Positioning compensation method for satellite communication signal

Abstract

The invention discloses a satellite communication signal positioning compensation method, which relates to the field of satellite positioning, and comprises the following steps: taking a ground reference station with a known position as a distance measurement reference to obtain distances from a plurality of satellites to a target; obtaining an initial position of the target through a maximum likelihood estimation method; setting a target state vector, and constructing a target state transition matrix; setting an initial value of a target state vector, and performing rough estimation iteration of the target state vector; and according to the positions of the plurality of satellites and the distances from the satellites to the target, correcting the rough estimation iteration process, correcting the target state vector, and extracting the position of the target. According to the invention, accurate positioning can be realized, high-speed moving targets and complex urban environments can be dealt with, and the robustness of the method is higher than that of the prior art.

Description

Technical Field

[0001] The present invention relates to the field of satellite positioning, and in particular to a positioning compensation method for satellite communication signals. Background Art

[0002] Satellite positioning systems are currently widely used for positioning and navigation services. However, due to limitations imposed by satellite orbit errors, clock errors, atmospheric delays, and multipath effects, their positioning accuracy is typically limited to a few meters, making it difficult to achieve higher accuracy.

[0003] To improve positioning accuracy, navigation satellites can be used to transmit data using signal communication capabilities, using ground reference stations at known locations as reference points to correct positioning errors. However, existing technologies are insufficient for handling high-speed moving targets and complex urban environments. Therefore, an improved positioning compensation method is urgently needed to address the issue of real-time error correction and further improve positioning accuracy. Summary of the Invention

[0004] In view of the above-mentioned deficiencies in the prior art, the present invention provides a positioning compensation method for satellite communication signals, which solves the problem that the existing method of using satellite communication to compensate for positioning accuracy is difficult to deal with high-speed moving targets.

[0005] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0006] A method for positioning compensation of satellite communication signals comprises the following steps:

[0007] S1. Using a ground reference station at a known location as a ranging reference, the time delay ranging is corrected by the communication signals between the station and multiple satellites to obtain the distances from multiple satellites to the target.

[0008] S2. Obtain the initial position of the target using the maximum likelihood estimation method based on the distances from multiple satellites to the target;

[0009] S3, setting the three-dimensional position and velocity of the target as the target state vector, and constructing the target state transfer matrix based on the discrete velocity and position relationship;

[0010] S4. Setting the initial value of the target state vector according to the initial position of the target, and performing a rough estimation iteration of the target state vector according to the target state transfer matrix;

[0011] S5. According to the positions of the multiple satellites and their distances to the target, the rough estimation iterative process is modified, the target state vector is corrected, and the position of the target is extracted from the target state vector.

[0012] Furthermore, the S1 includes the following sub-steps:

[0013] S11. Adding a timestamp to the communication signals transmitted by each satellite;

[0014] S12: The ground reference station and the target both receive the communication signals of the satellites, obtain the delay time of each signal based on the timestamp, and calculate the rough estimated distance from each satellite to the ground reference station and the target;

[0015] S13. Calculate the actual distance of each satellite from the ground reference station based on the positions of the ground reference station and each satellite, compare the estimated distance of each satellite from the ground reference station, and obtain a distance correction bias parameter for each satellite.

[0016] S14. Correct the roughly estimated distance from each satellite to the target according to the distance correction bias parameter of each satellite to obtain the distance from each satellite to the target.

[0017] Furthermore, the step S2 includes the following sub-steps:

[0018] S21, establishing a set of square relationship equations between the three-dimensional position coordinates of each satellite, the three-dimensional position coordinates of the target, and the distance from each satellite to the target;

[0019] S22. Subtract the Nth equation from the first N minus 1 equations of the square relationship equation group, and represent it in matrix form by factoring to obtain the satellite position difference matrix and the position distance quadratic term vector, where N is the number of satellites;

[0020] S23. Calculate the generalized inverse matrix of the satellite position difference matrix, multiply it by the quadratic term vector of the position distance, and obtain the initial position of the target in vector form.

[0021] Furthermore, the target state vector in S3 is set to: , x is the target horizontal coordinate, y is the target vertical coordinate, z is the target elevation, is the target lateral velocity, is the target longitudinal velocity, is the target elevation speed, and the superscript T is the transposition operator;

[0022] The target state transfer matrix is ​​set as:

[0023] ,

[0024] τ is the time interval of iterative operation.

[0025] Furthermore, the rough estimation iteration of S4 is as follows: multiplying the target state vector at the current moment by the target state transfer matrix to obtain a rough estimation vector of the target state at the next moment.

[0026] Furthermore, the S5 includes the following sub-steps:

[0027] S51. Set a diagonal matrix with the same dimension as the target state transfer matrix, denoted as the target noise matrix;

[0028] S52, calculating the target noise rough estimation matrix at the next moment according to the target state transfer matrix and the target noise matrix at the current moment;

[0029] S53, constructing a correction operator matrix at the current moment based on the positions of the multiple satellites and their distances to the target, and a rough estimate matrix of target noise at the next moment;

[0030] S54, based on the positions of the multiple satellites and their distances to the target, and the correction operator matrix at the current moment, correcting the target state rough estimate vector and the target noise rough estimate matrix at the next moment to obtain the target state vector and the target noise matrix at the next moment;

[0031] S55. Extract the target position from the target state vector.

[0032] Furthermore, the S52 calculates the target noise rough estimation matrix at the next moment according to the target state transfer matrix and the target noise matrix at the current moment by the following formula:

[0033] ,

[0034] in, is the target noise rough estimation matrix at time t+1, Q is the target state transfer matrix, Q T is the transpose of Q, R t is the target noise matrix at time t.

[0035] Furthermore, the S53 constructs a correction operator matrix by the following formula:

[0036] ,

[0037] Among them, C t is the correction operator matrix at time t, is the rough estimation matrix of target noise at time t+1, H t is the measured data matrix at time t, H t T H t The transpose of , W is the measurement noise matrix;

[0038] H t The elements include: the partial derivatives of each distance coordinate calculated based on the position of each satellite and its distance to the target.

[0039] Furthermore, the expression of S54 includes the following two formulas:

[0040] ,

[0041] ,

[0042] Among them, S t+1 is the target state vector at time t+1, D t is the distance vector of the satellite target at time t, C t is the correction operator matrix at time t, H t is the measured data matrix at time t, is the rough estimate vector of the target state at time t+1; R t+1 is the target noise matrix at time t+1, is the rough estimation matrix of the target noise at time t+1, and E is the unit matrix.

[0043] The beneficial effects of the present invention are:

[0044] (1) The present invention uses a ground reference station as a ranging reference, obtains the distance between the target and the satellite through satellite communication signals, and then sets the initial value of the iterative position through the maximum likelihood estimation method. The iterative process is dynamically corrected based on the distance between the target and the satellite. This allows the present invention to not only accurately locate but also cope with high-speed moving targets and complex urban environments, with a robustness that exceeds that of existing technologies.

[0045] (2) The maximum likelihood estimation method provided by the present invention can estimate the target distance with the greatest accuracy based on the coordinates of multiple satellites and the distances between multiple satellites and the target through the generalized inverse matrix solution of matrix theory. It is suitable for the positioning of static targets and the initial value solution of dynamic targets.

[0046] (3) The iterative process provided by the present invention only requires the use of the current measurement value and the state estimate at the previous moment each time the state estimate is updated, without the need to store a large amount of historical data. This recursive feature eliminates the need for large-scale data processing and complex matrix operations during the calculation process, greatly reducing the amount of computation and enabling fast operation even in situations with high real-time requirements.

[0047] (4) The setting and iteration of the target noise matrix make the present invention highly robust to the measurement noise of the satellite target distance and can operate stably in a noisy environment. Even if there is a certain amount of noise interference in the measurement data, the error can be converged through iteration to maintain the stability of the state estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 The present invention provides a flowchart of a method for compensating for positioning of satellite communication signals. DETAILED DESCRIPTION

[0049] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0050] like Figure 1 As shown, in one embodiment of the present invention, a positioning compensation method for satellite communication signals includes the following steps:

[0051] S1. Using a ground reference station at a known location as a ranging reference, the time delay ranging is corrected through the communication signals between the station and multiple satellites to obtain the distances from multiple satellites to the target.

[0052] S1 includes the following steps:

[0053] S11. Add a timestamp to the communication signals transmitted by each satellite.

[0054] S12. The ground reference station and the target both receive the communication signals from each satellite, obtain the delay time of each signal based on the timestamp, and calculate the rough estimated distance from each satellite to the ground reference station and the target.

[0055] In this embodiment, the calculation expression for the rough estimated distance is:

[0056] ,

[0057] Among them, d rough is a rough estimate of the distance, c is the speed of light, and Δt is the signal delay time.

[0058] S13. Calculate the actual distance of each satellite from the ground reference station based on the positions of the ground reference station and each satellite, compare the estimated distance of each satellite from the ground reference station, and obtain the distance correction bias parameter of each satellite.

[0059] In this embodiment, the expression of the distance correction offset parameter is:

[0060] ,

[0061] Among them, ε d is the distance correction bias parameter, d real is the actual distance, d rough For a rough estimate of distance.

[0062] S14. Correct the roughly estimated distance from each satellite to the target according to the distance correction bias parameter of each satellite to obtain the distance from each satellite to the target.

[0063] S2. Based on the distances from multiple satellites to the target, the initial position of the target is obtained through the maximum likelihood estimation method.

[0064] S2 includes the following sub-steps:

[0065] S21. Establish a set of square relationship equations between the three-dimensional position coordinates of each satellite, the three-dimensional position coordinates of the target, and the distance from each satellite to the target.

[0066] S22. Subtract the Nth equation from the first N minus 1 equations of the square relationship equation group, and represent it in matrix form by factorization to obtain the satellite position difference matrix and the position distance quadratic term vector, where N is the number of satellites.

[0067] Satellite position difference matrix, whose elements are:

[0068] ,

[0069] x1 to x N is the horizontal coordinate of the 1st to Nth satellite, y1 to y N The vertical coordinates of the 1st to Nth satellites, z1 to z N is the elevation of the 1st to Nth satellites, and N is the number of satellites.

[0070] Position distance quadratic term vector, whose elements are

[0071] ,

[0072] d1 to d N is the distance from the 1st to the Nth satellite to the target.

[0073] S23. Calculate the generalized inverse matrix of the satellite position difference matrix and multiply it by the quadratic term vector of the position distance to obtain the initial position of the target in vector form. The expression of this process is as follows:

[0074] ,

[0075] in, is the initial position vector of the target estimated by the maximum likelihood estimation method, whose elements are , is the initial value of the target horizontal coordinate, is the initial value of the target vertical coordinate, is the initial value of the target elevation; A is the satellite position difference matrix, A T is the transpose of A, and B is the position distance quadratic term vector.

[0076] The maximum likelihood estimation method provided by the present invention, through the generalized inverse matrix solution of matrix theory, can estimate the target distance with the greatest accuracy based on the coordinates of multiple satellites and the distances between multiple satellites and the target. It is suitable for the positioning of static targets and the initial value solution of dynamic targets.

[0077] S3. Set the three-dimensional position and velocity of the target as the target state vector, and construct the target state transfer matrix based on the discrete velocity and position relationship.

[0078] The target state vector is set as: , x is the target horizontal coordinate, y is the target vertical coordinate, z is the target elevation, is the target lateral velocity, is the target longitudinal velocity, is the target elevation speed, and the superscript T is the transposition operator;

[0079] The target state transfer matrix is ​​set as:

[0080] ,

[0081] τ is the time interval of iterative operation.

[0082] The target state transfer matrix provided by the present invention, and its product with the target state vector, is the position and velocity iterative equation group in the discrete time domain under the ideal state.

[0083] S4. Set the initial value of the target state vector according to the initial position of the target. In this embodiment, the initial value of the target state vector is , is the initial value of the target horizontal coordinate, is the initial value of the target vertical coordinate, is the initial value of the target elevation;

[0084] And according to the target state transfer matrix, the target state vector is roughly estimated and iterated. The process is: multiply the target state vector at the current moment by the target state transfer matrix to obtain the target state rough estimate vector at the next moment, which can be expressed by the following expression:

[0085] ,

[0086] in, is the rough estimate vector of the target state at time t+1, and Q is the target state transfer matrix.

[0087] S5. Based on the positions of the multiple satellites and their distances to the target, the rough estimation iterative process is corrected, the target state vector is corrected, and the position of the target is extracted from the target state vector. S5 includes the following sub-steps:

[0088] S51. Set a diagonal matrix with the same dimension as the target state transfer matrix, denoted as the target noise matrix.

[0089] In the process of setting the initial value of the target noise matrix, its main diagonal elements can be set to any value, because the subsequent iterative process will converge it into a noise power matrix whose elements correspond one-to-one with the elements at the same position in the target state matrix, which can also be called the covariance matrix.

[0090] However, in order to facilitate rapid convergence, the initial values ​​can also be set by repeatedly measuring the target horizontal coordinate, target vertical coordinate, and target elevation using steps S1 and S2 of the present invention. As for the last three diagonal elements, it is recommended to set them to an empirical value of around 100.

[0091] S52. Calculate the target noise rough estimation matrix at the next moment according to the target state transfer matrix and the target noise matrix at the current moment by the following formula:

[0092] ,

[0093] in, is the target noise rough estimation matrix at time t+1, Q is the target state transfer matrix, Q T is the transpose of Q, R t is the target noise matrix at time t.

[0094] The meaning of the above formula is to iterate the matrix R through the matrix Q t , and Q T Make it possible to obtain It is still a symmetrical array.

[0095] S53. Construct a correction operator matrix at the current moment according to the positions of multiple satellites and their distances to the target, as well as the rough estimate matrix of target noise at the next moment, using the following formula:

[0096] ,

[0097] Among them, C t is the correction operator matrix at time t, is the rough estimation matrix of target noise at time t+1, H t is the measured data matrix at time t, H t T H t The transpose of , W is the measurement noise matrix;

[0098] H t The elements of include: the partial derivatives of each distance coordinate calculated based on the position of each satellite and its distance to the target. In this embodiment, H t for:

[0099] ,

[0100] Among them, d 1,t to d N,t is the distance from the 1st to the Nth satellite to the target at time t, x 1,t to x N,t is the horizontal coordinate of the 1st to Nth satellite at time t, y 1,t to y N,t is the vertical coordinate of the 1st to Nth satellite at time t, z 1,t to z N,t is the altitude of the 1st to Nth satellite at time t, x t is the target horizontal coordinate extracted from the target state vector at time t, y t is the target ordinate extracted from the target state vector at time t, z t is the target elevation extracted from the target state vector at time t.

[0101] The correction operator matrix provided by the present invention can adaptively adjust the weights of the roughly estimated state and the measured distance in state estimation based on the uncertainty of the two. When the target noise rough estimate matrix is ​​large, it means that the uncertainty of the target state rough estimate vector is high, while when the measurement noise matrix is ​​small, it indicates that the measured data matrix is ​​relatively reliable. In this case, the correction operator matrix will be larger, and the measured data matrix will be more relied upon to correct the target state rough estimate vector during state update to improve the accuracy of state estimation. Conversely, if the target noise rough estimate matrix is ​​small and the measurement noise matrix is ​​large, the state vector update will be more inclined to the target state rough estimate vector, reducing the impact of measurement noise on state estimation.

[0102] The measurement noise matrix W should also be set as a diagonal matrix, and its dimension is also the same as the target state transfer matrix. It is worth noting that the measurement noise matrix W, like the initial value of the target noise matrix, is also a fuzzy value that is difficult to determine and does not need to be determined. As mentioned above, no matter what non-zero value the initial value of the target noise matrix is ​​set to, it can converge with iteration; the measurement noise matrix W is related to the noise condition of the satellite system. This noise comes not only from the satellite itself, but also from the environment. For example, in an environment with tall buildings in a city, the satellite signal may be interfered by the multipath effect, resulting in increased measurement errors. At this time, it is necessary to appropriately increase the values ​​of the elements of the main diagonal of the measurement noise matrix W. The present invention does not limit its numerical value, and it is subject to the practice of specific working conditions.

[0103] S54. According to the positions of multiple satellites and their distances to the target, as well as the correction operator matrix at the current moment, the target state rough estimate vector and the target noise rough estimate matrix at the next moment are corrected by the following two equations to obtain the target state vector and the target noise matrix at the next moment:

[0104] ,

[0105] ,

[0106] Among them, S t+1 is the target state vector at time t+1, D t is the distance vector of the satellite target at time t, C t is the correction operator matrix at time t, H t is the measured data matrix at time t, is the rough estimate vector of the target state at time t+1; R t+1 is the target noise matrix at time t+1, is the rough estimation matrix of the target noise at time t+1, and E is the unit matrix.

[0107] In this embodiment, D t The elements are:

[0108] ,

[0109] d 1,t to d N,t is the distance from the 1st to the Nth satellite to the target at time t, and the superscript T is the transposition operator

[0110] S55. Extract the target position from the target state vector.

[0111] The iterative process employed by the present invention only utilizes the current measurement and the previous state estimate each time the state estimate is updated, eliminating the need to store large amounts of historical data. This recursive nature eliminates the need for large-scale data processing and complex matrix operations during the calculation process, significantly reducing the computational effort and enabling rapid execution in applications requiring high real-time performance.

[0112] The setup and iteration of the target noise matrix make the present invention highly robust to satellite target range measurement noise, enabling stable operation in noisy environments. Even if the measurement data is subject to certain noise interference, the error can be converged through iteration, maintaining the stability of the state estimate.

[0113] In summary, the present invention uses a ground reference station as a ranging reference, obtains the distance between the target and the satellite through satellite communication signals, and then sets the initial value of the iterative position through the maximum likelihood estimation method. The iterative process is dynamically corrected based on the distance between the target and the satellite. This allows the present invention to not only accurately locate but also cope with high-speed moving targets and complex urban environments, with a robustness that exceeds that of existing technologies.

[0114] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A positioning compensation method for satellite communication signals, characterized in that: The following steps are involved: S1. Using a ground reference station at a known location as a ranging reference, the time delay ranging is corrected by the communication signals between the station and multiple satellites to obtain the distances from multiple satellites to the target. S2. Obtain the initial position of the target using the maximum likelihood estimation method based on the distances from multiple satellites to the target; S3, setting the three-dimensional position and velocity of the target as the target state vector, and constructing the target state transfer matrix based on the discrete velocity and position relationship; S4. Setting the initial value of the target state vector according to the initial position of the target, and performing a rough estimation iteration of the target state vector according to the target state transfer matrix; S5. According to the positions of the multiple satellites and their distances to the target, the rough estimation iterative process is modified, the target state vector is corrected, and the position of the target is extracted from the target state vector.

2. The positioning compensation method for satellite communication signals according to claim 1, wherein: The S1 comprises the following sub-steps: S11. Adding a timestamp to the communication signals transmitted by each satellite; S12: The ground reference station and the target both receive the communication signals of the satellites, obtain the delay time of each signal based on the timestamp, and calculate the rough estimated distance from each satellite to the ground reference station and the target; S13. Calculate the actual distance of each satellite from the ground reference station based on the positions of the ground reference station and each satellite, compare the estimated distance of each satellite from the ground reference station, and obtain a distance correction bias parameter for each satellite. S14. Correct the roughly estimated distance from each satellite to the target according to the distance correction bias parameter of each satellite to obtain the distance from each satellite to the target.

3. The positioning compensation method for satellite communication signals according to claim 1, wherein: The S2 comprises the following sub-steps: S21, establishing a set of square relationship equations between the three-dimensional position coordinates of each satellite, the three-dimensional position coordinates of the target, and the distance from each satellite to the target; S22. Subtract the Nth equation from the first N minus 1 equations of the square relationship equation group, and represent it in matrix form by factoring to obtain the satellite position difference matrix and the position distance quadratic term vector, where N is the number of satellites; S23. Calculate the generalized inverse matrix of the satellite position difference matrix, multiply it by the quadratic term vector of the position distance, and obtain the initial position of the target in vector form.

4. The positioning compensation method for satellite communication signals according to claim 1, wherein: The target state vector in S3 is set to: , x is the target horizontal coordinate, y is the target vertical coordinate, z is the target elevation, is the target lateral velocity, is the target longitudinal velocity, is the target elevation speed, and the superscript T is the transposition operator; The target state transfer matrix is ​​set as: ， τ is the time interval of iterative operation.

5. The positioning compensation method of satellite communication signals according to claim 1, characterized in that: The rough estimation iteration of S4 is as follows: multiplying the target state vector at the current moment by the target state transfer matrix to obtain a rough estimation vector of the target state at the next moment.

6. The positioning compensation method of satellite communication signals according to claim 1, characterized in that: The S5 comprises the following sub-steps: S51. Set a diagonal matrix with the same dimension as the target state transfer matrix, denoted as the target noise matrix; S52, calculating the target noise rough estimation matrix at the next moment according to the target state transfer matrix and the target noise matrix at the current moment; S53, constructing a correction operator matrix at the current moment based on the positions of the multiple satellites and their distances to the target, and a rough estimate matrix of target noise at the next moment; S54, based on the positions of the multiple satellites and their distances to the target, and the correction operator matrix at the current moment, correcting the target state rough estimate vector and the target noise rough estimate matrix at the next moment to obtain the target state vector and the target noise matrix at the next moment; S55. Extract the target position from the target state vector.

7. The positioning compensation method for satellite communication signals according to claim 6, characterized in that: The S52 calculates the target noise rough estimation matrix at the next moment according to the target state transfer matrix and the target noise matrix at the current moment by the following formula: ， in, is the target noise rough estimation matrix at time t+1, Q is the target state transfer matrix, Q T is the transpose of Q, R t is the target noise matrix at time t.

8. The positioning compensation method for satellite communication signals according to claim 6, characterized in that: The S53 constructs the correction operator matrix by the following formula: ， Among them, C t is the correction operator matrix at time t, is the rough estimation matrix of target noise at time t+1, H t is the measured data matrix at time t, H t T H t The transpose of , W is the measurement noise matrix; H t The elements include: the partial derivatives of each distance coordinate calculated based on the position of each satellite and its distance to the target.

9. The positioning compensation method for satellite communication signals according to claim 6, characterized in that: The expression of S54 includes the following two formulas: ， ， Among them, S t+1 is the target state vector at time t+1, D t is the distance vector of the satellite target at time t, C t is the correction operator matrix at time t, H t is the measured data matrix at time t, is the rough estimate vector of the target state at time t+1; R t+1 is the target noise matrix at time t+1, is the rough estimation matrix of the target noise at time t+1, and E is the unit matrix.

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