Adaptive random finite set tracking method based on low-cost spaceborne distributed radar

Abstract

The application discloses a kind of adaptive random finite set tracking methods based on low-cost spaceborne distributed radar, mainly solve the problem of high cost, poor adaptability of prior art.Its implementation scheme is: through auxiliary star forwarding mode to build equivalent one-to-many receiving model, realize low-cost recording echo data;According to echo data, form two equivalent long synthetic aperture;Through synthetic aperture imaging, clutter suppression and detection to obtain measurement point;Adaptively generate new target intensity using multi-step measurement points;Adaptively estimate the clutter rate at each step using multi-step measurement points;Adaptive random finite set target tracking is carried out using the intensity and clutter rate generated.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radars, and particularly relates to a self-adaptive random finite set tracking method, which can be used for real-time detection and tracking of low-cost distributed radar ground moving targets or low-altitude moving targets. BACKGROUND

[0002] A spaceborne distributed radar performs cooperative monitoring on an observation scene through space-based networking. Through spatial deployment of each satellite, combined with a specific signal transmission and reception mode, imaging, detection and other requirements can be achieved, and the spaceborne distributed radar has many advantages such as wide detection range, strong survivability and being not limited by national regions. However, the spaceborne distributed radar generally has a high cost, which is not conducive to large-scale deployment.

[0003] To alleviate the problem of high cost of the spaceborne distributed radar, a SIMO (Single Input Multiple Output) system can be used, in which a main satellite transmits a radio frequency signal to irradiate a detection area, and multiple auxiliary satellites simultaneously receive echo signals. In this system, the receiving auxiliary satellites only act as relay routes, do not sample and store the received echo signals, but modulate and forward them to the main satellite, which samples the echo signals after receiving them orthogonally. Both transmission and reception are completed by the main satellite. Compared with the traditional SIMO system, the cost is reduced and the structure is simplified, which is conducive to large-scale configuration of the auxiliary satellites. The echo signals are preprocessed at the main satellite and then jointly detected on the ground. After target detection processing, measurement data at each step is provided for subsequent target tracking processing.

[0004] Existing target tracking methods can be divided into data association processing methods and random finite set processing methods. Among them, the random finite set (RFS) target tracking method can achieve efficient target tracking in a complex environment where the number of targets is time-varying and unknown. However, the traditional RFS target tracking method is implemented under the assumption that the prior probability density of new target is known and the clutter rate is given, which greatly limits the further application and engineering implementation of the algorithm.

[0005] Currently, the adaptive random finite set target tracking with a probability hypothesis density of new targets mainly includes the following methods:

[0006] B. Ristic et al. proposed a measurement-driven adaptive random finite set tracking method for new targets in the TAES paper“Adaptive Target Birth Intensity for PHD and CPHD Filters”. The core idea is to introduce a label to distinguish new targets from surviving targets, construct intensity prediction update formulas for new targets and surviving targets respectively, model the PHD intensity of new targets in a measurement-driven manner, and then use the first-order Bayesian moment approximation formula for prediction update.

[0007] Xiaolong Zhou et al. proposed a new birth intensity estimation algorithm based on entropy distribution and coverage in the TII paper "GM-PHD-based multi-target visual tracking using entropy distribution and game theory" to automatically and accurately track the new birth target in noisy video.

[0008] The above method does not fully utilize the time dimension information because it only considers the adaptive new birth target intensity modeling problem under single-step observation and does not consider the comprehensive utilization of multi-step observation information. In addition, the above method only considers the adaptive new birth problem and does not simultaneously consider the adaptive estimation of clutter rate, so the adaptive degree is not strong enough. SUMMARY

[0009] The present application aims to overcome the shortcomings of the prior art and proposes a low-cost spaceborne distributed radar adaptive random finite set tracking method to iteratively perform adaptive new birth intensity modeling and parameter estimation by utilizing multi-step measurements, reduce the performance degradation caused by no parameter prior, and improve the adaptive degree of tracking.

[0010] The technical solution for achieving the object of the present application includes the following steps:

[0011] (1) A spaceborne distributed radar cooperative detection model including one transmitting main star and N receiving auxiliary stars is constructed, wherein each auxiliary star has two receiving channels with a spacing of B x , the main star uses a sliding beam mode to continuously observe the target, and each auxiliary star receives the scattered echo signal;

[0012] (2) The auxiliary star relay forwarding and main star orthogonal receiving mode of the spaceborne distributed radar system is designed, the echo signal is coherently mixed and AD sampled, and the double-channel echo signal Ω of the N auxiliary stars is obtained at the main star;

[0013] (3) In the kth observation, two equivalent long synthetic apertures and satisfying the offset phase center antenna DPCA condition are constructed by sequentially concatenating and splicing the double-channel echo signals of the N auxiliary stars;

[0014] (4) Based on the two long synthetic apertures and , SAR imaging, DPCA clutter suppression, and constant false alarm detection are performed in sequence to obtain the moving target measurement position set Z k of the kth observation;

[0015] (5) The target state and target state covariance matrix and design weight mapping function to adaptively generate new target intensity v of kth observation nb,k (x);

[0016] (6) record measurement total number of multi-step measurement sliding window, adaptively estimate clutter rate κ of kth observation k ;

[0017] (7) use Γ k obtained in step (5) and κ k obtained in step (6) to perform adaptive random finite set filtering on target measurement position set Z k of kth observation, obtain posterior intensity v k|k (x) of kth observation, and real-time extract and output multi-target tracking result of kth observation from the intensity;

[0018] (8) repeat steps (2) to (7) to realize real-time continuous detection and tracking of multi-target in observation scene.

[0019] Compared with the prior art, the present application has the following advantages:

[0020] 1) The present application adopts equivalent one-transmission and multiple-reception mode of main satellite transmission-assistant satellite retransmission-main satellite reception by designing a new system satellite-borne distributed radar signal transceiver system, so that low-cost data acquisition can be realized; by designing satellite formation, two equivalent synthetic apertures are formed, so that ground moving target indication can be realized, the coherent accumulation time is shortened, and fast moving target detection is realized.

[0021] 2) In the present application, adaptive random finite set tracking is used in multi-target tracking processing, so that multi-step measurement information can be jointly used, new target intensity and clutter rate are iteratively and real-time estimated, performance degradation caused by no parameter prior is reduced, and adaptive tracking performance is improved. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 is the implementation flowchart of the present application;

[0023] Figure 2 is the sub-flowchart of iteratively tracking measurement data in the present application;

[0024] Figure 3 is the OSPA index comparison chart of tracking simulation experiment by using the present application and the prior art;

[0025] Figure 4 is the potential estimation index comparison chart of tracking simulation experiment by using the present application and the prior art. DETAILED DESCRIPTION

[0026] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0027] It should be noted that the step numbers in the specification and claims of the present invention are only for the purpose of clearly describing the embodiments of the present invention and facilitating understanding, and the order of the step numbers is not limited.

[0028] Reference Figure 1 and Figure 2 , the implementation steps of the present invention are as follows:

[0029] Step 1: Build a spaceborne distributed radar collaborative detection model.

[0030] The spaceborne distributed radar cooperative detection model constructed in this step includes one transmitting primary satellite and N receiving auxiliary satellites;

[0031] The primary star continuously observes the target using a sliding beam mode, with the starting position at (x, y, z) and the ending position at (x, y + L, z), where L is the short aperture length;

[0032] Each of the N receiving satellites has two receiving channels with a spacing of half a wavelength for receiving scattered echo signals. These satellites are arranged at equal intervals. The starting position of the i-th satellite is (x, y + (2i-1)L, z) and the ending position is expressed as (x, y + 2iL, z), where i = 1, 2, ..., N.

[0033] Step 2: Design a satellite-borne distributed radar system solution with relay forwarding by the auxiliary satellite and orthogonal reception by the primary satellite, and obtain the dual-path echo signals Ω of N auxiliary satellites on the primary satellite.

[0034] 2.1) The primary satellite sends a direct reference signal f to the nth secondary satellite rn ;

[0035] 2.2) The echo received by the i-th receiving channel of the n-th auxiliary satellite With the direct reference signal f rn Superposition is performed to obtain a mixed signal

[0036] 2.3) Use a coherent mixer to mix the signals The frequency shift is The up-mixed signal is obtained by frequency shift and forwarded to the primary satellite, i = 1, 2;

[0037] 2.4) After receiving the forwarded signal, the primary satellite uses a coherent mixer to perform a frequency shift of The frequency shift is used to remove the orthogonal frequency modulation of the nth auxiliary satellite, and the coherent I / Q demodulator driven by the local oscillator is used for AD sampling, i = 1, 2;

[0038] 2.5) Perform range compression and azimuth Fourier transform on the digital signal after AD sampling, and separate the zero-frequency direct reference signal in the range Doppler domain. and echo signal

[0039] 2.6) Estimating the two reference signals f in the primary satellite rn and The amplitude and phase errors of the echo signal Compensation is performed to obtain the echo signal after correcting the up-down mixing error

[0040] 2.7) Repeat steps 2.1) to 2.6) to obtain the dual-path echo signals Ω of N auxiliary satellites on the primary satellite:

[0041]

[0042] Where n=1,...,N.

[0043] Step 3: Obtain two equivalent long apertures based on the echo signals of N auxiliary satellites and

[0044] In the kth observation, two equivalent long synthetic apertures that meet the DPCA conditions are constructed by sequentially connecting the echo signals of N auxiliary satellites. and

[0045]

[0046] The symbol || indicates serial splicing and overlapping positions.

[0047] Step 4: Based on two long synthetic apertures and Get the moving target measurement position set Z of the kth observation k .

[0048] 4.1) Use polar coordinate formatting algorithm to and The echo data in the image is focused to obtain the corresponding SAR image and

[0049] 4.2) Obtaining a difference image based on complex image cancellation where i x , y is the index of the two-dimensional pixel of the difference image, i x = 1,...,N x , i y = 1,...,N y , N x and N y represent the resolution unit number of the difference SAR image in azimuth and range direction respectively;

[0050] 4.3) Interferometric processing is performed on I and I to obtain the interferometric image I where (·) * represents taking the conjugate of the image;

[0051] 4.4) Set the set of moving target measurement positions as Z k , set the threshold value V T , and use constant false alarm detection to make a decision:

[0052] If ΔI(i x , i y ) ≥ V T , then the target exists, and the measurement point is recorded; Step 4.5) is performed;

[0053] If ΔI(i x , i y ) < V T , then the target does not exist;

[0054] where ΔI(i x , i y ) is the corresponding two-dimensional position of the difference image ΔI(i x , i y ) at the index i k , i nb,k , and the superscript q is the measurement point index;

[0055] 4.5) The interferometric phase φ is extracted from the corresponding interferometric image position of the measurement point

[0056] 4.6) The azimuth direction offset of the measurement point is calculated, where y0 is the slant range of the scene center; 4.7) The measurement point is compensated for the offset to obtain the repositioned measurement point

[0058]

[0059] where To relocate the azimuth position of the moving target, The distance and direction position of the moving target after repositioning;

[0060] 4.8) Repeat steps 4.4) to 4.7) until all the two-dimensional pixel indexes of the difference image are traversed to obtain the moving target measurement position set m k is the total number of measurements for the kth observation.

[0061] Step 5: Extract the target state through sliding window correlation of multi-step measurements and the target state covariance matrix And design a weight mapping function to adaptively generate the new target intensity v of the kth observation nb,k (x).

[0062] 5.1) Let L ≥ 3 be the sliding window length and compare it with the number of observation steps k:

[0063] If the number of observation steps k < L, then execute step 5.2).

[0064] If the number of observation steps k≥L, then execute step 5.3).

[0065] 5.2) Store the measured position set Z of the current observation step k , execute step eight to process the next observation step;

[0066] 5.3) Obtain the index set of the association pairs from the k-L+1th observation to the kth observation through the nearest neighbor measurement association Where M is the index set π (k-L+1):k The number of associated pairs in , represents the measurement index in the measurement position set with observation step j for association pair i, Represents π (k-L+1):k The index of the i-th associated pair in , j = k-L+1,…,k-1,k;

[0067] 5.4) Measure the index set Π of the association pairs from the k-L+1th observation to the kth observation (k-L+1):k The associated pair index p i , extract the corresponding measurements in each observation step and form the correlation pair measurement matrix and the corresponding set of measurement error covariance matrices for the associated pairs in is the measurement position of the jth observation step under which the corresponding measurement of pair i is concentrated. is the measurement error covariance matrix corresponding to the measurement position set association pair i under the j-th observation step;

[0068] 5.5) Estimate the position, velocity, and acceleration of the target at the kth observation based on the measurement matrix. Let T be the time interval between two adjacent observation steps, and let Calculate the target estimated velocity for the kth observation Estimated acceleration and the target estimated speed at the k-1th observation step

[0069]

[0070] in are the vectors corresponding to the kth, k-1th and k-2th columns in the correlation pair measurement matrix, are the components of the target estimated velocity in the x and y directions, are the components of the target estimated acceleration in the x and y directions, q=1,2,…,J nb,k , J nb,k is the number of new target Gaussian components in the k-th observation step;

[0071] 5.6) The measurement in step 5.4) and the target estimated speed in step 5.5) Estimated acceleration Write the estimated new target state in the form of the existing CA model state vector

[0072]

[0073] in[·] T Indicates transposition processing;

[0074] 5.7) Let H k is the observation matrix of the kth observation, according to the qth measurement error covariance matrix of the kth observation Get the new target state covariance matrix Among them, β1 and β2 are constant factors;

[0075] 5.8) The predicted strength of the k-th observation is expressed as a Gaussian mixture: Calculates the Gaussian distribution probability density function

[0076]

[0077] Among them, J k|k-1 is the number of Gaussian components of the predicted intensity, are the weight, mean and covariance matrix of the jth Gaussian component of the predicted intensity, j = 1, 2, ..., J k|k-1 , n is the newborn target state obtained in step 5.6) z is the measurement dimension;

[0078] 5.9) Calculate the accumulated value Λ q :

[0079]

[0080] 5.10) Define the mapping function as f(x) = e -βx , where β is a scaling factor, and the newborn density's Gaussian mixture component weight is set to the mapping function, i.e. q

[0081] 5.11) Take the maximum value of the newborn density weight

[0082] 5.12) Set the upper limit of the newborn target weight

[0083] 5.13) Define the limiting factor

[0084] 5.14) Scale the newborn density's Gaussian mixture component weight, obtaining the scaled newborn density's Gaussian mixture component weight:

[0085] 5.15) According to the newborn target state obtained in step 5.6) , the newborn density's Gaussian mixture component weight obtained in step 5.14) , and the kth observation's newborn target intensity v nb,k (x) is expressed as follows in the form of Gaussian mixture:

[0086]

[0087] where, is the Gaussian distribution symbol.

[0088] Step six, record the total number of measurements of the multi-step measurement sliding window, and adaptively estimate the kth observation's clutter rate κ k .

[0089] 6.1) Record the number of measurements m k′ in each step within the sliding window step length L, and sum up the number of measurements m k′ in each step to obtain the total number of measurements m sum within the sliding window step length:

[0090] ​

[0091] where k' = k - L + 1,..., k - 1, k;

[0092] 6.2) Record the potential estimate number n of the previous L - 1 steps within the sliding window step L k″ , to obtain the total number of potential estimates n sum within the sliding window step:

[0093]

[0094] where k" = k - L + 1,..., k - 1;

[0095] 6.3) Set p c as the probability density function of the clutter, according to the total measurement number m sum and the total number of potential estimates n sum , obtain the estimated clutter rate κ k of the kth observation:

[0096]

[0097] Step seven, use the Γ k obtained in step five and the κ k obtained in step six to perform adaptive random finite set filtering on the Z k of the kth observation to obtain the posterior intensity v k|k (x) of the kth observation, and extract and output the multi-target tracking result of the kth observation in real time from the intensity.

[0098] 7.1) Obtain the posterior intensity v k-1|k-1 (x) of the kth - 1 observation in the form of Gaussian mixture:

[0099]

[0100] where J k-1|k-1 is the number of Gaussian components of the posterior intensity v k-1|k-1 (x) of the kth - 1 observation, are the weight, mean and covariance matrix of the i-th Gaussian component of the posterior intensity v k-1|k-1 (x) of the kth - 1 observation, respectively, i = 1, 2,..., J k-1|k-1 ;

[0101] 7.2) Perform Kalman filter prediction on the mean of each Gaussian component of the posterior intensity v k-1|k-1 (x) of the kth - 1 observation in the form of Gaussian mixture to obtain the predicted mean

[0102]

[0103] Among them, F k,k-1 is the state transition matrix from the k-1th observation to the kth observation;

[0104] 7.3) The posterior intensity v expressed in the form of Gaussian mixture under the k-1th observation k-1|k-1 The covariance matrix of each Gaussian component of (x) Perform Kalman filter prediction to obtain the prediction covariance matrix of each Gaussian component

[0105]

[0106] Among them, Q k,k-1 is the covariance matrix of the state transfer error from the k-1th observation to the kth observation;

[0107] 7.4) Using the predicted mean and the forecast covariance matrix and the new target strength v obtained in step 5 nb,k (x), obtain the predicted strength v expressed in the form of Gaussian mixture from the k-1th observation to the kth observation k|k-1 (x):

[0108]

[0109] Among them, p S,k is the survival probability of the target under the k-th observation, is the Gaussian distribution symbol, J k|k-1 is the predicted strength v of the kth observation k|k-1 The number of Gaussian components of (x), are the predicted strength v of the kth observation respectively k|k-1 The weight, mean, and covariance matrix of the i-th Gaussian component of (x), i = 1, 2, ..., J k|k-1 ;

[0110] 7.5) Using the predicted intensity v represented by the Gaussian mixture form from the k-1th observation to the kth observation k|k-1 The covariance matrix of each Gaussian component of (x) Get the innovation covariance matrix of each Gaussian component and Kalman gain

[0111]

[0112] Among them, H k is the observation matrix under the k-th observation, R k is the measurement error covariance matrix;

[0113] 7.6) Predicted intensity v (x) from the k-1th observation to the kth observation is represented in Gaussian mixture form k|k-1 Mean of each Gaussian component of v (x) Perform Kalman filter update to obtain updated mean of each Gaussian component

[0114]

[0115] where z is the vector element in the measurement location set Z k

[0116] 7.7) Predicted intensity v (x) from the k-1th observation to the kth observation is represented in Gaussian mixture form k|k-1 Covariance matrix of each Gaussian component of v (x) Perform Kalman filter update to obtain updated covariance matrix of each Gaussian component

[0117]

[0118] 7.8) Obtain updated intensity v (x) of the kth observation using predicted intensity v (x) from the k-1th observation to the kth observation represented in Gaussian mixture form k|k-1 Covariance matrix of each Gaussian component of v (x) and clutter rate κ estimated in step six k Obtain updated weight of each Gaussian component

[0119]

[0120] where p D,k is the detection probability of the target at the kth observation step;

[0121] 7.9) Obtain posterior intensity v (x) of the kth observation using predicted intensity v (x) given in step 7.4) k|k-1 and updated intensity of each element z in the measurement location set Z k given in steps 7.5) to 7.8) k|k

[0122]

[0123] where J k|k is the number of Gaussian components of posterior intensity v k|k (x) of the kth observation;

[0124] 7.10) Extract and output multi-target tracking results of the kth observation from v k|k (x). ​​​

[0125] Step eight, repeating steps two to seven, to achieve real-time continuous detection tracking of multiple targets.

[0126] The effect of the application is further described below in combination with simulation.

[0127] 1. Simulation parameters:

[0128] The number of Monte Carlo experiments is set to 1000, the total observation time is 50s, the time interval between adjacent observation steps is 1s, the target detection probability is 0.99, the target survival probability is 0.98, the maximum Gaussian limit number is 100, the pruning threshold is 10, the merging threshold is 4. -5

[0129] 2. Simulation content:

[0130] Simulation 1, under the above simulation parameters, using the application and the existing 4x4 grid adaptive birth processing algorithm, 8x8 grid adaptive birth processing algorithm, and Ristic's adaptive birth processing algorithm for adaptive random finite set tracking, the optimal sub-pattern assignment (OSPA) distance curve of each tracking is obtained, which is used to evaluate the accuracy of target tracking state estimation, and the results are shown in Figure 3

[0131] As can be seen from Figure 3 , the distance error curve of the application is the lowest, and is better than the three existing methods, indicating that the target tracking state estimation of the application is more accurate.

[0132] Simulation 2, under the above simulation parameters, using the application and the existing 4x4 grid adaptive birth processing algorithm, 8x8 grid adaptive birth processing algorithm, and Ristic's adaptive birth processing algorithm for adaptive random finite set tracking, the target number estimation performance of each algorithm is evaluated, and the potential estimation curve of each comparative analysis tracking is obtained, and the results are shown in Figure 4

[0133] As can be seen from Figure 4 , the potential estimation curve of the application is closest to the true value curve, and is better than the three methods, and the target number estimation is more accurate.​​​

Claims

1. An adaptive random finite set tracking method based on low-cost spaceborne distributed radar, characterized in that: The steps include: (1) Construct a satellite-borne distributed radar cooperative detection model consisting of a transmitting primary satellite and N receiving auxiliary satellites, where each auxiliary satellite has two x The receiving channel of the satellite uses the sliding beam mode to continuously observe the target, and the auxiliary satellites receive the scattered echo signals. (2) Design a method for relaying by the auxiliary satellite and orthogonal reception by the primary satellite in the spaceborne distributed radar system, perform coherent mixing and AD sampling on the echo signal, and obtain the dual-path echo signal Ω of N auxiliary satellites on the primary satellite; (3) In the kth observation, two equivalent long synthetic apertures that meet the DPCA conditions of the offset phase center antenna are constructed by sequentially connecting the dual-path echo signals of N auxiliary satellites. and The symbol || indicates serial splicing and the aperture space positions are overlapped; (4) Based on two long synthetic apertures and After SAR imaging, DPCA clutter suppression and constant false alarm detection, the moving target measurement position set Z of the kth observation is obtained. k ; (5) Extracting target state through sliding window correlation of multi-step measurements and the target state covariance matrix And design a weight mapping function to adaptively generate the new target intensity v of the kth observation nb,k (x); (6) Record the total number of measurements in the multi-step measurement sliding window and adaptively estimate the clutter rate κ of the kth observation k ; (7) Using Γ obtained in step (5) k and κ obtained in step (6) k , the moving target measurement position set Z of the k-th observation k Perform adaptive random finite set filtering to obtain the posterior strength v of the kth observation k|k (x), extract and output the multi-target tracking result of the k-th observation in real time from the intensity; (8) Repeat steps (2) to (7) to achieve real-time continuous detection and tracking of multiple targets in the observation scene.

2. The method according to claim 1, characterized in that Step (1) constitutes the transmitting primary satellite and N receiving auxiliary satellites in the spaceborne distributed radar cooperative detection model, and their distribution positions are as follows: The starting position of the master star is (x, y, z) and the ending position is (x, y + L, z), where L is the short aperture length; N auxiliary stars are arranged at equal intervals. The starting position of the i-th auxiliary star is (x, y + (2i-1) L, z), and the ending position is expressed as (x, y + 2i L, z), where i = 1, 2, ..., N.

3. The method according to claim 1, characterized in that In step (2), the dual-path echo signals Ω of N auxiliary satellites are obtained from the primary satellite. The implementation steps include the following: 2a) The primary satellite sends a direct reference signal f to the nth secondary satellite rn ; 2b) The echo received by the i-th receiving channel of the n-th auxiliary satellite With the direct reference signal f rn Superposition is performed to obtain a mixed signal 2c) Use a coherent mixer to mix the signals The frequency shift is The up-mixed signal is obtained by frequency shift and forwarded to the primary satellite, i = 1, 2; 2d) After receiving the forwarded signal, the primary satellite uses a coherent mixer to perform a frequency shift of The frequency shift is used to remove the orthogonal frequency modulation of the nth auxiliary satellite, and the coherent I / Q demodulator driven by the local oscillator is used for AD sampling, i = 1, 2; 2g) Perform range compression and azimuth Fourier transform on the digital signal after AD sampling, and separate the zero-frequency direct reference signal in the range Doppler domain and echo signal 2f) Estimating the two reference signals f in the primary satellite rn and The amplitude and phase errors of the echo signal Compensation is performed to obtain the echo signal after correcting the up-down mixing error 2h) Repeat steps 2a) to 2f) to obtain dual-path echo signals from N auxiliary satellites on the primary satellite.

4. The method according to claim 1, wherein The moving target measurement position set Z of the kth observation is obtained in step (4) k , the implementation steps include the following: 4a) Use polar coordinate formatting algorithm to and The echo data in the image is focused to obtain the corresponding SAR image and 4b) Obtaining a difference image based on complex image cancellation Among them, i x ,i y is the two-dimensional pixel index of the difference image, i x =1,...,N x ,i y =1,...,N y , N x and N y Respectively represent the number of resolution units in the azimuth and range directions of the difference SAR image; 4c) Yes and Perform interference processing to obtain interference images in(·) * Indicates taking the conjugate of the image; 4d) Let the moving target measurement position set be Z k , set the threshold value V T , using constant false alarm detection to make a judgment: If ΔI(i x ,i y )≥V T , the target exists and the measurement point is recorded Go to step 4e); If ΔI(i x ,i y )<V T , then the target does not exist; in is the difference image ΔI(i x ,i y ) in i x ,i y The corresponding two-dimensional position under the index, the superscript q is the measurement point index; 4e) From the measurement point Extract the interference phase at the corresponding interference image position 4f) Calculate measurement points Azimuth offset Where y0 is the slant distance from the center of the scene; 4g) Compensate the offset of the measurement point to obtain the relocated measurement point in To relocate the azimuth position of the moving target, The distance and direction position of the moving target after repositioning; 4h) Repeat steps 4d) to 4g) until all the two-dimensional pixel indexes of the difference image are traversed to obtain the moving target measurement position set m k is the total number of measurements for the kth observation.

5. The method according to claim 1, wherein In step (5), the target state is extracted by sliding window correlation of multi-step measurements and the target state covariance matrix The implementation steps include the following: 5a) Let L ≥ 3 be the sliding window length and compare it with the number of observation steps k: If the number of observation steps k < L, then execute step 5b), If the number of observation steps k≥L, then execute step 5c); 5b) Store the measured position set Z of the current observation step k , implement step (8) in claim 1 and proceed to the next observation step; 5c) Obtain the index set of the association pairs from the k-L+1th observation to the kth observation through the nearest neighbor measurement association: Where M is the index set π k-L+1:k The number of associated pairs in , represents the index of the i-th associated pair, represents the measurement index in the measurement position set with observation step j for association pair i, j = k-L+1,…,k-1,k; 5d) Measure the index set Π of the association pairs from the k-L+1th observation to the kth observation k-L+1:k The associated pair index p i , extract the corresponding measurements in each observation step and form the correlation pair measurement matrix and the corresponding set of measurement error covariance matrices for the associated pairs in is the measurement position of the jth observation step under which the corresponding measurement of pair i is concentrated. is the measurement error covariance matrix corresponding to the measurement position set association pair i under the j-th observation step; 5e) Estimate the position, velocity, and acceleration of the target at the kth observation based on the measurement matrix. Let T be the time interval between two adjacent observation steps, and let Calculate the target estimated velocity for the kth observation Estimated acceleration and the target estimated speed at the k-1th observation step in are the vectors corresponding to the kth, k-1th and k-2th columns in the correlation pair measurement matrix, are the components of the target estimated velocity in the x and y directions, are the components of target estimated acceleration in the x and y directions respectively; 5f) The measured value in step 5d) and the target estimated speed in step 5e) Estimated acceleration Write the estimated new target state in the form of the existing CA model state vector 5g) Set H k is the observation matrix of the kth observation, according to the qth measurement error covariance matrix of the kth observation Get the new target state covariance matrix Among them, β1 and β2 are constant factors.

6. The method according to claim 1, characterized in that Step (5) Design a weight mapping function to adaptively generate the new target intensity v of the kth observation nb,k (x), the implementation steps include the following: 5h) The predicted strength of the k-th observation is expressed as a Gaussian mixture: Calculates the Gaussian distribution probability density function Among them, J k|k-1 is the number of Gaussian components of the predicted intensity, are the weight, mean and covariance matrix of the jth Gaussian component of the predicted intensity, j = 1, 2, ..., J k|k-1 , is the new target state obtained in step 5f), n z is the measurement dimension; 5i) Calculation The accumulated value Λ q : Among them J nb,k is the number of new target Gaussian components in the k-th observation step; 5j) Define the mapping function as f(x) = e -βx , where β is a scaling factor that weights the Gaussian mixture component of the new density Set to Λ q The mapping function, that is 5k) Take the maximum value of the newborn density weight 5l) Set the upper limit of the new student target weight 5m) Define the limiting factor 5n) Scale the Gaussian mixture component weights of the newborn density to obtain the scaled Gaussian mixture component weights of the newborn density: 5o) The new target state obtained according to step 5f) Step 5g) The new target state covariance matrix obtained Gaussian mixture component weights of the new density obtained in step 5n) The new target intensity v of the k-th observation is converted into nb,k (x) represents the following: in, is the Gaussian distribution symbol.

7. The method according to claim 1, characterized in that In step (6), the clutter rate κ of the kth observation is adaptively estimated k , the implementation steps include the following: 6a) Record the number of measurements m at each step within the sliding window step length L k′ , and sum and accumulate to get the total number of measurements m within the sliding window step sum : where k′=k-L+1,…,k-1,k; 6b) Record the number of potential estimates n for the first L-1 steps within the sliding window step size L k″ , get the total number of potential estimates n within the sliding window step sum : Where k″=k-L+1,…,k-1; 6c) Let p c is the probability density function of the clutter, and according to the total amount m sum Total number of potential estimates n sum , obtain the estimated clutter rate κ of the kth observation k :

8. The method according to claim 1, characterized in that The measured position set Z of the moving target observed for the kth time in step (7) is k Perform adaptive random finite set filtering to obtain the posterior strength v of the kth observation k|k (x), the implementation steps include the following: 7a) Obtain the posterior strength v expressed in the form of a Gaussian mixture under the k-1th observation k-1|k-1 (x): Among them, J k-1|k-1 is the posterior strength v of the k-1th observation k-1|k-1 The number of Gaussian components of (x), are the posterior strength v of the k-1th observation respectively k-1|k-1 The weight, mean and covariance matrix of the i-th Gaussian component of (x), i=1,2,…,J k-1|k-1 ; 7b) The posterior intensity v expressed in the form of Gaussian mixture for the k-1th observation k-1|k-1 The mean of each Gaussian component of (x) Perform Kalman filter prediction to obtain the predicted mean of each Gaussian component Among them, F k,k-1 is the state transition matrix from the k-1th observation to the kth observation; 7c) The posterior intensity v expressed in the form of Gaussian mixture for the k-1th observation k-1|k-1 The covariance matrix of each Gaussian component of (x) Perform Kalman filter prediction to obtain the prediction covariance matrix of each Gaussian component Among them, Q k,k-1 is the covariance matrix of the state transfer error from the k-1th observation to the kth observation; 7d) Using the predicted mean and the forecast covariance matrix and the new target strength v obtained in step (5) nb,k (x), obtain the predicted strength v expressed in the form of Gaussian mixture from the k-1th observation to the kth observation k|k-1 (x): Among them, p S,k is the survival probability of the target under the k-th observation, is the Gaussian distribution symbol, J k|k-1 is the predicted strength v of the kth observation k|k-1 The number of Gaussian components of (x), are the predicted strength v of the kth observation respectively k|k-1 The weight, mean, and covariance matrix of the i-th Gaussian component of (x), i = 1, 2, ..., J k|k-1 ; 7e) Using the clutter rate κ estimated in step (6) k , the predicted intensity v expressed in the form of Gaussian mixture from the k-1th observation to the kth observation k|k-1 The mean of each Gaussian component of (x) and covariance matrix Perform Kalman filter update and weight calculation to obtain the new information covariance matrix of each Gaussian component Kalman gain Update mean Update the covariance matrix And update the weights 7f) Using the predicted intensity v given in step 7d) k|k-1 (x) and step 7e) for the measurement position set Z k Updated intensity of element z Get the posterior strength v of the kth observation k|k (x): Among them, J k|k is the posterior strength v of the kth observation k|k The number of Gaussian components of (x).

9. The method according to claim 1, characterized in that Step 7e) Obtain the innovation covariance matrix of each Gaussian component Kalman gain Update mean Update the covariance matrix and update weights The formula is as follows: Where i = 1, 2, ..., J k|k-1 , H k is the observation matrix under the k-th observation, R k is the measurement error covariance matrix, z is the measurement position set Z k The vector elements in p D,k is the detection probability of the target under the k-th observation step.

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