A method for positioning compensation of satellite communication signals

Abstract

The application discloses a satellite communication signal positioning compensation method and relates to the field of satellite positioning, which comprises the following steps: taking a ground reference station with a known position as a ranging reference to obtain distances from multiple satellites to a target; obtaining an initial position of the target by a maximum likelihood estimation method; setting a target state vector and constructing a target state transition matrix; setting an initial value of the target state vector to perform coarse estimation iteration of the target state vector; correcting the coarse estimation iteration process, correcting the target state vector and extracting the position of the target according to the positions of the multiple satellites and the distances from the multiple satellites to the target. The application can not only accurately position but also cope with high-speed moving targets and complex urban environments, and has robustness exceeding that of the prior art.

Description

Technical Field

[0001] This invention relates to the field of satellite positioning, and more specifically to a method for positioning compensation of satellite communication signals. Background Technology

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

[0003] To improve positioning accuracy, data can be transmitted using the signal communication capabilities of navigation satellites, with ground reference stations at known locations serving as a reference to correct positioning errors. However, current technology is insufficient to handle 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 enhance positioning accuracy. Summary of the Invention

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

[0005] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

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

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

[0008] S2. Based on the distances from multiple satellites to the target, the initial position of the target is obtained using the maximum likelihood estimation method;

[0009] S3. Set the target's three-dimensional position and velocity as the target state vector, and construct the target state transition matrix based on the discrete velocity and position relationship;

[0010] S4. Set the initial value of the target state vector according to the initial position of the target, and perform a coarse estimation iteration of the target state vector according to the target state transition matrix;

[0011] S5. Based on the positions of multiple satellites and their distances to the target, correct the coarse estimation iteration process, adjust the target state vector, and extract the target's position from the target state vector.

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

[0013] S11. Add timestamps to the communication signals transmitted by each satellite;

[0014] S12. The ground reference station and the target both receive communication signals from each satellite. Based on the timestamps, the delay time of each signal is known, and the rough estimated distance from each satellite to the ground reference station and the target is calculated.

[0015] S13. Based on the positions of the ground reference station and each satellite, calculate the actual distance from each satellite to the ground reference station, compare it with the rough estimate of the distance from each satellite to the ground reference station, and obtain the distance correction offset parameters for each satellite.

[0016] S14. Correct the rough estimated distance from each satellite to the target based on the distance correction offset parameter of each satellite, and obtain the distance from each satellite to the target.

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

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

[0019] S22. Subtract the Nth equation from the first N minus 1 equations of the quadratic relation equation system, and represent it in matrix form through factorization to obtain the satellite position difference matrix and the position distance quadratic term vector, where N is the number of satellites.

[0020] S23. Find 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 as follows: x is the x-coordinate of the target, y is the y-coordinate of the target, and z is the elevation of the target. For the target lateral velocity, For the target longitudinal velocity, The target elevation velocity is given by the superscript T, which is the transpose operator.

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

[0023] ,

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

[0025] Furthermore, the coarse estimation iteration of S4 is as follows: multiply the target state transition matrix by the target state vector at the current moment to obtain the coarse estimation vector of the target state at the next moment.

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

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

[0028] S52. Calculate the target noise rough estimation matrix for the next time step based on the target state transition matrix and the target noise matrix at the current time step.

[0029] S53. Based on the positions of multiple satellites and their distances to the target, as well as the target noise coarse estimation matrix for the next time step, construct the correction operator matrix for the current time step.

[0030] S54. Based on 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 coarse estimation vector and target noise coarse estimation matrix at the next moment are corrected to obtain the target state vector and target noise matrix at the next moment.

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

[0032] Further, step S52 calculates the target noise coarse estimation matrix for the next time step using the following formula, based on the target state transition matrix and the target noise matrix at the current time step:

[0033] ,

[0034] in, Let Q be the target noise coarse estimation matrix at time t+1, and let Q be the target state transition matrix. T R is the transpose of Q. t Let be the target noise matrix at time t.

[0035] Furthermore, S53 constructs the modified operator matrix using the following formula:

[0036] ,

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

[0038] H t The elements include: partial derivatives of various distance coordinates calculated based on the positions of each satellite and their distances to the target.

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

[0040] ,

[0041] ,

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

[0043] The beneficial effects of this invention are as follows:

[0044] (1) This invention uses a ground reference station as a ranging reference, obtains the distance between the target and the satellite through satellite communication signals, and sets the initial position value of the iteration through the maximum likelihood estimation method. The iterative process is dynamically corrected by the distance between the target and the satellite, so that this invention can not only accurately locate, but also cope with high-speed moving targets and complex urban environments, and has robustness exceeding that of the prior art.

[0045] (2) The maximum likelihood estimation method set up in this invention can estimate the target distance with the maximum accuracy based on the coordinates of multiple stars and the distance between multiple stars and the target by solving the generalized inverse matrix of matrix theory. It is applicable to the positioning of static targets and the initial value solution of dynamic targets.

[0046] (3) The iterative process set up in this invention only needs to use the current measurement value and the state estimate of the previous moment when updating the state estimate, without storing a large amount of historical data. This recursive characteristic makes it unnecessary to perform large-scale data processing and complex matrix operations during the calculation process, which greatly reduces the amount of computation and enables it to run quickly under 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 satellite target distance, and can work stably in noisy environments. Even if there is some noise interference in the measurement data, the error can be converged through iteration, and the stability of the state estimation can be maintained. Attached Figure Description

[0048] Figure 1 A flowchart of a satellite communication signal positioning compensation method provided in an embodiment of the present invention. Detailed Implementation

[0049] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

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

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

[0052] S1 includes the following steps:

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

[0054] S12. The ground reference station and the target both receive communication signals from each satellite. Based on the timestamps, the delay time of each signal is known, and the rough estimated distance from each satellite to the ground reference station and the target is calculated.

[0055] In this embodiment, the calculation expression for the coarse distance estimate is:

[0056] ,

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

[0058] S13. Based on the positions of the ground reference station and each satellite, calculate the actual distance from each satellite to the ground reference station, compare it with the rough estimate of the distance from each satellite to the ground reference station, and obtain the distance correction offset parameters for each satellite.

[0059] In this embodiment, the expression for the distance correction bias parameter is:

[0060] ,

[0061] Where, ε d For distance correction bias parameters, d real d represents the actual distance. rough This is for a rough estimate of the distance.

[0062] S14. Correct the rough estimated distance from each satellite to the target based on the distance correction offset parameter of each satellite, and 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 steps:

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

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

[0067] The satellite position difference matrix has the following elements:

[0068] ,

[0069] x1 to x N Let y1 be the x-coordinate of satellites 1 to N, and y1 be the x-coordinate of satellite N. N Let z1 be the ordinate of satellites 1 to N, and z2 be the ordinate of satellites 1 to N. N The elevations are for satellites 1 through N, where N is the number of satellites.

[0070] The quadratic vector of positional distances, whose elements are...

[0071] ,

[0072] d1 to d N The distances from satellites 1 to N to the target.

[0073] S23. Calculate the generalized inverse 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. The expression for this process is as follows:

[0074] ,

[0075] in, The initial position vector of the target estimated by the maximum likelihood estimation method, whose elements are... , The initial value of the target x-coordinate, The initial value of the target's ordinate. Let A be the initial value of the target elevation; A is the satellite position difference matrix. T Let A be the transpose of A, and B be the quadratic vector of positional distance.

[0076] The maximum likelihood estimation method proposed in this invention, through the solution of the generalized inverse matrix in matrix theory, can estimate the target distance with maximum accuracy based on the coordinates of multiple stars and the distance between multiple stars and the target. It is applicable to the positioning of static targets and the initial value solution of dynamic targets.

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

[0078] The target state vector is set as follows: x is the x-coordinate of the target, y is the y-coordinate of the target, and z is the elevation of the target. For the target lateral velocity, For the target longitudinal velocity, The target elevation velocity is given by the superscript T, which is the transpose operator.

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

[0080] ,

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

[0082] The target state transition matrix set in this invention, when multiplied by the target state vector, is the set of position and velocity iterative equations in the discrete time domain under ideal conditions.

[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... , The initial value of the target x-coordinate, The initial value of the target's ordinate. The initial value of the target elevation;

[0084] Then, based on the target state transition matrix, a coarse estimation of the target state vector is performed iteratively. The process is as follows: multiply the target state transition matrix by the target state vector at the current moment to obtain the coarsely estimated target state vector for the next moment, which can be expressed by the following expression:

[0085] ,

[0086] in, Let t+1 be the coarse estimate vector of the target state, and Q be the target state transition matrix.

[0087] S5. Based on the positions of multiple satellites and their distances to the target, correct the coarse estimation iteration process, adjust the target state vector, and extract the target's position from the target state vector. S5 includes the following sub-steps:

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

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

[0090] However, for faster convergence, the initial values ​​can be determined by taking multiple measurements using steps S1 and S2 of this invention to calculate the variances of the target x-coordinate, target y-coordinate, and target elevation, and then using these variances to set the first three diagonal elements. As for the last three diagonal elements, it is recommended to set them to empirical values ​​of around 100.

[0091] S52. Using the following formula, calculate the rough estimate matrix of the target noise at the next time step based on the target state transition matrix and the target noise matrix at the current time step:

[0092] ,

[0093] in, Let Q be the target noise coarse estimation matrix at time t+1, and let Q be the target state transition matrix. T R is the transpose of Q. t Let be the target noise matrix at time t.

[0094] The above equation means that the matrix Q is iterated over the matrix R. t And Q T This makes the obtained It remains a symmetric matrix.

[0095] S53. Using the following formula, based on the positions of multiple satellites and their distances to the target, as well as the target noise coarse estimation matrix for the next time step, construct the correction operator matrix for the current time step:

[0096] ,

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

[0098] H t The elements include: partial derivatives of various distance coordinates calculated based on the positions of each satellite and their distances to the target. In this embodiment, H t for:

[0099] ,

[0100] Where, d 1,t to d N,t Let x be the distance from the 1st to the Nth satellite to the target at time t. 1,t To x N,t Let y be the x-coordinate of satellites 1 to N at time t. 1,t To y N,t Let z be the ordinate of satellites 1 to N at time t. 1,t To z N,t Let x be the elevation of satellites 1 to N at time t. t Let y be the x-coordinate of the target extracted from the target state vector at time t. t Let z be the target ordinate extracted from the target state vector at time t. t The target elevation is extracted from the target state vector at time t.

[0101] The correction operator matrix in this invention adaptively adjusts the weights of the coarsely estimated state and the measured distance in state estimation based on their uncertainties. When the target noise coarse estimation matrix is ​​large, it indicates high uncertainty in the target state coarse estimation vector, while a small measurement noise matrix suggests relatively reliable measured data. In this case, the correction operator matrix will be larger, relying more on the measured data matrix to correct the target state coarse estimation vector during state updates, thus improving the accuracy of state estimation. Conversely, if the target noise coarse estimation matrix is ​​small while the measurement noise matrix is ​​large, the state vector update will be more inclined towards the target state coarse estimation vector, reducing the impact of measurement noise on state estimation.

[0102] The measurement noise matrix W should also be a diagonal matrix, with the same dimensions as the target state transition matrix. It is worth noting that the initial value of the measurement noise matrix W, like the target noise matrix, is an ambiguity that is neither easily nor necessary to determine. As mentioned earlier, regardless of the initial non-zero value of the target noise matrix, it will converge with iteration; however, the measurement noise matrix W is related to the noise conditions of the satellite system. This noise originates not only from the satellite itself but also from the environment. For example, in an environment with many high-rise buildings in a city, the satellite signal may be affected by multipath interference, leading to increased measurement errors. In this case, it is necessary to appropriately increase the values ​​of the elements on the main diagonal of the measurement noise matrix W. This invention does not limit the values; the specific practical application under specific working conditions shall prevail.

[0103] S54. Using the following two equations, based on 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 coarse estimation vector and target noise coarse estimation matrix for the next moment are corrected to obtain the target state vector and target noise matrix for the next moment:

[0104] ,

[0105] ,

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

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

[0108] ,

[0109] d 1,t to d N,t Let T represent the distances from the 1st to the Nth satellites to the target at time t, with the superscript T indicating the transpose operator.

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

[0111] The iterative process described in this invention only requires the current measurement value and the state estimate from the previous moment to update the state estimate each time, without needing to store a large amount of historical data. This recursive characteristic eliminates the need for large-scale data processing and complex matrix operations during the calculation process, greatly reducing the computational load and enabling rapid operation under high real-time requirements.

[0112] The setting and iteration of the target noise matrix make this invention highly robust to noise in satellite target distance measurements, enabling it to operate stably in noisy environments. Even if the measurement data contains some noise interference, iteration can bring the error together and maintain the stability of the state estimation.

[0113] In summary, this invention utilizes 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 position value for iteration using the maximum likelihood estimation method. The iterative process is dynamically corrected based on the distance between the target and the satellite, enabling this invention to not only provide accurate positioning but also cope with high-speed moving targets and complex urban environments, exhibiting robustness exceeding that of existing technologies.

[0114] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for positioning compensation of satellite communication signals, characterized in that, Includes the following steps: S1. Using a ground reference station at a known location as the ranging reference, the distance from multiple satellites to the target is obtained by correcting the time delay through the communication signals between the station and multiple satellites. S2. Based on the distances from multiple satellites to the target, the initial position of the target is obtained using the maximum likelihood estimation method; S3. Set the target's three-dimensional position and velocity as the target state vector, and construct the target state transition matrix based on the discrete velocity and position relationship; The target state vector is set as follows: x is the x-coordinate of the target, y is the y-coordinate of the target, and z is the elevation of the target. For the target lateral velocity, For the target longitudinal velocity, The target elevation velocity is given by the superscript T, which is the transpose operator. The target state transition matrix is ​​set as follows: ， τ is the time interval of the iterative operation; S4. Set the initial value of the target state vector according to the initial position of the target, and perform a coarse estimation iteration of the target state vector according to the target state transition matrix; S5. Based on the positions of multiple satellites and their distances to the target, correct the coarse estimation iteration process, adjust the target state vector, and extract the target's position from the target state vector; S5 includes the following steps: S51. Set a diagonal matrix with the same dimensions as the target state transition matrix, denoted as the target noise matrix; S52. Calculate the target noise rough estimation matrix for the next time step based on the target state transition matrix and the target noise matrix at the current time step. S53. Based on the positions of multiple satellites and their distances to the target, as well as the target noise coarse estimation matrix for the next time step, construct the correction operator matrix for the current time step. S54. Based on 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 coarse estimation vector and target noise coarse estimation matrix at the next moment are corrected to obtain the target state vector and target noise matrix at the next moment. S55. Extract the target's position from the target state vector; S52 calculates the rough estimate matrix of the target noise at the next time step using the following formula, based on the target state transition matrix and the target noise matrix at the current time step: ， in, Let Q be the target noise coarse estimation matrix at time t+1, and let Q be the target state transition matrix. T R is the transpose of Q. t Let be the target noise matrix at time t; S53 constructs the modified operator matrix using the following formula: ， Among them, C t Let be the correction operator matrix at time t. H is the target noise coarse estimation matrix at time t+1. t Let H be the measured data matrix at time t. t T For H t The transpose of , where W is the measurement noise matrix; H t The elements include: partial derivatives of various distance coordinates calculated based on the positions of each satellite and their distances to the target; The expression in S54 includes the following two formulas: ， ， Among them, S t+1 Let D be the target state vector at time t+1. t Let C be the range vector of the satellite target at time t. t Let H be the correction operator matrix at time t. t Let be the measured data matrix at time t. R is the coarse estimate vector of the target state at time t+1; t+1 Let be the target noise matrix at time t+1. Let E be the target noise coarse estimation matrix at time t+1, and E be the identity matrix.

2. The satellite communication signal positioning compensation method according to claim 1, characterized in that, S1 includes the following steps: S11. Add timestamps to the communication signals transmitted by each satellite; S12. The ground reference station and the target both receive communication signals from each satellite. Based on the timestamps, the delay time of each signal is known, and the rough estimated distance from each satellite to the ground reference station and the target is calculated. S13. Based on the positions of the ground reference station and each satellite, calculate the actual distance from each satellite to the ground reference station, compare it with the rough estimate of the distance from each satellite to the ground reference station, and obtain the distance correction offset parameters for each satellite. S14. Correct the rough estimated distance from each satellite to the target based on the distance correction offset parameter of each satellite, and obtain the distance from each satellite to the target.

3. The satellite communication signal positioning compensation method according to claim 1, characterized in that, S2 includes the following steps: S21. Establish a set of equations relating the three-dimensional position coordinates of each satellite, the three-dimensional position coordinates of the target, and the square relationship between the distance from each satellite to the target; S22. Subtract the Nth equation from the first N minus 1 equations of the quadratic relation equation system, and represent it in matrix form through factorization to obtain the satellite position difference matrix and the position distance quadratic term vector, where N is the number of satellites. S23. Find 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 satellite communication signal positioning compensation method according to claim 1, characterized in that, The coarse estimation iteration of S4 is as follows: multiply the target state transition matrix by the target state vector at the current time to obtain the coarse estimation vector of the target state at the next time.

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