Space-time synchronization method for space-based distributed satellite array

Abstract

The invention discloses a space-time synchronization method for a space-based distributed satellite array. The method comprises the following steps: acquiring an initial clock error between each satellite in the space-based distributed satellite array and a reference point, and observation position and time information containing a space error; according to the initial clock difference between the satellites and the reference point, measuring the time difference and the observation time when one satellite transmits signals to the other satellite in any two satellites; according to the observation positions, the time differences and the observation time of all satellites and a preset iteration initial spatial position and a preset iteration initial clock correction, searching a real spatial position of each satellite and a clock correction between the real spatial position and the reference point when the inter-satellite total error function converges to a minimum value based on a backtracking line search gradient descent optimization method; and adjusting the position of the satellite according to the real spatial position of the satellite and the clock difference between the satellite and the reference point so as to realize 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 the unit radar is equipped with an independent clock and local oscillator system, the unevenness of the trigger clock and the instability of the feeder link introduce time synchronization errors, and the accuracy and stability of the oscillator introduce random initial phase errors. Clock deviations and position deviations of devices on different platforms are inevitable. Especially for signal-level positioning algorithms, extremely small errors can cause huge changes in the phase of the array signal, resulting in positioning failure. In space-based distributed satellite arrays, the basis of ranging is time measurement, and the premise of orbit determination and positioning is the time synchronization of each observable. Therefore, time synchronization is the key to the construction of distributed satellite arrays. Space-time synchronization technology can accurately align the time and space information between different devices, so that data accuracy and uniformity can be effectively guaranteed.

[0003] like Figure 1 As shown in the figure, the existing inter-satellite two-way time synchronization method is that two satellites send and receive timing signals through their respective communication equipment, and calculate the time required for the signal to go back and forth, combining the propagation path delay and equipment characteristics, so as to deduce the clock difference between the two places and the distance between the satellites. This method can eliminate the uncertainty of the propagation path and the systematic error of the equipment delay through two-way signal propagation, and can improve the measurement accuracy through subsequent data processing of the ground base station.

[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. 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 considered, 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 space-time synchronization method for a space-based distributed satellite array provided by the present invention 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 space-time synchronization method for a space-based distributed satellite array is provided, comprising the steps of:

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

[0009] S2, based on the initial clock difference between the satellite and the reference point, measure the time difference and observation time of a signal transmitted by one of any two satellites to the other satellite;

[0010] S3, according to the observed positions, time differences and observed times of all satellites and the preset iterative initial spatial positions and iterative initial clock errors, the true spatial position of each satellite and the clock error with the reference point when the inter-satellite total error function converges to the minimum value are found by the gradient descent optimization method based on the backtracking line search;

[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; Δt n is the clock difference between satellite n and the reference point; P n and are the real 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; T mn 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; d mn = c·τ mn and d m0 = c·τ m0 are all functions of parameters, τ mn is the intersatellite link propagation delay between satellites m and n, τ m0 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 as follows: the intersatellite total error function constructed by this solution transforms the time-space synchronization problem into a multi-objective optimization problem, thereby avoiding the use of an external reference source and the introduction of new errors through intersatellite 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] y(t)=s(t)exp{j2πft}

[0018] Where y(t) is a single-frequency continuous wave signal; s(t) is the complex envelope of the signal; f is the carrier frequency of the signal; t is time; j is an imaginary unit; exp(·) is an 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 observed signal is:

[0020]

[0021] Among them, y mn (t) is the transmission signal of satellite m received by satellite n; y m0 (t) is the transmitted signal of satellite m received at the reference point;

[0022] When the phase difference When equation (1) is satisfied, the expression for measuring the time difference and observation time of a signal transmitted from one satellite to another satellite between any two satellites is:

[0023] T mn =Δt n -(τ mn -τ m0 ),

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

[0025] Furthermore, the intersatellite link propagation delay τ mn and τ m0 The expressions are:

[0026] τ mn =||p m -p n || / c, τ m0 =||p m -p base || / c

[0027] Among them, p m and p base 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; [·]T is the transpose; x n ,y n and z n is the real space coordinate of satellite n, [x n y n z n ] T =P n ; Δt n is the clock difference between satellite n and the reference point; is the total inter-satellite error function Δt n The partial derivative of is the total intersatellite error function for x n The partial derivative of is the total intersatellite error function for y n The partial derivative of is the total intersatellite error function for z n The partial derivative of

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

[0034] S34, update t k+1 =βt k , x k+1 =x k +t k+1 Δx k , k=k+1, and substitute the updated parameters into the inter-satellite total error function to obtain the total error value, and then return to step S32; wherein, t k and t k+1 are the step sizes for the kth and k+1th iterations respectively; x k =[Δt n (k) x n (k) y n (k) z n (k)]| n∈[1,N] is a variable, x n (k), y n (k) and z n (k) 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; β is the step attenuation factor, 0<β<1;

[0035] S35, output the total error value F(x) obtained at the kth iteration k ) and the variable x k .

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

[0037]

[0038] Among them, α is a constant; for The transpose of .

[0039] The beneficial effects of the above technical solution are as follows: since the inter-satellite total error function of this solution is a multivariable locally convex property, the gradient descent method can be used for optimization, 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 satisfies the descent condition of the inter-satellite total error function by gradually reducing the step size, avoiding non-convergence or slow convergence speed that may be caused by a fixed step size, thereby improving the convergence of the optimization and the accuracy of the results. Through iterative calculation, the convergence of the error function is finally achieved, and the actual clock error and spatial position correction value of the satellite are obtained, which significantly improves the spatiotemporal synchronization accuracy of the space-based distributed satellite array.

[0040] Furthermore, the partial derivative and The expressions are:

[0041]

[0042] in, and is the observed coordinate of satellite m with spatial error, is the observed position of satellite m with spatial error; x 0 ,y 0 and z 0 is the real space coordinate of the reference point; [x 0 y 0 z 0 ] T =P base is the real space position of the reference point; x m ,y m and z m is the real space coordinate of satellite m; [x m y m z m ] T =P m is the real spatial position of satellite m.

[0043] The beneficial effects of the present invention are as follows: the present scheme sets a reference point, and performs space-time synchronization based on the satellite array through the intersatellite link and the reference point signal. During space-time synchronization, the intersatellite total error function converges to the minimum value based on the gradient descent optimization method of the backtracking line search, thereby obtaining the real spatial position of each satellite and the clock difference with the reference point. The constructed intersatellite total error function converts the space-time synchronization problem into a multi-objective optimization problem, thereby avoiding the use of an external reference source and the introduction of new errors through intersatellite data transmission. .

[0044] This scheme adopts 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; through the phase difference observation of the rotation signal reception and transmission of multiple satellites and the reference point signal, the time clock error 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

[0045] Figure 1 This is a schematic diagram of inter-satellite bidirectional measurement in the prior art.

[0046] Figure 2 This is a schematic diagram of satellite rotation communication in the space-based distributed satellite array of this scheme.

[0047] Figure 3 Schematic diagram of local signal reception and transmission in a space-based distributed satellite array.

[0048] Figure 4 The present invention is a flow chart of a method for spatiotemporal synchronization of space-based distributed satellite arrays.

[0049] Figure 5 It is a schematic diagram of space-based distributed satellites and reference points in a specific example.

[0050] Figure 6 It is a schematic diagram of the time synchronization result of the satellite platform in a specific example.

[0051] Figure 7 It is a schematic diagram of the spatial synchronization result of the satellite platform in a specific example.

[0052] Figure 8 It is a schematic diagram of the change process of the total inter-satellite error function with the number of iterations in a specific example.

[0053] Fig. 9 It is a schematic diagram of the clock error iteration process of each satellite platform in the space-based distributed satellite array in a specific example. DETAILED DESCRIPTION

[0054] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0055] In order to facilitate the understanding of this scheme, this scheme gives a space-time synchronization scenario of a space-based distributed satellite array. There are N satellites in the space-based distributed satellite array, and the signal transmission and reception between two satellites are realized through inter-satellite links. At the same time, all satellites transmit signals to the same reference point as a reference signal. The reference point is an arbitrary imaginary point of the model. The schematic diagram of the array satellite rotation communication is as follows Figure 2 As shown, the local schematic diagram is as follows Figure 3 shown.

[0056] In the implementation process of this scheme, the spatial position and time base of the preset reference point are known and accurate, and are set as P base =[x 0 y 0 z 0 ] T and T base =t 0 The real spatial position of the nth satellite is P n =[x n y n z n ] T , the observation position with spatial error is The clock difference with the reference point is Δt n =t n -t 0 , all satellites transmit the same single-frequency continuous wave signal y(t)=s(t)exp{j2πft} in rotation.

[0057] refer to Figure 4 , Figure 4 A flow chart of a space-time synchronization method for a space-based distributed satellite array is shown; Figure 4 As shown, the method S includes steps S1 to S5.

[0058] In step S1, the initial clock difference between each satellite and the reference point in the space-based distributed satellite array 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 the iterative initial spatial position is preferably set to the real spatial position plus random deviations in three directions, and the initial clock difference is set to 0.

[0059] In step S2, the time difference and observation time of a signal transmitted from one satellite to another satellite among any two satellites are measured according to the initial clock difference between the satellite and the reference point;

[0060] 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:

[0061] y(t)=s(t)exp{j2πft}

[0062] Where y(t) is a single-frequency continuous wave signal; s(t) is the complex envelope of the signal; f is the carrier frequency of the signal; t is time; j is an imaginary unit; exp(·) is an exponential with base e;

[0063] 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 observed signal is:

[0064]

[0065] Among them, y mn (t) is the transmission signal of satellite m received by satellite n; y m0 (t) is the transmitted signal of satellite m received at the reference point;

[0066] When the phase difference When equation (1) is satisfied, the expression for measuring the time difference and observation time of a signal transmitted from one satellite to another satellite between any two satellites is:

[0067] T mn =Δt n -(τ mn -τ m0 ),

[0068] Among them, n mn is the observation noise of the signal transmitted from satellite m to satellite n.

[0069] Intersatellite link propagation delay τ mn and τ m0 The expressions are:

[0070] τ mn =||p m -p n || / c, τ m0 =||p m -p base || / c

[0071] Among them, p m and p base are the real spatial positions of satellite m and reference point respectively.

[0072] In step S3, according to the observation positions, time differences and observation times of all satellites and the preset iterative initial spatial positions and iterative initial clock errors, the gradient descent optimization method based on the backtracking line search is used to find the real spatial position of each satellite and the clock error with the reference point when the inter-satellite total error function converges to the minimum value; when implemented, the expression of the inter-satellite total error function is preferably:

[0073]

[0074] Where F is the total inter-satellite error function; Δt n is the clock difference between satellite n and the reference point; P n and are the real 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; T mn 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; d mn = c·τ mn and d m0 = c·τ m0 are all functions of parameters, τ mn is the intersatellite link propagation delay between satellites m and n, τ m0 is the intersatellite link propagation delay between the reference point and satellite m; is the measured value.

[0075] 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.

[0076] In one embodiment of the present invention, step S3 further comprises:

[0077] 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;

[0078] S32. Calculate the gradient of the error function based on the total error value:

[0079]

[0080] in, is the gradient of the total intersatellite error function; [·] T is the transpose; x n ,y n and z n is the real space coordinate of satellite n, [x n y n zn ] T =P n ; Δt n is the clock difference between satellite n and the reference point; is the total inter-satellite error function Δt n The partial derivative of is the total intersatellite error function for x n The partial derivative of is the total intersatellite error function for y n The partial derivative of is the total intersatellite error function for z n The partial derivative of

[0081] S33, determine whether the current total error value meets the Armijo-Goldstein condition, if so, proceed to step S34, otherwise proceed to step S35; wherein the Armijo-Goldstein condition is:

[0082]

[0083] Among them, α is a constant; for The transpose of .

[0084] S34, update t k+1 =βt k , x k+1 =x k +t k+1 Δx k , k=k+1, and substitute the updated parameters into the inter-satellite total error function to obtain the total error value, and then return to step S32; wherein, t k and t k+1 are the step sizes for the kth and k+1th iterations respectively; x k =[Δt n (k) x n (k) y n (k) z n (k)]| n∈[1,N] is a variable, x n (k), y n (k) and z n (k) 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; β is the step attenuation factor, 0<β<1;

[0085] S35, output the total error value F(x) obtained at the kth iteration k ) and the variable x k .

[0086] Partial derivatives in step S32 and The expressions are:

[0087]

[0088] in, and is the observed coordinate of satellite m with spatial error, is the observed position of satellite m with spatial error; x 0 ,y 0 and z 0 is the real space coordinate of the reference point; [x 0 y 0 z 0 ] T =P base is the real space position of the reference point; x m ,y m and z m is the real space coordinate of satellite m; [x m y m z m ] T =P m is the real spatial position of satellite m.

[0089] In this scheme, when the total error value F(x k ), the final spatiotemporal synchronization error correction value error can be calculated based on this parameter as:

[0090] error=F real -F(x k )

[0091] Among them, F real is the value of F before the iteration starts.

[0092] 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, a specific example is given below to illustrate.

[0093] Space-based distributed satellites and reference point locations Figure 5 As shown, black represents satellites, red represents reference points, and the number of satellites is N sat =6, the initial position is selected from the actual situation, such as Figure 5 As shown. The reference point coordinates are set to P_base = [0, 0, 100km], and the time base is set to t_base = 0. Assume that the initial clock offset of each satellite is randomly generated with a zero-mean normal distribution, and the initial step size of the gradient descent is μ 0=1, backtracking line search step attenuation factor β = 0.2, constant α = e -9 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 the reference point refer to Table 1.

[0094] Table 1 Satellite initial coordinates

[0095]

[0096]

[0097] 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 pass Figure 6 and Figure 7 It can be seen that the method proposed in this scheme can achieve effective correction of the overall error within the range of time error 3ns and spatial error 30cm.

[0098] by Figure 6 For example, the time error before correction is 3ns, and after correction 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 30 cm, and after correction it is 10 mm, with a correction degree of 96%. The main reason why the correction degree cannot reach 100% is that there is an inevitable observation error n mn , and F can only drop to near the minimum value.

[0099] In this noise case, the error function F changes with the iteration process as follows: Figure 8 As shown in Figure 2, the actual clock error and estimated clock error of each satellite platform change as shown in Figure 2. Fig. 9 As shown. Figure 8 and Fig. 9 It can be seen that after the number of iterations reaches 100, the changes in various 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 the positioning accuracy and clock error synchronization efficiency.

Claims

1. A space-time synchronization method for a space-based distributed satellite array, characterized in that: Includes steps: S1. Obtain the initial clock difference between each satellite and the reference point in the space-based distributed satellite array and the observed position and time information containing spatial errors; S2, based on the initial clock difference between the satellite and the reference point, measure the time difference and observation time of a signal transmitted by one of the two satellites to the other satellite; S3, according to the observed positions, time differences and observed times of all satellites and the preset iterative initial spatial positions and iterative initial clock errors, the true spatial position of each satellite and the clock error with the reference point when the inter-satellite total error function converges to the minimum value are found by the gradient descent optimization method based on the backtracking line search; 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.

2. The time-space synchronization method for a space-based distributed satellite array according to claim 1, characterized in that: The expression of the inter-satellite total error function is: Where F is the total inter-satellite error function; Δt n is the clock difference between satellite n and the reference point; P n and are the real 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; T mn 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; d mn = c·τ mn and d m0 = c·τ m0 are all functions of parameters, τ mn is the intersatellite link propagation delay between satellites m and n, τ m0 is the intersatellite link propagation delay between the reference point and satellite m; is the measured value.

3. The time-space synchronization method for a space-based distributed satellite array according to claim 2, characterized in that: All satellites in the space-based distributed satellite array transmit the same single-frequency continuous wave signal in rotation, and the expression is: y(t)=s(t)exp{j2πft} Where y(t) is a single-frequency continuous wave signal; s(t) is the complex envelope of the signal; f is the carrier frequency of the signal; t is time; j is an imaginary unit; exp(·) is an 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 observed signal is: Among them, y mn (t) is the transmission signal of satellite m received by satellite n; y m0 (t) is the transmitted signal of satellite m received at the reference point; When the phase difference When equation (1) is satisfied, the expression for measuring the time difference and observation time of a signal transmitted from one satellite to another satellite between any two satellites is: T mn =Δt n -D(t mn -t m0 ), Among them, n mn is the observation noise of the signal transmitted from satellite m to satellite n.

4. The time-space synchronization method for a space-based distributed satellite array according to claim 2, characterized in that: Intersatellite link propagation delay τ mn and τ m0 The expressions are: τ mn J||p m -p n || / c,τ m0 J||p m -p base || / c Among them, p m and p base are the real spatial positions of satellite m and reference point respectively.

5. The time-space synchronization method for a space-based distributed satellite array according to claim 2, characterized in that: 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; [·] T is the transpose; x n ,y n and z n is the real space coordinate of satellite n, [x n y n z n ] T =P n ; Δt n is the clock difference between satellite n and the reference point; is the total inter-satellite error function Δt n The partial derivative of is the total intersatellite error function for x n The partial derivative of is the total inter-satellite error function for y n The partial derivative of is the total intersatellite error function for z n The partial derivative of S33, determine whether the current total error value meets the Armijo-Goldstein condition, if so, proceed to step S34, otherwise proceed to step S35; S34, update t k+1 =βt k , x k+1 =x k +t k+1 Δx k , k = k + 1, and the updated parameter x k Substitute into the intersatellite total error function to obtain the total error value, and then return to step S32; where t k and t k+1 are the step sizes for the kth and k+1th iterations respectively; x k =[Δt n (k) x n (k) y n (k) z n (k)]| n∈[1,N] is a variable, x n (k), y n (k) and z n (k) 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; β is the step attenuation factor, 0<β<1; S35, output the total error value F(x) obtained at the kth iteration k ) and the variable x k .

6. The time-space synchronization method for a space-based distributed satellite array according to claim 5, characterized in that: The Armijo-Goldstein conditions are: Where α is a constant; ▽F(x k ) T =▽F(x k ) is the transpose of .

7. The time-space synchronization method for a space-based distributed satellite array according to claim 5, characterized in that: Partial derivatives and The expressions are: in, and is the observed coordinate of satellite m with spatial error, is the observed position of satellite m with spatial error; x0, y0 and z0 are the real space coordinates of the reference point; [x0 y0 z0] T =P base is the real space position of the reference point; x m ,y m and z m is the real space coordinate of satellite m; [x m y m z m ] T =P m is the real spatial position of satellite m.

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