A spatiotemporal synchronization method for space-based distributed satellite arrays

Abstract

The present invention discloses a spatiotemporal synchronization method for a space-based distributed satellite array, comprising obtaining an initial clock difference between each satellite in the space-based distributed satellite array and a reference point, as well as observation position and time information containing spatial errors; measuring the time difference and observation time of a signal transmitted by one satellite to the other satellite between any two satellites based on the initial clock difference between the satellite and the reference point; finding the true spatial position of each satellite and the clock difference with the reference point when the total inter-satellite error function converges to a minimum value using a gradient descent optimization method based on backtracking line search based on the observation positions, time differences and observation times of all satellites and preset iterative initial spatial positions and iterative initial clock differences; and adjusting the position of the satellite based on the true spatial position of the satellite and the clock difference with the reference point to achieve spatial synchronization.

Description

Technical Field

[0001] The present invention relates to satellite space-time synchronization technology, and in particular to a space-time synchronization method for a space-based distributed satellite array. Background Art

[0002] In actual engineering applications, since unit radars are equipped with independent clock and local oscillator systems, variations in trigger clocks and feeder link instability introduce time synchronization errors. Oscillator accuracy and stability introduce random initial phase errors, making clock and position deviations between devices on different platforms inevitable. Especially for signal-level positioning algorithms, even minimal errors can cause significant shifts in the array signal phase, leading to positioning failure. In space-based distributed satellite arrays, ranging is based on timing, while orbit determination and positioning require the time synchronization of all observables. Therefore, time synchronization is crucial for the construction of distributed satellite arrays. Spatiotemporal synchronization technology precisely aligns temporal and spatial information between different devices, effectively ensuring data accuracy and consistency.

[0003] like Figure 1 As shown, the existing inter-satellite two-way time synchronization method involves two satellites sending and receiving timing signals through their respective communication equipment. The time required for the signal to travel back and forth is calculated, combining propagation path delays and equipment characteristics. This method, in turn, derives the clock difference between the two locations and the inter-satellite distance. This method, through two-way signal transmission, eliminates propagation path uncertainties and systematic errors in equipment delays, and improves measurement accuracy through subsequent data processing by ground base stations.

[0004] In the above method, it is necessary to introduce additional motion parameters such as the satellite radial velocity observed by the ground base station for error correction. However, the additional reference source itself often has a certain synchronization error, which affects the synchronization accuracy of the satellite constellation. The error introduced by the transmission signal between the base station and the satellite is not taken into account, resulting in deviations in satellite synchronization, which affects the satellite positioning accuracy to a certain extent. Summary of the Invention

[0005] In view of the above-mentioned deficiencies in the prior art, the present invention provides a space-time synchronization method for a space-based distributed satellite array, which avoids the use of an external reference source and the introduction of new errors by performing only inter-satellite measurements.

[0006] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0007] A method for spatiotemporal synchronization of a space-based distributed satellite array is provided, comprising the steps of:

[0008] S1. Obtain the initial clock difference between each satellite in the space-based distributed satellite array and the reference point, as well as the observed position and time information containing spatial errors;

[0009] S2. Measure the time difference and observation time of a signal transmitted from one of two satellites to the other satellite based on the initial clock difference between the satellite and the reference point.

[0010] S3. Based on the observed positions, time differences, and observation times of all satellites and the preset iterative initial spatial positions and iterative initial clock errors, a gradient descent optimization method based on backtracking line search is used to find the true spatial position of each satellite and the clock error from the reference point when the total inter-satellite error function converges to the minimum value.

[0011] S4. Adjust the position of the satellite according to its real spatial position and the clock difference with the reference point to achieve spatial synchronization.

[0012] Furthermore, the expression of the inter-satellite total error function is:

[0013]

[0014] Where F is the total inter-satellite error function; is the clock difference between satellite n and the reference point; and are the true spatial position of satellite n and the observed position with spatial error, respectively; N is the total number of satellites in the space-based distributed satellite array; c is the speed of light; is the time difference of transmitting signals from satellite m to satellite n; is the observation time of the signal transmitted by satellite m to satellite n; is the Euclidean norm of the vector; and are functions of parameters, is the inter-satellite link propagation delay between satellites m and n, is the intersatellite link propagation delay between the reference point and satellite m; is the measured value.

[0015] The beneficial effects of the above technical solution are: the inter-satellite total error function constructed by this solution transforms the spatiotemporal synchronization problem into a multi-objective optimization problem, thereby avoiding the use of external reference sources and the introduction of new errors through inter-satellite data transmission.

[0016] Furthermore, all satellites in the space-based distributed satellite array transmit the same single-frequency continuous wave signal in rotation, and the expression is:

[0017]

[0018] in, is a single-frequency continuous wave signal; is the complex envelope of the signal; f is the carrier frequency of the signal; t is time; j is the imaginary unit; To take the exponential with base e;

[0019] When the time delay of the single-frequency continuous wave signal is much smaller than the inverse of the broadband, the phase difference between the intersatellite signal and the observation signal is:

[0020]

[0021] in, The transmitted signal of satellite m received by satellite n; The transmitted signal of satellite m is received at the reference point;

[0022] When the phase difference When , the expression for measuring the time difference between any two satellites transmitting signals to another satellite and the observation time is:

[0023] ,

[0024] in, is the observation noise of the signal transmitted from satellite m to satellite n.

[0025] Furthermore, the intersatellite link propagation delay and The expressions are:

[0026] ,

[0027] in, and are the real spatial positions of satellite m and reference point respectively.

[0028] Furthermore, step S3 further includes:

[0029] S31, substituting the preset iterative initial spatial position, iterative initial clock error, observed position and time difference, and observation time of all satellites into the inter-satellite total error function to obtain a total error value;

[0030] S32. Calculate the gradient of the error function based on the total error value:

[0031]

[0032] in, is the gradient of the total intersatellite error function; is transposed; 、 and is the real space coordinate of satellite n, ; is the clock difference between satellite n and the reference point; is the total inter-satellite error function The partial derivative of is the total inter-satellite error function The partial derivative of is the total inter-satellite error function The partial derivative of is the total inter-satellite error function The partial derivative of

[0033] S33, determine whether the current total error value meets the Armijo-Goldstein condition, if so, go to step S34, otherwise go to step S35;

[0034] S34, Update , , , and substitute the updated parameters into the intersatellite total error function to obtain the total error value, and then return to step S32; wherein, and are the step sizes at the kth and k+1th iterations respectively; is a variable, 、 and is the real space coordinate of satellite n at the kth iteration; is the direction of gradient descent; is the gradient of the total inter-satellite error function at the kth iteration; is the step size attenuation factor, ;

[0035] S35. Output the total error value obtained at the kth iteration and variables .

[0036] Furthermore, the Armijo-Goldstein condition is:

[0037]

[0038] in, is a constant; for The transpose of .

[0039] The beneficial effects of the above technical solution are as follows: Because the inter-satellite total error function (TIES) in this solution is multivariable and locally convex, it can be optimized using the gradient descent method. The partial derivatives of the error function with respect to the clock error and position parameters are calculated to form a gradient vector, and the step size is dynamically adjusted in combination with the backtracking line search method. The backtracking line search method satisfies the descent condition of the TIES by gradually reducing the step size, avoiding the non-convergence or slow convergence that may result from a fixed step size, thereby improving the convergence of the optimization and the accuracy of the results. Through iterative calculation, the error function is ultimately converged, and the actual clock error and spatial position correction values ​​of the satellite are obtained, significantly improving the spatiotemporal synchronization accuracy of the space-based distributed satellite array.

[0040] The beneficial effects of the present invention are as follows: By setting a reference point and performing spatiotemporal synchronization based on the satellite array via intersatellite links and the reference point signal, this solution uses a gradient descent optimization method based on backtracking line search to find the minimum value of the intersatellite total error function. This method determines the true spatial position of each satellite and its clock difference from the reference point. The constructed intersatellite total error function transforms the spatiotemporal synchronization problem into a multi-objective optimization problem. This avoids the use of external reference sources and the introduction of new errors through intersatellite data transmission.

[0041] This scheme uses the backtracking line search method to dynamically adjust the step size of gradient descent, taking into account the balance between convergence speed and optimization accuracy, significantly improving the convergence of the inter-satellite total error function and the effectiveness of the optimization results; by observing the phase difference between the rotating signal reception and transmission of multiple satellites and the reference point signal, the time clock difference and spatial position error of each satellite are dynamically optimized to achieve high-precision spatiotemporal synchronization of the entire distributed satellite array. This method can be widely used in navigation, communication and other tasks of space-based distributed satellite arrays. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is a schematic diagram of intersatellite bidirectional measurement in the prior art.

[0043] Figure 2 Schematic diagram of satellite rotation communication in the space-based distributed satellite array of this scheme.

[0044] Figure 3 Schematic diagram of local signal transmission and reception in a space-based distributed satellite array.

[0045] Figure 4 The flowchart of the spatiotemporal synchronization method for space-based distributed satellite arrays is shown.

[0046] Figure 5 Schematic diagram of space-based distributed satellites and reference points in a specific example.

[0047] Figure 6 Schematic diagram of the time synchronization result of the satellite platform in a specific example.

[0048] Figure 7 Schematic diagram of the spatial synchronization result of the satellite platform in a specific example.

[0049] Figure 8 This is a schematic diagram of the change of the total inter-satellite error function with the number of iterations in a specific example.

[0050] Figure 9 Schematic diagram of the clock error iteration process of each satellite platform in a space-based distributed satellite array in a specific example. DETAILED DESCRIPTION

[0051] 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.

[0052] To facilitate understanding of this solution, this solution presents a space-time synchronization scenario for a space-based distributed satellite array. There are N satellites in the space-based distributed satellite array, and signals are transmitted and received between each two satellites through inter-satellite links. At the same time, all satellites transmit signals to the same reference point as a baseline signal. The reference point is an arbitrary imaginary point in the model. The schematic diagram of the array satellite rotation communication is shown below. Figure 2 As shown, the local schematic diagram is as follows Figure 3 shown.

[0053] In the implementation process of this solution, the preset reference point spatial position and time base are known and accurate, respectively and The real spatial position of the nth satellite is , the observation position with spatial error is , and the clock difference with the reference point is All satellites transmit the same single-frequency continuous wave signal in rotation .

[0054] refer to Figure 4 , Figure 4 FIG. 4 shows a flow chart of a space-time synchronization method for a space-based distributed satellite array; FIG. Figure 4 As shown, the method S includes steps S1 to S5.

[0055] In step S1, the initial clock difference between each satellite in the space-based distributed satellite array and the reference point and the observed position and time information containing spatial errors are obtained; the initial real spatial position and initial clock difference corresponding to each satellite are randomly set, and it is preferred that the iterative initial spatial position is set to the real spatial position plus random deviations in three directions, and the initial clock difference is set to 0.

[0056] In step S2, based on the initial clock difference between the satellite and the reference point, the time difference and observation time of the signal transmitted by one satellite to the other satellite are measured;

[0057] During implementation, this solution preferably transmits the same single-frequency continuous wave signal in rotation among all satellites in the space-based distributed satellite array, and its expression is:

[0058]

[0059] in, is a single-frequency continuous wave signal; is the complex envelope of the signal; f is the carrier frequency of the signal; t is time; j is the imaginary unit; To take the exponential with base e;

[0060] When the time delay of the single-frequency continuous wave signal is much smaller than the inverse of the broadband, the phase difference between the intersatellite signal and the observation signal is:

[0061]

[0062] in, The transmitted signal of satellite m received by satellite n; The transmitted signal of satellite m is received at the reference point;

[0063] When the phase difference When , the expression for measuring the time difference between any two satellites transmitting signals to another satellite and the observation time is:

[0064] ,

[0065] in, is the observation noise of the signal transmitted from satellite m to satellite n.

[0066] Intersatellite link propagation delay and The expressions are:

[0067] ,

[0068] in, and are the real spatial positions of satellite m and reference point respectively.

[0069] In step S3, based on the observed positions, time differences, and observation times of all satellites and the preset iterative initial spatial positions and iterative initial clock errors, a gradient descent optimization method based on backtracking line search is used to find the true spatial position of each satellite and the clock error from the reference point when the inter-satellite total error function converges to the minimum value. During implementation, the preferred expression of the inter-satellite total error function in this scheme is:

[0070]

[0071] Where F is the total inter-satellite error function; is the clock difference between satellite n and the reference point; and are the true spatial position of satellite n and the observed position with spatial error, respectively; N is the total number of satellites in the space-based distributed satellite array; c is the speed of light; is the time difference of transmitting signals from satellite m to satellite n; is the observation time of the signal transmitted by satellite m to satellite n; is the Euclidean norm of the vector; and are functions of parameters, is the inter-satellite link propagation delay between satellites m and n, is the intersatellite link propagation delay between the reference point and satellite m; is the measured value.

[0072] In step S4, the position of the satellite is adjusted according to the real spatial position of the satellite and the clock difference with the reference point to achieve spatial synchronization.

[0073] In one embodiment of the present invention, step S3 further includes:

[0074] S31, substituting the preset iterative initial spatial position, iterative initial clock error, observed position and time difference, and observation time of all satellites into the inter-satellite total error function to obtain a total error value;

[0075] S32. Calculate the gradient of the error function based on the total error value:

[0076]

[0077] in, is the gradient of the total intersatellite error function; is transposed; 、 and is the real space coordinate of satellite n, ; is the clock difference between satellite n and the reference point; is the total inter-satellite error function The partial derivative of is the total inter-satellite error function The partial derivative of is the total inter-satellite error function The partial derivative of is the total inter-satellite error function The partial derivative of

[0078] S33. Determine whether the current total error value satisfies the Armijo-Goldstein condition. If so, proceed to step S34; otherwise, proceed to step S35. The Armijo-Goldstein condition is:

[0079]

[0080] in, is a constant; for The transpose of .

[0081] S34, Update , , , and substitute the updated parameters into the intersatellite total error function to obtain the total error value, and then return to step S32; wherein, and are the step sizes at the kth and k+1th iterations respectively; is a variable, 、 and is the real space coordinate of satellite n at the kth iteration; is the direction of gradient descent; is the gradient of the total inter-satellite error function at the kth iteration; is the step size attenuation factor, ;

[0082] S35. Output the total error value obtained at the kth iteration and variables .

[0083] In this scheme, the total error value obtained when the kth iteration is obtained is The final time-space synchronization error correction value can be calculated based on this parameter for:

[0084]

[0085] in, Before the iteration starts The value of .

[0086] In order to verify the relevant performance of the proposed spatiotemporal synchronization method for space-based distributed satellite arrays, which can quickly and accurately correct the clock difference and spatial position error between satellites, the following is explained with specific examples.

[0087] Space-based distributed satellites and reference point locations such as Figure 5 As shown, black represents satellites, red represents reference points, and the number of satellites , the initial position is selected from the actual situation, such as Figure 5 The reference point coordinates are set as , the time base is set to Assuming that the initial clock bias of each satellite is randomly generated with a zero-mean normal distribution, the initial step size of the gradient descent is , backtracking line search step size attenuation factor ,constant To prevent the search time from being too long or falling into an infinite loop, the maximum number of step attenuation is limited to 150 times. The initial real space coordinates of the satellite and reference point refer to Table 1.

[0088] Table 1 Satellite initial coordinates

[0089]

[0090] Figure 6 and Figure 7 The Y axis is the spatial error value before correction. , the X-axis is the time error value before correction . Through Figure 6 and Figure 7 It can be seen that the method proposed in this scheme can , spatial error The overall error can be effectively corrected within the specified range.

[0091] by Figure 6 For example, the time error before correction is 3ns, and after correction it is 30ps, with a correction degree of 90%. Figure 7 Taking the point (0, 30) in the figure as an example, the spatial error before correction is 30cm, and after correction it is 10mm, with a correction degree of 96%. The main reason why the correction degree cannot reach 100% is that there are unavoidable observation errors. ,as well as It can only drop to near the lowest value.

[0092] In this noise case, the error function The trend of the iteration process is as follows Figure 8 As shown in the figure, the changes of the real clock error and the estimated clock error of each satellite platform are as follows: Figure 9 As shown. Figure 8 and Figure 9 It can be seen that after the number of iterations reaches 100, the changes in the clock errors tend to be smooth and the error function converges successfully. The simulation results show that the method of the present invention can significantly improve positioning accuracy and clock synchronization efficiency.

Claims

1. A space-time synchronization method for a space-based distributed satellite array, characterized in that: Including steps: S1. Obtain the initial clock difference between each satellite in the space-based distributed satellite array and the reference point, as well as the observed position and time information containing spatial errors; S2. Measure the time difference and observation time of a signal transmitted from one of two satellites to the other satellite based on the initial clock difference between the satellite and the reference point. S3. Based on the observed positions, time differences, and observation times of all satellites and the preset iterative initial spatial positions and iterative initial clock errors, a gradient descent optimization method based on backtracking line search is used to find the true spatial position of each satellite and the clock error from the reference point when the total inter-satellite error function converges to the minimum value. S4. Adjust the position of the satellite according to its real spatial position and the clock difference with the reference point to achieve spatial synchronization; The expression of the intersatellite total error function is: Where F is the total inter-satellite error function; is the clock difference between satellite n and the reference point; and are the true spatial position of satellite n and the observed position with spatial error, respectively; N is the total number of satellites in the space-based distributed satellite array; c is the speed of light; is the time difference of transmitting signals from satellite m to satellite n; is the observation time of the signal transmitted by satellite m to satellite n; is the Euclidean norm of the vector; and are functions of parameters, is the inter-satellite link propagation delay between satellites m and n, is the intersatellite link propagation delay between the reference point and satellite m; is the measured value.

2. The spatiotemporal synchronization method for a space-based distributed satellite array according to claim 1, characterized in that: All satellites in the space-based distributed satellite array transmit the same single-frequency continuous wave signal in rotation, and its expression is: in, is a single-frequency continuous wave signal; is the complex envelope of the signal; f is the carrier frequency of the signal; t is time; j is the imaginary unit; To take the exponential with base e; When the time delay of the single-frequency continuous wave signal is much smaller than the inverse of the broadband, the phase difference between the intersatellite signal and the observation signal is: in, The transmitted signal of satellite m received by satellite n; The transmitted signal of satellite m is received at the reference point; When the phase difference When , the expression for measuring the time difference between any two satellites transmitting signals to another satellite and the observation time is: ， in, is the observation noise of the signal transmitted from satellite m to satellite n.

3. The spatiotemporal synchronization method for a space-based distributed satellite array according to claim 1, characterized in that: Intersatellite link propagation delay and The expressions are: ， in, and are the real spatial positions of satellite m and reference point respectively.

4. The spatiotemporal synchronization method for a space-based distributed satellite array according to claim 1, wherein: Step S3 further comprises: S31, substituting the preset iterative initial spatial position, iterative initial clock error, observed position and time difference, and observation time of all satellites into the inter-satellite total error function to obtain a total error value; S32. Calculate the gradient of the error function based on the total error value: in, is the gradient of the total intersatellite error function; is transposed; 、 and is the real space coordinate of satellite n, ; is the clock difference between satellite n and the reference point; is the total inter-satellite error function The partial derivative of is the total inter-satellite error function The partial derivative of is the total inter-satellite error function The partial derivative of is the total inter-satellite error function The partial derivative of S33, determine whether the current total error value meets the Armijo-Goldstein condition, if so, go to step S34, otherwise go to step S35; S34, Update , , , and the updated parameters Substitute the intersatellite total error function to obtain the total error value, and then return to step S32; wherein, and are the step sizes at the kth and k+1th iterations respectively; is a variable, 、 and is the real space coordinate of satellite n at the kth iteration; is the direction of gradient descent; is the gradient of the total inter-satellite error function at the kth iteration; is the step size attenuation factor, ; S35. Output the total error value obtained at the kth iteration and variables .

5. The time-space synchronization method for a space-based distributed satellite array according to claim 4, characterized in that: The Armijo-Goldstein conditions are: in, is a constant; for The transpose of .

Images