Multi-satellite system high-precision space-time synchronization method based on Bayesian weight subspace fitting

Abstract

The invention belongs to the technical field of space-time synchronization of a multi-satellite system, and particularly relates to a multi-satellite system high-precision space-time synchronization method based on Bayesian weight subspace fitting. According to the method, a space-time joint estimation framework of Bayesian maximum posteriori optimization is constructed, inter-satellite signal level measurement is utilized, satellite position error and time error vectors are solved synchronously, and the problem of error transmission in a traditional step-by-step calibration method is effectively avoided. Meanwhile, by means of weight subspace fitting and an incremental updating mechanism, the method remarkably improves the allowable range of the initial space-time error of the satellite group, accelerates the convergence speed of solving the space-time error parameter, improves the solving precision of the space-time error parameter, and provides an innovative solution for high-precision space-time synchronization of a distributed system.

Description

Technical Field

[0001] This invention belongs to the field of spatiotemporal synchronization technology for multi-star systems, specifically relating to a high-precision spatiotemporal synchronization method for multi-star systems based on Bayesian weighted subspace fitting. Background Technology

[0002] In the fields of aerospace and satellite communications, the spatiotemporal synchronization accuracy of multi-satellite systems has a decisive impact on the precision of mission execution. Space-based signal-level processing systems such as constellation coherent radar and distributed synthetic aperture radar require spatiotemporal synchronization accuracy at the sub-nanosecond and picosecond levels to ensure the accurate implementation of functions such as navigation enhancement. However, existing navigation enhancement technologies based on Global Navigation Satellite Systems (GNSS), such as Precise Point Positioning (PPP) and Real-Time Kinematics (RTK), while providing an initial spatiotemporal reference, only achieve spatiotemporal synchronization accuracy at the nanosecond to decimeter level due to ionospheric delay, multipath effects, and satellite clock bias. This falls short of the high-precision requirements for signal-level fusion. These error factors severely restrict the performance of multi-satellite systems in high-precision applications, becoming a bottleneck that urgently needs to be overcome in current technological development.

[0003] Traditional time synchronization methods generally employ a step-by-step calibration strategy, first calibrating the satellite position error, and then calibrating the time error after the position parameters are determined. When calibrating the position error, ranging signals or observation data between satellites are used to construct a position error model and employ estimation methods such as least squares to determine the position deviation. When calibrating the time error, based on the calibrated position information, the time deviation is estimated and calibrated using timestamp information from the time synchronization signal or observation data. However, this method neglects the coupling between spatiotemporal parameters. In scenarios where satellite orbital offsets and clock errors interact, error propagation and accumulation can easily occur, limiting the final spatiotemporal synchronization accuracy. In low-Earth orbit satellite constellations, rapid changes in satellite position and minute clock deviations are coupled, making it difficult for the spatiotemporal synchronization error after step-by-step calibration to meet the requirements of high-precision applications.

[0004] Existing self-calibration algorithms typically rely on small initial errors. They construct spatiotemporal error models, utilize signal observation data between satellites and initial error information, and employ iterative optimization methods to estimate spatiotemporal synchronization errors and correct them. However, this differs by orders of magnitude from the large initial spatiotemporal errors (centimeter to nanosecond levels) provided by Global Navigation Satellite Systems (GNSS), resulting in insufficient convergence of parameter estimation and making it difficult to meet the high-precision synchronization requirements of complex application scenarios. Summary of the Invention

[0005] To address the limitations of existing technologies, this invention proposes a high-precision spatiotemporal synchronization method for multiple stars based on Bayesian weighted subspace fitting.

[0006] The technical solution of this invention is as follows:

[0007] A high-precision spatiotemporal synchronization method for multi-satellite systems based on Bayesian weighted subspace fitting is defined as follows: The multi-satellite system consists of N satellites existing in three-dimensional space, and the initial spatiotemporal synchronization errors of the N satellites are known. The initial coordinates of the s-th satellite are set as follows: , Actual satellites have positional errors. The physical location of the s-th satellite is represented as: Meanwhile, the initial time error value of the s-th satellite is The true time error of the s-th satellite is expressed as: ,in It is a time error caused by the channel delay and sampling clock error of the signal received by each satellite; characterized in that the method includes:

[0008] S1. Construct a signal model for mutual signal transmission and reception between satellites in a multi-satellite system, and define the narrowband signal transmission and reception between satellites. ,in Let s represent the transmitted signal of the s-th satellite at time t. In a multi-satellite system, each satellite takes turns acting as the transmitting satellite, and the rest as receiving satellites. The resulting MIMO signal model with alternating transmission and reception is:

[0009] ,

[0010] in, This represents the combination of signals received by the s-th satellite from the other N-1 satellites. for The noise vector, with noise power of , for The steering vector consists of the propagation delay and time error caused by the positional spacing:

[0011] ,

[0012] in, This represents the actual propagation delay between the transmitting and receiving satellites when satellite r receives a signal transmitted by satellite s. Error with the actual time of the received satellite r The sum of The actual position coordinates of the launched satellite s To receive the true position coordinates of satellite r, m / s is the speed of light Distance calculation for vectors; This is the transpose operation for a vector; The column vector representation of the true spatial location and true time error:

[0013] ,

[0014] in, , For the initial spatiotemporal error, These are the spatiotemporal error parameters to be estimated.

[0015] S2. Establish the joint estimation cost function for the original spatiotemporal parameters based on the subspace orthogonality principle:

[0016] ,

[0017] in, This is the cost function based on the subspace orthogonality principle; for The new guide vector, which contains each guide vector Column-wise stack, i.e. , Operations on vector column stacks; weight matrix for A block diagonal matrix, where each diagonal block corresponds to the weight of the noise subspace under the signals transmitted by the satellites in turn. ,Right now , To perform operations by stacking the matrices diagonally, For the noise subspace of the signal transmitted by satellite s, This is the conjugate transpose operation for a vector;

[0018] S3. By using the first-order Taylor approximation of the new guiding vector and combining it with Bayesian maximum a posteriori (MAP) weighted subspace fitting, a high-precision and fast-converging joint estimation cost function for spatiotemporal parameters is constructed:

[0019] ,

[0020] in, For the new cost function; This is the guiding vector under the initial spatiotemporal synchronization error; for The Jacobian matrix contains right The first-order partial derivative; and These are the covariance matrices of the spatial location error and the time error to be estimated, respectively. The new weighted matrix is ​​based on Bayesian weighted subspace fitting:

[0021] ,

[0022] in:

[0023] ,

[0024] in, This is for steering vector estimation based on known information; and It is directly through the covariance matrix of the received signal The numerical characteristic decomposition yields the signal subspace and the noise subspace; It is the eigenvalue of the signal subspace, that is, the largest eigenvalue;

[0025] S4. Solving the joint estimation cost function constructed in S3 yields the parameters to be estimated. The closed-form solution is defined. The form is:

[0026] ,

[0027] in, To perform first-order partial derivative calculations, the formula contains... , , Corresponding satellite coordinates;

[0028] when The quantity in the calculation is related to the launch of satellite s. When considering partial derivatives of coordinates, the Jacobian matrix expression is:

[0029] ,

[0030] when The quantity in the middle is related to the received satellite r. When considering partial derivatives of coordinates, the Jacobian matrix expression is:

[0031] ,

[0032] Seeking information about , The form of partial derivatives of coordinates and finding about Consistency;

[0033] Define variables and as follows:

[0034] ,

[0035] beg The closed-form solution expression is:

[0036] ,

[0037] in, Perform the matrix inversion operation; iterate through the loop, updating each time. Substitute The new system parameters are obtained, and the steering vector is then approximated until... Converging to the expected threshold At this point, a convergent solution is obtained, which means that the satellite has completed its self-spatiotemporal synchronization.

[0038] The beneficial effects of this invention are as follows: By constructing a Bayesian maximum a posteriori optimization spatiotemporal joint estimation framework and utilizing inter-satellite signal-level measurements, the method simultaneously solves for satellite position and time error vectors, effectively avoiding the error propagation problem in traditional step-by-step calibration methods. Simultaneously, by employing weighted subspace fitting and incremental update mechanisms, this method significantly improves the tolerance range for initial spatiotemporal errors of the satellite constellation, accelerates the convergence speed of solving spatiotemporal error parameters, and enhances the accuracy of spatiotemporal error parameter solutions, providing an innovative solution for high-precision spatiotemporal synchronization of distributed systems. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of satellite spatiotemporal self-calibration without a precise calibration source according to the present invention;

[0040] Figure 2 This is a schematic diagram illustrating the relationship between spatial synchronization estimation error and the number of iterations.

[0041] Figure 3 A schematic diagram illustrating the relationship between time synchronization estimation error and the number of iterations;

[0042] Figure 4 A schematic diagram of the three-dimensional spatial spectrum of the target detection after correction;

[0043] Figure 5 A schematic diagram of the three-dimensional spatial spectrum of the target detection after correction;

[0044] Figure 6 Two-dimensional heat map of target detection before correction;

[0045] Figure 7 This is a two-dimensional heat map of the target detection after correction. Detailed Implementation

[0046] The present invention will now be described in detail with reference to the accompanying drawings.

[0047] like Figure 1 As shown, assume there are N satellites in three-dimensional space, and the initial spatiotemporal synchronization errors of the N satellites are known. The initial coordinates of the nth satellite are... However, actual satellites have positional errors. Then the physical location of the nth satellite can be represented as Meanwhile, the initial time error value of the nth satellite is Due to the channel delay and sampling clock error of each satellite receiving the signal, a time error will be caused. Then the true time error of the nth satellite can be expressed as: .

[0048] The method of the present invention includes the following steps:

[0049] Step 1: Construct a MIMO signal model for multi-satellite mutual transmission and reception. N satellites in the constellation mutually transmit and receive narrowband signals, with a center frequency of... Narrowband signal form is Now, let each satellite in the constellation take turns acting as the transmitter, and the rest as receivers, to obtain a MIMO signal model with alternating transmission and reception:

[0050]

[0051] All received signals are divided into N groups, where the s-th group represents the combination of signals received by the transmitting satellite by the other N-1 satellites when the s-th satellite transmits its signal. ; for The noise vector, with noise power of ; This refers to the transmission signal of satellite s; For a specific moment; for The steering vector, composed of propagation delay and time error caused by positional spacing, takes the following form:

[0052]

[0053] in, This represents the actual propagation delay between satellites s (transmitting a signal) and r (receiving satellite). The actual time error with the received satellite r The sum of The actual coordinates of the launched satellite In order to receive the satellite's true position coordinates, m / s is the speed of light Distance calculation for vectors; This is the transpose operation for a vector; The column vector representation of the true spatial location and true time error is as follows:

[0054]

[0055] in, , For the initial spatiotemporal error, These are the spatiotemporal error parameters to be estimated.

[0056] Step 2: Establish the joint estimation cost function for the original spatiotemporal parameters based on the subspace orthogonality principle:

[0057]

[0058] in, This is the cost function based on the subspace orthogonality principle; for The new guide vector, which contains each guide vector Column-wise stack, i.e. , Operations on vector column stacks; weight matrix for A block diagonal matrix, where each diagonal block corresponds to the weight of the noise subspace under the signals transmitted by the satellites in turn. ,Right now , To perform operations by stacking the matrices diagonally, For the noise subspace of the signal transmitted by satellite s, This is the conjugate transpose operation for a vector.

[0059] Step 3: Construct a high-precision, fast-converging joint estimation cost function for spatiotemporal parameters by using the first-order Taylor approximation of the new guiding vector and combining it with Bayesian maximum a posteriori (MAP) weighted subspace fitting.

[0060]

[0061] in, For the new cost function; This is the guiding vector under the initial spatiotemporal synchronization error; and These are the covariance matrices of the spatial location error and the time error to be estimated, respectively. The new weighted matrix based on Bayesian weighted subspace fitting is in the form of...

[0062]

[0063] in:

[0064]

[0065] in, This is a guide vector estimation based on known information. and It is directly through the covariance matrix of the received signal The numerical characteristic decomposition yields the signal subspace and the noise subspace; It is the eigenvalue of the signal subspace, that is, the largest eigenvalue.

[0066] Step 4: Solve for the joint estimated cost function, in equation (5) above. for The Jacobian matrix contains right The first-order partial derivative of is of the following form:

[0067]

[0068] in, To perform operations for first-order partial derivatives.

[0069] The specific partial derivative expression within the Jacobian matrix is ​​given here, when When calculating the partial derivative of the quantity in the equation with respect to the launched satellite s, the expression is as follows:

[0070]

[0071] when When calculating the partial derivative of the quantity in the equation with respect to the receiving satellite r, the expression is as follows:

[0072]

[0073] when The value in the parameter is 0 when it is neither a transmitting nor receiving satellite. Seeking information about , The form of partial derivatives of coordinates and finding about Since the principles are consistent, I will not elaborate further.

[0074] Obtain the parameters to be estimated The closed-form solution is used to iteratively solve for the estimated spatiotemporal error parameters until convergence.

[0075] Define variables and as follows:

[0076]

[0077] Seeking Closed-form solution expression

[0078]

[0079] in, Invert a matrix.

[0080] Due to the step size limitation of the first-order Taylor approximation, the above closed-form solution of equations (8)-(12) requires iterative iteration, updating once. Substituting the new system parameters into equation (3), we can then continue to approximate the steering vector until... Converging to the expected threshold At this point, a convergent solution is obtained, which means that the satellite has completed its self-spatiotemporal synchronization.

[0081] Table 1. Detailed Explanation of the Iterative Solution Process for Spatiotemporal Parameters

[0082]

[0083] Assumption In a satellite environment, via After the Monte Carlo experiment, the spatiotemporal synchronization error is defined as follows:

[0084] 1) Space Synchronization Error (SSE) is characterized as the global root mean square value of the deviation between the actual and estimated positions of a satellite, defined as:

[0085] ,

[0086] in, For the first In the experiment, the first The estimated position vectors of the satellites; For the first The true position vector of each satellite.

[0087] 2) Time Synchronization Error (TSE) is characterized as the global root mean square value between the estimated and actual satellite time deviation, and is defined as:

[0088] ,

[0089] in, For the first In the experiment, the first The estimated time deviation of each satellite; For the first The actual time deviation of each satellite.

[0090] Assume there are 8 satellites in space taking turns transmitting and receiving signals. The initial spatiotemporal synchronization conditions are 30 cm and 3 nanoseconds. The satellite receivers can receive 100 samples, the carrier frequency is 300 MHz, and the satellites are arranged in an approximately circular formation with a spacing between 50 km and 200 km. The satellite altitude is 7371e3 km (Earth's radius + 1000 km Earth's surface altitude). Each satellite transmits a Gaussian random signal. The relationship between the space synchronization error estimate and the time synchronization error estimate after 200 independent Monte Carlo experiments and the number of iterations is plotted as follows: Figure 2 and Figure 3 As shown.

[0091] The comparison of spatial error convergence speed and temporal error convergence speed under the two different weighting methods shows that, under the initial conditions, the weighting scheme 2 using Bayesian weighted subspace fitting converges faster and has higher parameter estimation accuracy than the traditional weighting scheme 1 using the noise subspace as the weight matrix for spatiotemporal joint correction of spatiotemporal synchronization error. Furthermore, the spatiotemporal synchronization algorithm of this invention can converge to spatial precision synchronization of 45.2 mm and temporal precision synchronization of 11.58 ps under these large error initial conditions, indicating that the weight matrix replacement strategy in the Bayesian weighted subspace fitting method enables the cost function to converge quickly and efficiently, effectively improving the spatiotemporal synchronization efficiency and accuracy of the system.

[0092] Verification of improved target detection performance before and after satellite spatiotemporal synchronization correction: Assuming the above satellites form a distributed array to detect the target, which is located at the origin, with a signal-to-noise ratio of 0dB, and the target detection method is a subspace-based multi-signal classification method. The normalized spatial spectrum and two-dimensional heatmap for each satellite are shown below. Figure 4 , Figure 5 , Figure 6 and Figure 7 As shown, the spatial spectrum before correction showed many spurious peaks, while after correction, a single peak appeared only at the target location, eliminating the original fuzzy spurious peaks. This verifies that the satellite spatiotemporal synchronization correction significantly improves the target detection performance.

Claims

1. A high-precision spatiotemporal synchronization method for multi-satellite systems based on Bayesian weighted subspace fitting. The multi-satellite system is defined as consisting of N satellites existing in three-dimensional space, and the initial spatiotemporal synchronization errors of the N satellites are known. The initial coordinates of the s-th satellite are set as follows: , Actual satellites have positional errors. The physical location of the s-th satellite is represented as: Meanwhile, the initial time error value of the s-th satellite is The true time error of the s-th satellite is expressed as: ,in It is a time error caused by the channel delay and sampling clock error of the signal received by each satellite; its characteristic is that... The method includes: S1. Construct a signal model for mutual signal transmission and reception between satellites in a multi-satellite system, and define the narrowband signal transmission and reception between satellites. ,in Let s represent the transmitted signal of the s-th satellite at time t. In a multi-satellite system, each satellite takes turns acting as the transmitting satellite, and the rest as receiving satellites. The resulting MIMO signal model with alternating transmission and reception is: ， in, This represents the combination of signals received by the s-th satellite from the other N-1 satellites. for The noise vector, with noise power of , for The steering vector is composed of the propagation delay and time error caused by the positional spacing: ， in, This represents the actual propagation delay between the transmitting and receiving satellites when satellite r receives a signal transmitted by satellite s. Error with the actual time of the received satellite r The sum of The actual position coordinates of the launched satellite s To receive the true position coordinates of satellite r, m / s is the speed of light Distance calculation for vectors; This is the transpose operation for a vector; The column vector representation of the true spatial location and true time error: ， in, , For the initial spatiotemporal error, These are the spatiotemporal error parameters to be estimated. S2. Establish the joint estimation cost function for the original spatiotemporal parameters based on the subspace orthogonality principle: ， in, This is the cost function based on the subspace orthogonality principle; for The new guide vector, which contains each guide vector Column-wise stack, i.e. , Operations on vector column stacks; weight matrix for A block diagonal matrix, where each diagonal block corresponds to the weight of the noise subspace under the signals transmitted by the satellites in turn. ,Right now , To perform operations by stacking the matrices diagonally, For the noise subspace of the signal transmitted by satellite s, This is the conjugate transpose operation for a vector; S3. By using the first-order Taylor approximation of the new guiding vector and combining it with Bayesian maximum a posteriori (MAP) weighted subspace fitting, a high-precision and fast-converging joint estimation cost function for spatiotemporal parameters is constructed: ， in, For the new cost function; This is the guiding vector under the initial spatiotemporal synchronization error; for The Jacobian matrix contains right The first-order partial derivative; and These are the covariance matrices of the spatial location error and the time error to be estimated, respectively. The new weighted matrix is ​​based on Bayesian weighted subspace fitting: ， in: ， in, This is for steering vector estimation based on known information; and It is directly through the covariance matrix of the received signal The numerical characteristic decomposition yields the signal subspace and the noise subspace; It is the eigenvalue of the signal subspace, that is, the largest eigenvalue; S4. Solving the joint estimation cost function constructed in S3 yields the parameters to be estimated. The closed-form solution is defined. The form is: ， in, To perform first-order partial derivative calculations, the formula contains... , , Corresponding satellite coordinates; when The quantity in the calculation is related to the launch of satellite s. When considering partial derivatives of coordinates, the Jacobian matrix expression is: ， when The quantity in the middle is related to the received satellite r. When considering partial derivatives of coordinates, the Jacobian matrix expression is: ， Seeking information about , The form of partial derivatives of coordinates and finding about Consistency; Define variables and as follows: ， beg The closed-form solution expression is: ， in, Perform the matrix inversion operation; iterate through the loop, updating each time. Substitute The new system parameters are obtained, and the steering vector is then approximated until... Converging to the expected threshold At this point, a convergent solution is obtained, which means that the satellite has completed its self-spatiotemporal synchronization.

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