Doppler and pseudo-range fusion positioning method and system for low-orbit satellite conduction signals

Abstract

The invention discloses a Doppler and pseudo-range fusion positioning method and system for low-orbit satellite conduction signals, and relates to satellite positioning. The method comprises the steps that a Doppler and pseudo-range observation equation is established; performing least square residual calculation on the calculated Doppler and pseudo-range theoretical values and the observed Doppler and pseudo-range measured values, and taking a grid center point coordinate corresponding to a two-norm minimum value as a receiver position initial value; performing Taylor series expansion on the Doppler and pseudo-range observation equation, and representing a state updating matrix by using the established state transition matrix and receiver position, clock error and frequency offset correction; the inverse matrix of the observation noise covariance is used as a weight matrix to be distributed to the state transition matrix; and iterating the initial position value of the receiver, updating the state updating matrix, and stopping iteration until the two-norm of the residual solution is smaller than a set threshold value, so as to obtain the position, clock error and frequency offset results of the receiver. According to the method, the low-orbit satellite positioning algorithm model can be optimized, the convergence time is shortened, and the positioning precision is improved.

Description

Technical Field

[0001] This application relates to the field of satellite positioning technology, and particularly to a method and system for fusing Doppler and pseudorange of low-earth orbit satellite communication and navigation signals for positioning. Background Art

[0002] Low-earth orbit satellites use communication channels to broadcast communication and navigation integrated signals for navigation enhancement services. Their signals have characteristics such as high ground power, short transmission delay, and wide coverage. Receivers can simultaneously obtain Doppler frequency shift and pseudorange measurement values, and can independently perform navigation positioning and timing without relying on GNSS in special cases, which will effectively broaden the application scenarios of low-earth orbit satellites and improve their application value in complex environments.

[0003] Currently, low-earth orbit satellite navigation positioning methods often use Doppler independent positioning combined with other algorithm optimization means. Patent application CN 106772502 A discloses a Doppler positioning and calculation method for a low-earth orbit satellite backup navigation system. This method is applicable to any number of visible stars, combines large-area grid search for rough positioning with Newton least squares iterative calculation, and smooths the multi-epoch positioning and calculation results after removing gross errors to further improve positioning accuracy.

[0004] Patent CN 113589337 B discloses a method and system for single satellite positioning of communication and navigation integrated low-earth orbit satellites. This method first performs a large-area grid search to obtain the calculation initial value, then uses the Newton least squares iterative algorithm to solve the residual solution of single satellite Doppler positioning, and finally uses the Newton downhill method for recursion to expand the initial value range and enhance recursive convergence, ensuring that the single satellite positioning result can be calculated.

[0005] In existing low-earth orbit satellite navigation positioning methods, Doppler frequency shift is often used for position calculation. However, Doppler frequency shift alone has low positioning accuracy, long convergence time, high requirements for frequency measurement accuracy, and cannot effectively estimate the receiver clock error. Summary of the Invention

[0006] An embodiment of this application provides a method and system for fusing Doppler and pseudorange of low-earth orbit satellite communication and navigation signals, establishes a method for fusing Doppler and pseudorange for positioning, estimates the receiver position, clock error, and frequency offset as unknowns, improves the timing accuracy and frequency measurement accuracy, and adds the inverse matrix of the observation noise covariance as the weight matrix to further optimize the low-earth orbit satellite positioning algorithm model, shorten the convergence time, and improve the positioning accuracy.

[0007] An embodiment of this application provides a method for fusing Doppler and pseudorange of low-earth orbit satellite communication and navigation signals, including:

[0008] Obtain the ephemeris information of the visible low-earth orbit satellites of the receiver at the same moment, and calculate their three-dimensional position coordinates and velocities in the Earth-Centered Earth-Fixed (ECEF) coordinate system. Also, obtain the Doppler and pseudorange observables of the low-earth orbit satellite communication and navigation signals, and establish the Doppler and pseudorange observation equations;

[0009] Divide the satellite coverage area into grids according to longitude and latitude, calculate the theoretical values of Doppler and pseudorange between the grid center points and the satellites respectively, perform least-squares residual calculations with the observed Doppler and pseudorange measurement values, and take the grid center point coordinates corresponding to the minimum value of the two-norm as the initial value of the receiver position;

[0010] Perform Taylor series expansion on the Doppler and pseudorange observation equations, establish the state transition matrix using the coefficients of the first derivative, and represent the state update matrix using the state transition matrix and the receiver position, clock error, and frequency offset correction amount;

[0011] Assign the inverse matrix of the observation noise covariance as the weight matrix to the state transition matrix;

[0012] Iterate on the initial value of the receiver position and update the state update matrix until the two-norm of the residual solution is less than the set threshold, and then stop the iteration to obtain the receiver position, clock error, and frequency offset results.

[0013] An embodiment of the present application also proposes a Doppler and pseudorange fusion positioning system for low-earth orbit satellite communication and navigation signals, including a processor and a memory. A computer program is stored on the memory, and when the computer program is executed by the processor, it implements the steps of the aforementioned Doppler and pseudorange fusion positioning method for low-earth orbit satellite communication and navigation signals.

[0014] The present application establishes a Doppler and pseudorange fusion positioning method, estimates the receiver position, clock error, and frequency offset as unknowns, improves the timing accuracy and frequency measurement accuracy, adds the inverse matrix of the observation noise covariance as the weight matrix, further optimizes the low-earth orbit satellite positioning algorithm model, shortens the convergence time, and improves the positioning accuracy.

[0015] The above description is only an overview of the technical solution of the present application. In order to be able to understand the technical means of the present application more clearly, it can be implemented according to the content of the specification. And in order to make the above and other purposes, features, and advantages of the present application more obvious and understandable, the following specifically illustrates the specific embodiments of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] By reading the detailed description of the preferred embodiments below, various other advantages and benefits will become clear to those of ordinary skill in the art. The drawings are only for the purpose of showing the preferred embodiments and are not considered to be a limitation of the present application. And throughout the drawings, the same reference numerals are used to represent the same components. In the drawings:

[0017] Figure 1 Schematic of the basic process of the Doppler and pseudorange fusion positioning method according to an embodiment of the present application. Detailed implementation manners

[0018] Hereinafter, exemplary embodiments of the present disclosure will be described in more detail with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so that the present disclosure can be more thoroughly understood and the scope of the present disclosure can be fully conveyed to those skilled in the art.

[0019] An embodiment of the present application provides a Doppler and pseudorange fusion positioning method for low-earth orbit satellite communication and navigation signals, as Figure 1 shown, including:

[0020] In step S101, obtain the ephemeris information of the visible low-earth orbit satellites of the receiver at the same moment, and calculate their three-dimensional position coordinates and velocities in the Earth-centered Earth-fixed coordinate system (ECEF). In addition, obtain the Doppler and pseudorange observables of the low-earth orbit satellite communication and navigation signals, and establish Doppler and pseudorange observation equations.

[0021] In step S102, use the large-area grid search method based on Doppler and pseudorange to calculate the initial value of the receiver. Specifically, divide the satellite coverage area into grids according to longitude and latitude, calculate the theoretical values of Doppler and pseudorange between the grid center points and the satellites respectively, perform least-squares residual calculation with the observed Doppler and pseudorange measurement values, and take the grid center point coordinates corresponding to the minimum value of the two-norm as the initial value of the receiver position.

[0022] In step S103, perform Taylor series expansion on the Doppler and pseudorange observation equations, establish a state transition matrix using the coefficients of the first derivative, and represent the state update matrix using the state transition matrix and the receiver position, clock error, and frequency offset correction amount.

[0023] In step S104, assign the inverse matrix of the observation noise covariance as the weight matrix to the state transition matrix to improve the weights between different observables.

[0024] In step S105, iterate on the initial value of the receiver position and update the state update matrix until the two-norm of the residual solution is less than the set threshold, and then stop the iteration to obtain the receiver position, clock error, and frequency offset results.

[0025] In some embodiments, establishing the Doppler and pseudorange observation equations includes:

[0026] Specify that the receiver is stationary on the ground, then the Doppler and pseudorange positioning observation equations are expressed as:

[0027]

[0028] Among them, the first three equations are Doppler positioning observation equations, and the last three equations are pseudorange positioning observation equations. d i (u) and ρ i (u) (i = 1, 2,..., n) respectively represent the Doppler and pseudorange measurement values of the receiver observing the i-th satellite, and n is the total number of satellites that the receiver can observe simultaneously. represents the running speed of the i-th satellite; c is the speed of light; represents the position coordinates of the i-th satellite; r u = [x u y u z u T represents the receiver position coordinates; f s represents the satellite signal transmission frequency; is the receiver frequency offset; ∈ di is the Doppler measurement noise of the i-th satellite; Δt u represents the receiver clock error; t represents the current signal time of the receiver; t0 represents the initial value time of the receiver signal; ∈ ρi is the pseudorange measurement noise of the i-th satellite. are the 5 unknowns to be solved for the receiver.

[0029] Before performing the least squares positioning solution, considering that the orbital altitude of the low-earth orbit satellite is much smaller than the radius of the earth, the initial value of the receiver position is specified, otherwise the positioning result cannot converge.

[0030] In some embodiments, the satellite coverage area is divided into grids by longitude and latitude, and the theoretical values of Doppler and pseudorange between the grid center point and the satellite are calculated respectively, and the least squares residual calculation is performed with the observed Doppler and pseudorange measurement values. The grid center point coordinates corresponding to the minimum value of the two-norm are taken as the receiver initial value, including:

[0031] The satellite coverage area is divided into m grids of N°×N° by longitude and latitude;

[0032] Calculate the longitude and latitude coordinates of the grid center point and give the corresponding altitude value;

[0033] Convert the longitude-latitude-altitude value to the space rectangular coordinates in ECEF;

[0034] According to the selected space rectangular coordinates of the grid center point, the satellite position and speed at a certain moment, calculate the theoretical values of Doppler and pseudorange between the grid center point and the satellite respectively, and perform the least squares residual calculation with the observed Doppler and pseudorange measurement values:

[0035]

[0036] ​

[0037] Among them, r j =[x j y j z j ] T is the coordinate of the jth grid center point (j=1, 2, ..., m); d i (u j ) and ρ i (u j ) is the theoretical calculated value of Doppler and pseudorange of the jth grid of the ith satellite;

[0038] The binary norm values of ΔX at different grid center points are calculated in turn, and the grid center point coordinates corresponding to the minimum residual value are taken as the initial value of the receiver position.

[0039] In some embodiments, performing Taylor series expansion on the Doppler and pseudorange observation equations includes:

[0040] Define the initial value as Expand the observation equation by Taylor series to get:

[0041]

[0042]

[0043] In the formula, is a high-order infinitesimal, where:

[0044]

[0045] Among them, r u0 =[x u0 y u0 z u0 ] T represents the initial value of the receiver position, and the state transfer matrix H can be expressed as:

[0046]

[0047] In some embodiments, performing Taylor series expansion on the Doppler and pseudorange observation equations further comprises:

[0048] After the user receives n low-orbit satellites at the same time, multiple Doppler and pseudo-range observation equations are combined to express the state update matrix as:

[0049]

[0050] in: ε is the residual vector, k is the number of iterations, is the estimated value of u after the kth iteration.

[0051] In some embodiments, assigning the inverse matrix of the observation noise covariance as the weight matrix to the state transition matrix includes:

[0052] Taking the inverse of the observation noise covariance matrix as the weight matrix, the observation noise covariance matrix R is expressed as:

[0053]

[0054] The corresponding weight matrix W is expressed as:

[0055]

[0056] The transition matrix with the weight matrix added is expressed as:

[0057] H w = H T WH

[0058] Then Δu k is expressed as:

[0059] Δu k = (H w T H w ) -1 H w T ΔX = ((H T WH) T (H T WH)) -1 (H T WH) T ΔX.

[0060] In some embodiments, iterating on the initial value of the receiver position and updating the state update matrix includes: substituting the initial value of the receiver position calculated by the large-area grid, after iterating k times, the two-norm of Δu k is less than a certain threshold and the iteration stops. At this time, u k+1 = Δu k + Δu k is used as the final results of the receiver position, clock error, and frequency offset.

[0061] The method of this application establishes a theoretical model for Doppler and pseudorange fusion positioning. Compared with single-Doppler positioning, it optimally estimates the receiver clock error and frequency offset, effectively improving the timing accuracy and frequency measurement accuracy. The method of this application combines the measured values and theoretical values of Doppler and pseudorange, and uses the large-area grid search method to determine the initial position of the receiver, ensuring that the positioning result can effectively converge and improving the positioning and timing efficiency.

[0062] This application assigns the inverse matrix of the observation noise covariance as the weight matrix to the state transition matrix, adjusts the weights during the fusion calculation of Doppler and pseudorange, reduces the interference of the singular matrix on the solution, and significantly improves the accuracy and robustness of position calculation.

[0063] An embodiment of this application also proposes a Doppler and pseudorange fusion positioning system for low-earth orbit satellite communication and navigation signals, including a processor and a memory. A computer program is stored on the memory, and when the computer program is executed by the processor, the steps of the Doppler and pseudorange fusion positioning method for low-earth orbit satellite communication and navigation signals as described above are implemented.

[0064] It should be noted that in each embodiment of this application, the terms "include", "comprise" or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not explicitly listed, or further includes elements inherent to such a process, method, article or device. Without further limitations, an element defined by the statement "including one..." does not exclude the existence of additional identical elements in the process, method, article or device including that element.

[0065] The serial numbers of the embodiments of this application above are only for description and do not represent the advantages or disadvantages of the embodiments.

[0066] Through the description of the above embodiments, those skilled in the art can clearly understand that the above embodiment methods can be implemented by means of software plus a necessary general hardware platform. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on such an understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disc), and includes several instructions for causing a terminal (which can be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in each embodiment of this application.

[0067] The embodiments of this application have been described above in conjunction with the accompanying drawings, but this application is not limited to the above specific implementation manners. The above specific implementation manners are only illustrative and not restrictive. Under the inspiration of this application, those of ordinary skill in the art can also make many forms without departing from the purpose of this application and the scope protected by the claims. These all belong to the protection scope of this application.

Claims

1. A Doppler and pseudorange fusion positioning method for low-earth orbit satellite communication and navigation signals, characterized in that, include: Obtain the ephemeris information of the low-orbit satellite visible to the receiver at the same time, and calculate its three-dimensional position coordinates and velocity in the Earth-centered Earth-fixed coordinate system ECEF, as well as obtain the Doppler and pseudo-range observations of the low-orbit satellite communication signal and establish the Doppler and pseudo-range observation equations; The satellite coverage area is divided into grids according to longitude and latitude, and the theoretical values of Doppler and pseudorange between the grid center and the satellite are calculated respectively. The least squares residuals are calculated with the observed Doppler and pseudorange measurements, and the coordinates of the grid center corresponding to the minimum value of the two-norm are taken as the initial value of the receiver position. The Doppler and pseudorange observation equations are expanded by Taylor series, the state transfer matrix is established using the coefficients of the first-order derivative, and the state update matrix is represented by the state transfer matrix and the receiver position, clock error, and frequency offset corrections. The inverse matrix of the observation noise covariance is assigned to the state transfer matrix as the weight matrix; The initial value of the receiver position is iterated, and the state update matrix is updated until the second norm of the residual solution is less than the set threshold. Then the iteration is stopped to obtain the receiver position, clock error and frequency offset results.

2. The Doppler and pseudorange fusion positioning method for low-orbit satellite communication and navigation signals according to claim 1, characterized in that The Doppler and pseudorange observation equations are established as follows: Assuming the receiver is stationary on the ground, the Doppler and pseudorange positioning observation equations are expressed as: where d i (u) and ρ i (u) (i = 1, 2, …, n) respectively represent the Doppler and pseudorange measurement values of the i-th satellite observed by the receiver, where n is the total number of satellites that can be observed by the receiver simultaneously, represents the running speed of the i-th satellite; c is the speed of light; represents the position coordinates of the i-th satellite; r u = [x u y u z u T represents the receiver position coordinates; f s represents the satellite signal transmission frequency; is the receiver frequency offset; ∈ di is the Doppler measurement noise of the i-th satellite; Δt u represents the receiver clock error; t represents the current signal time of the receiver; t0 represents the initial signal time of the receiver; ∈ ρi is the pseudorange measurement noise of the i-th satellite; are the 5 unknowns to be solved for the receiver.​ 3. The Doppler and pseudorange fusion positioning method for low-orbit satellite communication and navigation signals according to claim 2, characterized in that, The satellite coverage area is divided into grids according to longitude and latitude, and the Doppler and pseudo-range theoretical values between the grid center and the satellite are calculated respectively. The least squares residuals are calculated with the observed Doppler and pseudo-range measurement values, and the coordinates of the grid center corresponding to the minimum value of the two norm are taken as the initial values of the receiver, including: The satellite coverage area is divided into m grids of N°×N° according to longitude and latitude; Calculate the longitude and latitude coordinates of the center point of the grid and give the corresponding height value; Convert the latitude, longitude and altitude values into spatial rectangular coordinates under ECEF; According to the selected spatial rectangular coordinates of the grid center point, the satellite position and velocity at a certain moment, the theoretical values of Doppler and pseudorange between the grid center point and the satellite are calculated respectively, and the least squares residuals are calculated with the observed Doppler and pseudorange measurements: where r j = [x j y j z j T is the coordinate of the center point of the j-th grid (j = 1, 2,..., m); d i (u j ) and ρ i (u j ) are the theoretically calculated values of the Doppler and pseudorange of the j-th grid for the i-th satellite;​ The binary norm values of ΔX at different grid center points are calculated in turn, and the grid center point coordinates corresponding to the minimum residual value are taken as the initial value of the receiver position.

4. The Doppler and pseudorange fusion positioning method for low-earth orbit satellite communication and navigation signals according to claim 3, wherein The Taylor series expansion of the Doppler and pseudorange observation equations includes: Define the initial value as Expand the observation equation by Taylor series to obtain: In the formula, is an infinitesimal of higher order, where: where r u0 = [x u0 y u0 z u0 T represents the initial value of the receiver position, and the state transition matrix H can be expressed as:​ 5. The Doppler and pseudorange fusion positioning method for low-earth orbit satellite communication and navigation signals according to claim 4, characterized in that Taylor series expansion of the Doppler and pseudorange observation equations also includes: After the user receives n low-orbit satellites at the same time, multiple Doppler and pseudo-range observation equations are combined to express the state update matrix as: Wherein: ε is the residual vector, k is the number of iterations, is the estimated value of u after the k-th iteration.

6. The Doppler and pseudorange fusion positioning method for low-earth orbit satellite communication and navigation signals according to claim 5, characterized in that, Assigning the inverse matrix of the observation noise covariance as the weight matrix to the state transfer matrix includes: Taking the inverse of the observation noise covariance matrix as the weight matrix, the observation noise covariance matrix R is expressed as: The corresponding weight matrix W is expressed as: The transfer matrix with the weight matrix added is expressed as: Then Δu k is expressed as: Δu k = (H w T H w ) -1 H w T ΔX = ((H T WH) T (H T WH)) -1 (H T WH) T ΔX 7. The Doppler and pseudorange fusion positioning method for low-orbit satellite communication and navigation signals according to claim 5, characterized in that, Iterating the initial value of the receiver position and updating the state update matrix includes: Substitute the initial value of the receiver position for large-area grid calculation. After k iterations, if the two-norm of Δu k is less than the specified threshold, stop the iteration. The obtained u k+1 = u k + Δu k is used as the final results of the receiver position, clock error, and frequency offset.

8. A Doppler and pseudorange fusion positioning system for low-earth orbit satellite communication and navigation signals, characterized in that, The method comprises a processor and a memory, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the steps of the Doppler and pseudo-range fusion positioning method for the low-orbit satellite communication signal are implemented as described in any one of claims 1 to 7.

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