-orbit satellite precise orbit determination system in GNSS denial conditions according to claim 5, characterized in that: The GNSS rejection satellite orbit determination module sets a priori constraints on dynamic parameters in the process of solving the GNSS rejection satellite orbit using the dynamic orbit determination method, and is expressed as follows: In the formula, y q , R q represent the a priori dynamic parameters and a priori dynamic parameter accuracy of the GNSS rejection satellite in period q respectively; represent the dynamic parameters and dynamic parameter accuracy of the anchor star in time period q respectively; among which, the dynamic parameter accuracy Obtained by the following method: Collect GNSS data of the anchor satellite and GNSS denial satellite before interference occurs, and then solve the dynamic parameters of the anchor satellite and GNSS denial satellite in the same period respectively; The dynamic parameters of the anchor satellite and the GNSS rejection satellite in the same period are subtracted and the root mean square value is calculated, and the root mean square value or its magnitude is used as the accuracy of the dynamic parameters.

9. An electronic terminal, characterized in that: include: a memory having a computer program stored thereon; A processor is used to load and execute the computer program to implement the method for precise orbit determination of low-orbit satellites in GNSS denial conditions as described in any one of claims 1 to 4.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for precise orbit determination of low-orbit satellites in GNSS denial conditions as described in any one of claims 1 to 4 is implemented.

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