A combined tracking passive radar fluctuation target detection method

Abstract

The application discloses a combined tracking passive radar fluctuation target detection method and belongs to the field of radar target detection. In view of the nonlinearity problem of the measurement equation under the passive radar system, the volume Kalman filter is adopted to update the posterior state of the fluctuation target in the current frame, and the posterior state of the current frame is used to predict the prior state of the next frame, and the prior state is used as the support set prior information for reconstructing the range-Doppler image of the next frame. A dynamic extension orthogonal matching pursuit method is adopted to determine the selection range of the target support set by using the prior state information of the target in the current frame. When the target tracking information accurately generates the target RD image, the CKF is adopted to track the motion of the fluctuation target under the passive radar system, and higher approximation accuracy is provided. The application is suitable for the field of radar target detection, can accurately reconstruct the RD image of the fluctuation target, and improves the continuous detection performance of the fluctuation target under the passive radar system.

Description

TECHNICAL FIELD

[0001] The present application relates to a passive radar fluctuation target detection method based on joint tracking, and belongs to the field of radar target detection. BACKGROUND

[0002] Passive radar is a variant of bistatic radar, which utilizes non-cooperative illuminators such as commercial signals like Digital Video Broadcasting-terrestrial (DVB-T) and Frequency Modulation (FM) broadcast signals to detect targets. Passive radar systems have the advantages of operational concealment, low cost and spectrum conservation due to the absence of a dedicated transmitter. Passive radar systems have a wide range of applications in aviation surveillance, stealth aircraft detection and maritime target early warning.

[0003] Traditional passive radar target detection methods are based on the theory of matched filtering (MF), which utilizes cross-correlation function and fast Fourier transform (FFT) to obtain the bistatic range-doppler (RD) image. However, since commercial signals are not designed for radar target detection, their ambiguity functions usually have high sidelobes, and the signal-to-noise ratio of the bistatic RD image is not ideal. When the target's attitude changes or the radar cross section (RCS) fluctuates due to electromagnetic interaction, the target is easily submerged in noise when the RCS is low, which is not conducive to continuous target detection. Traditional passive radar ignores the state relationship between adjacent frames of RCS fluctuation targets during the generation of RD images, and only produces each frame of RD image independently through cross-correlation and FFT technology. When the target's RCS is low, the signal-to-noise ratio of the RD image is not ideal, which leads to a sharp decline in the performance of subsequent target tracking.

[0004] In a conventional passive radar target detection scenario, the number of radars is relatively small and only occupies a small part of the radar line-of-sight range, so the radar echo signal naturally has the signal sparsity property. The principle of compressed sensing (CS) indicates that as long as the signal is sparse (only a limited number of non-zero value elements) or can be sparsely represented in a certain transform domain, the signal can be reconstructed with high precision by solving an optimization problem. Therefore, the compressed sensing theory can be used to reconstruct the bistatic RD image of the passive radar. In addition, compressed sensing uses the structural information of sparsity as a statistical priori, which can bring further advantages in reconstructing the bistatic RD image, such as removing noise and suppressing sidelobes. The basic sparse signal reconstruction algorithm for reconstructing the bistatic RD image in the current CS theory mainly includes the orthogonal matching pursuit (OMP) algorithm, the extended orthogonal matching pursuit (EOMP) algorithm and the like. The conventional CS theory does not consider the sparsity characteristic relationship between adjacent sequences when recovering the time-varying sparse vector sequence, which limits the reconstruction performance of the RD image. SUMMARY

[0005] In view of the problem that the current passive radar detection technology has low signal-to-noise ratio in generating fluctuating target RD images, and the continuous detection performance of the target is poor. The main target of the present application is to provide a joint tracking passive radar fluctuating target detection method. Considering the motion state relationship of the fluctuating target in adjacent frames, the method takes the predicted target motion state of the previous frame as the support set prior information of the current frame, and sequentially generates the bistatic RD image of the fluctuating target by the dynamic compressed sensing (DCS) method, so as to improve the signal-to-noise ratio of part of the RD image when the RCS of the fluctuating target is low, and enhance the continuous detection performance of the fluctuating target.

[0006] The object of the present application is realized by the following technical solutions:

[0007] The application discloses a passive radar fluctuation target detection method based on joint tracking, and aims at the nonlinearity problem of a measurement equation under a passive radar system.

[0008] The passive radar fluctuation target detection method based on joint tracking comprises the following steps:

[0009] S1: segment received passive radar reference signals and multi-element echo signals to obtain a reference signal matrix representing the segmented reference signals and an echo signal matrix representing the segmented echo signals of each element;

[0010] The segmented length is set, the echo signals of each element are segmented with overlap according to the segmented length and a maximum time delay, the segmented echo signals are obtained, and a Y matrix is generated, the dimension of the Y matrix being L*M*N; the reference signals are segmented and zero-padded according to the segmented length, segmented reference signals with the same dimension as the segmented echo signals are obtained, and a Y matrix is generated, the dimension of the Y matrix being M*N. ref The segmented length is set, the echo signals of each element are segmented with overlap according to the segmented length and a maximum time delay, the segmented echo signals are obtained, and a Y matrix is generated, the dimension of the Y matrix being L*M*N; the reference signals are segmented and zero-padded according to the segmented length, segmented reference signals with the same dimension as the segmented echo signals are obtained, and a Y matrix is generated, the dimension of the Y matrix being M*N.

[0011] S2: respectively correlate each element echo signal in the range direction according to the reference signal matrix to obtain the range-compressed signals of each element echo;

[0012] The range-compressed signals of each element echo are obtained, and are specifically shown in formula (1):

[0013]

[0014] Wherein s l,m (n) represents the segmented range echo signal; represents the complex conjugate signal of the corresponding range reference signal; represents the range-compressed signal; wherein Representing the time delay unit, l and m are the array element index and segment number index, respectively; all M segments of the distance-compressed signal are concatenated into Y. l Its dimensions are M×N;

[0015] S3: Construct a dictionary of appropriate size in the direction of the Doppler frequency based on the signal dimensions of the received echoes of each array element after range compression;

[0016] The aforementioned dictionary of Doppler frequency upwards is specifically represented as follows:

[0017] Θ = [a1 a2 … a m … a M ]

[0018] in, j represents the imaginary unit; π represents pi; f represents the Doppler frequency; t m Indicates slow time; M is the number of Doppler frequency grids, and m is the column number of the dictionary;

[0019] S4: Initialize CKF and the target support set information of the first frame based on the target prior information;

[0020] The initialization parameters include the initial motion state of the undulating target in the Cartesian coordinate system. Initial state covariance matrix P 0|0 and the initial support set range I1.

[0021] S5: Based on the Doppler frequency dictionary constructed in S3 and the target support set information of the current frame, the signal after range compression of the echo of each array element is processed by the dynamic extended orthogonal matching pursuit method, and the result of the first array element is used as the bistatic RD image of the target in the current frame.

[0022] S51: Initialization: Residual R = Y l,k Support set Signal to be recovered X0 = 0 M×N The number of iterations q = 1, so the number of iterations q is set. max ; where Y l,k It is the signal of the l-th element and the k-th frame echo after range compression;

[0023] S52: Based on the target support set range I of the current frame k And equation (2) determines the index:

[0024]

[0025] Where I k Let Θ be the range of the target support set in the current frame, Θ be the M×M observation matrix, and a q and b q They are respectively |Θ HR| within the support set range I k The row and column number of the largest element in the array, (·) H Represents transpose and conjugate;

[0026] S53: Index set expansion: T(q,b) q ) = a q And K T =Ind{T[b q ]}, where Ind{·} represents a non-zero element in a vector, T[b q ] represents the b-th element of matrix T q List;

[0027] S54: Perform vector estimation according to equations (3), (4), and (5):

[0028] A = Θ[K] T (3)

[0029]

[0030] X0[K T ,b q ]=x (5)

[0031] in Represents the pseudo-inverse of a matrix;

[0032] S55: Residual Iteration: R[b] q ] = Y l,k [b q ]-Ax;

[0033] S56: Iteration: q = q + 1, if q ≤ q max If the result is positive, return to step S52; otherwise, end the iteration and output the final result X0.

[0034] Thus, from S51 to S56, the dynamic extended orthogonal matching tracking of the range-compressed signals of each array element echo is completed, and the bistatic RD image of the current frame is output: in This represents the RD image of the l-th element and the k-th frame;

[0035] S6: Perform constant false alarm rate (CFAR) detection on the bistatic RD image of the current frame to obtain the current bistatic measurement value r. k with f kThe algorithm uses Multiple Signal Classification (MUSIC) to process the array element signals under the current frame measurement values ​​to obtain the target's Direction of Arrival (DOA) estimate θ for the current frame. k ;

[0036] S6 specifically includes the following sub-steps:

[0037] S61: Perform constant false alarm rate (CFAR) detection on the bistatic distance-Doppler image of the current frame to obtain the current bistatic measurements, including the bistatic distance r. k With bistatic Doppler frequency f k ;

[0038] S62: Based on the signal value x of each array element signal after two-dimensional correlation at the current range-Doppler unit. k Calculate the covariance matrix R DOA The approximate value is shown in equation (6).

[0039]

[0040] Where U is the number of snapshots; x k It is an L×1 dimensional vector. It is its complex conjugate signal; L is the number of antenna array elements;

[0041] S63: The covariance matrix R DOA Perform eigenvalue decomposition to obtain L-num smaller and equal eigenvalues, and construct a matrix from their corresponding eigenvectors. Where num represents the number of targets whose arrival direction is to be estimated;

[0042] S64: Calculate the spectral estimation formula Ψ(θ), where the direction corresponding to the peak is the DOA estimate θ of the target in the current frame. k The spectral estimation formula is shown in equation (7):

[0043]

[0044] Where s e (θ t ) is the manifold matrix vector, as shown in equation (8), θ t This is represented as the entire angular observation interval. Perform t max When sampling uniformly at points, the angle corresponding to the t-th sampled value;

[0045]

[0046] Where j represents the imaginary unit; κ is the wave number, z l The coordinate distribution of array elements;

[0047] Thus, from S61 to S64, the determination of the bistatic measurements for the current frame is complete, including r. k f k Compared with the DOA estimate θ k ;

[0048] S7: Update the posterior state of the target in the current frame in the Cartesian coordinate system using CKF;

[0049] S7 specifically includes the following sub-steps:

[0050] S71: The predicted state volume point is obtained according to equation (9):

[0051]

[0052] in This represents the posterior state of the target in the Cartesian coordinate system of the previous frame. n x For the target posterior state vector The dimension of P; k-1|k-1 Let be the posterior state covariance matrix of the previous frame, and For P k-1|k-1 Cholesky decomposition can yield ξ i The volume point of the i-th standard Gaussian distribution is obtained from equation (10):

[0053]

[0054] in[·] i Represents the i-th column of the matrix;

[0055] S72: The volume point is obtained through the target state transition matrix F: γ i k|k-1 =Fα i According to equations (11) and (12), the variance between the state prediction estimate and the state prediction estimate is:

[0056]

[0057]

[0058] Q k The state covariance matrix;

[0059] S73: The updated state volume point is obtained according to equation (13):

[0060]

[0061] in For Pk|k-1 Cholesky decomposition can yield ξ i Let be the volume point of the i-th standard Gaussian distribution, obtained by equation (10);

[0062] S74: The volume point is obtained through the measurement function h: Based on equations (14), (15), and (16), the one-step predicted value, prediction variance, and cross-covariance of the measurement can be obtained as follows:

[0063]

[0064]

[0065]

[0066] Where R k The measurement covariance matrix;

[0067] S75: Calculate the filtering gain of the current frame according to equations (17), (18), and (19). Posterior state estimation And estimate the covariance P k|k for:

[0068]

[0069]

[0070]

[0071] Where z k Based on the current frame bistatic measurement value r k f k And the target direction of arrival (DOA) estimate θ k composition;

[0072] Thus, from S71 to S75, the determination of the target's posterior state is complete;

[0073] S8: Determine the target support set information for the next frame based on the posterior state obtained from CKF;

[0074] S8 specifically includes the following sub-steps:

[0075] S81: Based on the target's posterior state in the current frame The target state transition matrix F and the measurement function h are used to obtain the target's motion state in the Cartesian coordinate system in the next frame, as well as its corresponding measurement value in the bistatic coordinate system, as shown in equations (20) and (21):

[0076]

[0077]

[0078] S82: Based on the predicted state r k+1|k and f k+1|k Centered on the target, determine the target support set range I for the next frame. k+1 As shown in equation (22):

[0079]

[0080] Where Δr and Δf are the target support set range parameters, which are set according to the target motion state;

[0081] Thus, from S81 to S82, the determination of the target support set for the next frame is completed;

[0082] S9: Receives new echo data frames from each array element and sequentially generates a bistatic RD image of the target by combining prior information from target tracking, thereby improving the continuous detection performance of undulating targets in passive radar systems.

[0083] In S9, the target posterior state, posterior state covariance, and target support set information of the current frame are used as the prior information for the next frame. As new matrix data frames arrive, the aforementioned prior information for target tracking is used to sequentially generate a bistatic RD image of the undulating target.

[0084] Beneficial effects:

[0085] 1. This invention discloses a passive radar undulating target detection method based on joint tracking. It employs a Dynamic Extended Orthogonal Matching Pursuit (DEOMP) method, which considers the motion state relationship of the target in adjacent frames when generating the undulating target RD image. Compared to traditional methods, the DEOMP method can effectively utilize the prior state information obtained when tracking the target in the current frame to determine the target's support set range, thereby accurately reconstructing the undulating target RD image and improving the passive radar's detection performance for undulating targets.

[0086] 2. This invention discloses a passive radar undulating target detection method with joint tracking. When the target tracking information accurately generates the target RD image, the CKF algorithm is used to track the motion of the undulating target under the passive radar system. Compared to other nonlinear filtering algorithms, such as the Extended Kalman Filter (EKF), the CKF has more rigorous mathematical theoretical support in the nonlinear approximation process, providing higher approximation accuracy. Furthermore, even with ambiguous initialization information, the CKF maintains high tracking performance. This allows the CKF to provide more accurate target support set information for the DEOMP algorithm, further accurately reconstructing the RD image of the undulating target. Attached Figure Description

[0087] Figure 1 This is a flowchart illustrating a passive radar undulating target detection method based on joint tracking according to the present invention.

[0088] Figure 2 These are bistatic RD images of undulating targets generated in the 6th frame using different methods when SNR = -18dB, total number of data frames K = 15, and initialization error Δ = 200.

[0089] Figure (a) is the RD image generated by FFT, Figure (b) is the RD image generated by FFT near the target prediction location, Figure (c) is the RD image generated by EOMP, Figure (d) is the RD image generated by the DEOMP algorithm using EKF tracking, and Figure (e) is the RD image generated by the algorithm proposed in this patent.

[0090] Figure 3 The mean square error curves of the detected position of fluctuating targets are compared with those of other existing methods under different signal-to-noise ratio conditions when the number of data frames K=15 and the initialization error Δ=100.

[0091] Figure 4 The mean square error curves of the position of fluctuating targets were compared between the method proposed in this patent and other existing methods under different signal-to-noise ratio conditions when the number of data frames K=30 and the initialization error Δ=200. Detailed Implementation

[0092] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. The technical problems solved by the present invention and its beneficial effects are also described. It should be noted that the described embodiments are only intended to facilitate understanding of the present invention and do not constitute any limitation thereof.

[0093] Example 1

[0094] This embodiment illustrates the specific implementation of a passive radar undulating target detection method based on joint tracking as described in this invention, such as...Figure 1 As shown, it includes the following steps:

[0095] S1: Receive the valid echo signal of the current frame and segment it, including the range-direction multi-element echo signal and the reference signal. In specific implementation, the multi-element echo signal of the current frame is segmented and an S matrix is ​​generated with a dimension of 10×32×512, where 10 is the number of antenna elements, 32 is the number of segments of the echo signal, and 512 represents the number of sampling points in each segment.

[0096] The process involves: receiving the reference signal of the current frame, segmenting the reference signal according to the segment length and padding it with zeros to obtain a segmented reference signal with the same dimension as the segmented echo signal, and generating S. ref The matrix has dimensions of 32×512, where 32 represents the number of segments in the reference signal and is the same as the number of segments in the echo signal; 512 represents the number of sampling points in each segment and is the same as the number of sampling points in each segment of the echo signal.

[0097] S2: Obtain the range-compressed signal of the echoes from each array element, as shown below:

[0098]

[0099] Where s l,m (n) represents the segmented range echo signal; This represents the complex conjugate signal of the corresponding range-guided reference signal; Represents the distance envelope signal; where Representing the time delay unit, l and m are the array element index and segment number index, respectively; all 32 range envelope signals are spliced ​​into Y. l Its dimensions are 32×512;

[0100] S3: Construct a dictionary of appropriate size along the Doppler frequency direction based on the signal dimensions of the received echoes from each array element after range compression. Specifically:

[0101] Θ = [a1 a2 … a m … a M ]

[0102] in, j represents the imaginary unit, π represents pi, exp(·) represents exponential operation with the natural constant as the base; f0 = 0MHz represents the initial Doppler frequency, and the frequency step Δf = 1.8311kHz; t m This represents slow time, with a starting time of t0 = 0s and a slow time interval of Δt. m =1.7067×10 -5 s; M=32 is the number of Doppler frequency grids, and m represents the column number of the dictionary;

[0103] S4: Initialize CKF and target support set information based on the target prior information, including the initial motion state of the undulating target in the Cartesian coordinate system. Initial state covariance matrix Initial support set range

[0104] Where [x0,y0,v] x0 ,v y0 ]′ represent the initial x-coordinate position, y-coordinate position, x-coordinate velocity, and y-coordinate velocity of the target in the Cartesian coordinate system in this embodiment, respectively. p is a Gaussian random number with an expectation of 0 and a variance Δ = 100, representing the degree of control over the target's prior information.

[0105] S5: Based on the constructed Doppler frequency-direction dictionary and the target support set information of the current frame, the DEOMP algorithm is used to process the range envelope of the echo signal of each array element, and the result of the first array element is used as the bistatic RD image of the target in the current frame.

[0106] S5, specifically:

[0107] S51: Initialization: Residual R = Y l,k Support set Signal to be recovered X0 = 0 M×N The number of iterations q = 1, so the number of iterations q is set. max ; where Y l,k It is the range-compressed signal of the echo of the l-th element and the k-th frame, M=32, N=512, q max In this embodiment, q is related to the target number. max =1;

[0108] S52: Based on the target support set range I of the current frame k And the index is determined by equation (1):

[0109]

[0110] Where I k Let Θ be the range of the target support set in the current frame, Θ be a 32×32 observation matrix, and a be the range of the target support set in the current frame. q and b q They are respectively |Θ H R| within the support set range I k The row and column number of the largest element in the array, (·) H Represents transpose and conjugate;

[0111] S53: Index set expansion: T(q,b) q ) = a q And K T =Ind{T[b q]}, where Ind{·} represents a non-zero element in a vector, T[b q ] represents the b-th element of matrix T q List;

[0112] S54: Perform vector estimation according to equations (2), (3), and (4):

[0113] A = Θ[K] T (2)

[0114]

[0115] X0[K T ,b q ]=x (4)

[0116] in Represents the pseudo-inverse of a matrix;

[0117] S55: Residual Iteration: R[b] q ] = Y l,k [b q ]-Ax;

[0118] S56: Iteration: q = q + 1, if q ≤ q max If the result is positive, return to step S52; otherwise, end the iteration and output the final result X0.

[0119] Thus, from S51 to S56, the dynamically extended orthogonal matching pursuit algorithm was completed, outputting the bistatic RD image of the current frame: in This represents the RD image of the l-th element and the k-th frame;

[0120] S6: Perform constant false alarm rate (CFAR) detection on the bistatic RD image of the current frame to obtain the current bistatic measurement value r. k with f k The algorithm uses Multiple Signal Classification (MUSIC) to process the array element signals under the current frame measurement values ​​to obtain the target's Direction of Arrival (DOA) estimate θ for the current frame. k ;

[0121] S6, specifically:

[0122] S61: Perform constant false alarm rate (CFAR) detection on the current frame's bistatic distance-Doppler image to obtain the current bistatic measurement index, including the bistatic distance index. With bistatic Doppler frequency sequence The bistatic measurement values ​​are obtained based on the serial number and unit quantity, as shown in equations (50) and (6):

[0123]

[0124]

[0125] Where dr = 10m; PRF = 5.8594 × 10 4 Hz; M = 32; λ = 0.4451m;

[0126] S62: Based on the signal value x of each array element signal after two-dimensional correlation at the current range-Doppler unit. k Calculate the covariance matrix R DOA The approximate value is shown in equation (7).

[0127]

[0128] Where U = 1 represents the number of snapshots; x k It is a 10×1 dimensional vector, where 10 represents the number of antenna array elements;

[0129] S63: Perform eigenvalue decomposition on the covariance matrix R, and the eigenvectors corresponding to the nine smaller and equal eigenvalues ​​form matrix Q. n The number of targets whose arrival direction is to be estimated is 1;

[0130] S64: Calculate the spectral estimation formula Ψ(θ), where the direction corresponding to the peak is the arrival direction θ of the target in the current frame. k The spectral estimation formula is shown in equation (8).

[0131]

[0132] Where s e (θ t ) is the manifold matrix vector, as shown in equation (9), θ t This is represented as the entire angular observation interval. When performing uniform sampling at 200 points, the angle corresponding to the t-th sample value;

[0133]

[0134] Where κ = 14 is the wave number, z L The coordinate distribution of the array elements is given by z0 = 0m and dz = 0.22m.

[0135] Thus, from S61 to S64, the determination of the bistatic measurements for the current frame has been completed, including r. k f k Compared with the DOA estimate θ k ;

[0136] S7: Update the posterior state of the target in the current frame in the Cartesian coordinate system using CKF;

[0137] S7, specifically:

[0138] S71: The predicted state volume point is obtained according to equation (10):

[0139]

[0140] in This represents the posterior state of the target in the Cartesian coordinate system of the previous frame. n x =4 represents the target posterior state vector The dimension of P; k-1|k-1 Let be the posterior state covariance matrix of the previous frame, and For P k-1|k-1 Cholesky decomposition yields S k-1|k-1 ξ i The volume point of the i-th standard Gaussian distribution is obtained from equation (11):

[0141]

[0142] in[·] i Represents the i-th column of the matrix;

[0143] S72: The volume point is obtained through the target state transition matrix F: γ i k|k-1 =Fα i According to equations (12) and (13), the variance between the state prediction estimate and the state prediction estimate is:

[0144]

[0145]

[0146] Q k The state covariance matrix can be set to 0. 4×4 In this embodiment, F is set as the state transition matrix of the uniform motion model, which can be expressed as equation (14):

[0147]

[0148] Where T = 0.0005s;

[0149] S73: The updated state volume point is obtained according to equation (15):

[0150]

[0151] in For P k|k-1 Cholesky decomposition can yield ξ i The volume point of the i-th standard Gaussian distribution is obtained by equation (11);

[0152] S74: The volume point is obtained through the measurement function h: According to equations (16), (17), and (18), the one-step predicted value, prediction variance, and cross-covariance of the measurement can be obtained as follows:

[0153]

[0154]

[0155]

[0156] in Let h be the measurement covariance matrix; in this embodiment, the measurement function h can be expressed as equation (19).

[0157]

[0158] Where D = 1000m is the baseline distance; transmitter position [x Tx ,y Ty ]′=[-1000m,0m]′, the receiver is set at the origin;

[0159] S75: Calculate the filtering gain of the current frame according to equations (20), (21), and (22). Posterior state estimation And estimate the covariance P k|k for:

[0160]

[0161]

[0162]

[0163] Where z k =[r k ,f k ,θ k ] T ;

[0164] Thus, from S71 to S75, the determination of the target's posterior state has been completed;

[0165] S8: Determine the target support set information for the next frame based on the posterior state obtained from CKF;

[0166] S8, specifically:

[0167] S81: Based on the target's posterior state in the current frame The target state transition matrix F and the measurement function h are used to obtain the target's motion state in the Cartesian coordinate system in the next frame, its corresponding measurement value in the bistatic coordinate system, and the measurement value number, as shown in equations (23), (24), (25), and (26).

[0168]

[0169]

[0170]

[0171]

[0172] Where dr = 10m; PRF = 5.8594 × 10 4 Hz; M = 32; λ = 0.4451m;

[0173] S82: Based on the predicted state and Centered on the target, determine the target support set range I for the next frame. k+1 As shown in equation (27):

[0174]

[0175] Where Δr = 8 and Δf = 3 are the support set range parameters;

[0176] S9: The target posterior state, posterior state covariance, and target support set information of the current frame are used as the prior information for the next frame. As new multi-array data frames arrive, bistatic RD images of undulating targets are sequentially generated.

[0177] The beneficial effects of the method described in this invention are further illustrated by the following simulations:

[0178] The simulation experiment in this embodiment was compiled on Matlab R2020a.

[0179] 1. Simulation Content

[0180] Simulation Experiment 1: Under the conditions of SNR = -18dB, total number of data frames K = 15, initialization error Δ = 200, and full sampling, bistatic RD images of Swerling type I targets were generated by FFT, EOMP, and the algorithm proposed in this patent using EKF and CKF respectively. The true positions of the targets in the bistatic RD images are shown in Table 1; the experimental results of each method are shown in Tables 2, 3, 4, and 5 respectively, and some of the generated RD images are shown in Table 5. Figure 2 .

[0181] Table 1. True locations of undulating targets on a bistatic RD map (rounded to integers)

[0182] K 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 f 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 r 406 407 408 408 409 410 411 411 412 413 414 415 415 416 417

[0183] Table 2 shows the locations of undulating targets detected in each frame using the bistatic RD map generated by FFT.

[0184] K 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 f 17 18 17 17 18 5 18 18 18 18 18 18 18 16 14 r 407 408 409 409 410 343 411 412 413 414 414 415 416 286 362

[0185] Table 3. Locations of fluctuating targets in each frame detected by the bistatic RD map generated by EOMP.

[0186] K 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 f 17 18 17 17 18 5 18 18 18 18 18 18 18 16 14 r 407 408 409 409 410 343 411 412 413 414 414 415 416 286 362

[0187] Table 4. Locations of fluctuating targets detected in each frame using the bistatic RD map generated by DEOMP_EKF.

[0188] K 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 f 17 18 17 17 18 16 17 17 17 17 15 16 17 14 16 r 407 408 409 409 412 401 411 412 413 414 411 413 416 413 417

[0189] Table 5 shows the locations of fluctuating targets detected in each frame using the bistatic RD map generated by DEOMP_CKF.

[0190] K 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 f 17 18 17 17 18 18 18 18 18 18 18 18 18 18 18 r 407 408 409 409 410 411 411 412 413 414 414 415 416 419 417

[0191] Simulation Experiment 2: With data frame number K=15 and initialization error Δ=100, the mean square error of the detected position of undulating targets is analyzed by comparing the method proposed in this patent with existing methods under different signal-to-noise ratio conditions. Figure 3 As shown.

[0192] Simulation Experiment 3: With data frame number K=30 and initialization error Δ=200, the mean square error of the detected position of undulating targets is analyzed by comparing the method proposed in this patent with existing methods under different signal-to-noise ratio conditions. Figure 4 As shown.

[0193] Analyzing the results in Tables 2 and 3, the FFT and static EOMP algorithms ignore the motion relationship between adjacent frames when generating data frames of undulating targets, resulting in a large deviation between the detected position and the actual position of the target in some data frames, as shown in the results of frames 6, 14 and 15.

[0194] Analyzing the results in Table 4, although the DEOMP algorithm using EKF for tracking considers the motion state of the undulating target in adjacent frames, its detection results are still limited. For example, in frame 6, although its detection result is closer to the true target position than FFT and EOMP, the detected position is still inaccurate. This is because the measurement function of passive radar has a high degree of nonlinearity, causing EKF to produce a large error when approximating a nonlinear function. Under imperfect initialization, the tracking performance of EKF degrades, leading to deviations in the target support set information, which in turn affects the accuracy of DEOMP's reconstructed position, resulting in a large deviation in the target detection position and poor robustness.

[0195] Analysis of Table 5 shows that the DEOMP method proposed in this patent, which uses CKF for tracking, achieves more accurate target detection results compared to other methods. This method fully considers the motion state of fluctuating targets in adjacent frames, and CKF can more accurately approximate the measurement function compared to EKF. Even under imperfect initialization, CKF still possesses good tracking capabilities, making the algorithm proposed in this patent highly robust.

[0196] Figure 2 Chinese figure (a) and Figure 2 Figure (b) shows the global RD image of the fluctuating target generated in the 6th frame using the FFT method, and the local RD image within the target prediction range, respectively. Figure 2 Chinese Figure (c) Figure 2 Chinese map (d) and Figure 2 The middle figure (e) shows the undulating target RD image generated in the 6th frame using EOMP, DEOMP_EKF, and DEOMP_CKF, respectively, where r and f d The target detection location is shown. It can be found that the signal-to-noise ratio of the RD image generated by FFT is not ideal, and the target is submerged in noise, which is not conducive to target detection; however, it can be clearly observed in its local image that the target has higher energy relative to the surrounding noise; the RD images generated by EOMP and DEOMP_EKF have high signal-to-noise ratios, but their reconstructed locations are inaccurate; the DEOMP_CKF method proposed in this invention has a high signal-to-noise ratio and accurate reconstructed locations, indicating that the method of this invention is more conducive to the continuous detection of undulating targets.

[0197] Figure 3 and Figure 4The mean square error (MSE) curves of the proposed method for detecting undulating targets were compared with those of other existing methods under different signal-to-noise ratios (SNRs) when the number of data frames K=15 and the initialization error Δ=100, and when the number of data frames K=30 and the initialization error Δ=200. It can be observed that when the initialization error is low, the proposed DEOMP_CKF method exhibits the smallest MSE of target detection position at all SNRs, and the detection performance of DEOMP_EKF is similar to that of DEOMP_CKF. As the number of frames and the initialization error increase, the MSE of the detection position of FFT, EOMP, and DEOMP_EKF all increase to varying degrees, while the proposed DEOMP_CKF method still maintains the lowest MSE, and the error does not show a significant upward trend, demonstrating the excellent performance of the proposed method for detecting undulating targets.

[0198] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is merely a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A passive radar undulating target detection method with joint tracking, characterized in that: Includes the following steps, S1: The received passive radar reference signal and multi-element echo signal are segmented to obtain a reference signal matrix representing the segmented reference signal and an echo signal matrix representing the echo signal of each segmented element. S2: Cross-correlate the echo signals of each array element in the range direction according to the reference signal matrix to obtain the range-compressed signal of each array element echo. S3: Construct a dictionary of appropriate size in the direction of the Doppler frequency based on the signal dimensions of the received echoes of each array element after range compression; S4: Initialize CKF and the target support set information of the first frame based on the target prior information; S5: Based on the Doppler frequency dictionary constructed in S3 and the target support set information of the current frame, the signal after range compression of the echo of each array element is processed by the dynamic extended orthogonal matching pursuit method, and the result of the first array element is used as the bistatic RD image of the target in the current frame. S6: Perform constant false alarm rate (CFAR) detection on the bistatic RD image of the current frame to obtain the current bistatic measurement value r. k with f k The system then uses a multi-signal classification algorithm to process the array element signals under the current frame measurement values ​​to obtain the target's direction of arrival estimate θ for the current frame. k ; S7: Update the posterior state of the target in the current frame in the Cartesian coordinate system using CKF; S8: Determine the target support set information for the next frame based on the posterior state obtained from CKF; S9: Receives new echo data frames from each array element, and sequentially generates a bistatic RD image of the target by combining prior information of target tracking, thereby improving the continuous detection performance of undulating targets in passive radar systems. The target posterior state, posterior state covariance, and target support set information of the current frame are used as the prior information for the next frame. As new matrix data frames arrive, the aforementioned prior information for target tracking is used to sequentially generate a bistatic RD image of the undulating target.

2. The passive radar undulating target detection method with joint tracking as described in claim 1, characterized in that: The implementation method for step S1 is as follows: By setting the segment length, and based on the segment length and the maximum time delay, the echo signal of each array element is segmented with overlap to obtain the segmented echo signal and generate a Y matrix with dimensions L×M×N; where L is the number of antenna array elements, M is the number of echo signal segments, and N is the number of sampling points per segment of the echo signal; the reference signal is segmented and zero-padded according to the segment length to obtain a segmented reference signal with the same dimension as the segmented echo signal, and a Y matrix is ​​generated. ref The matrix has dimensions M×N; where M is the number of segments of the reference signal and is the same as the number of segments of the echo signal; and N is the number of sampling points per segment of the reference signal and is the same as the number of sampling points per segment of the echo signal.

3. The passive radar undulating target detection method with joint tracking as described in claim 2, characterized in that: The implementation method for step S2 is as follows: The obtained signal after range compression of the echo of each array element is shown in Equation (1): Where s l,m (n) represents the segmented range echo signal; This represents the complex conjugate signal of the corresponding range-guided reference signal; This represents the signal after distance compression; where Representing the time delay unit, l and m are the array element index and segment number index, respectively; all M segments of the distance-compressed signal are concatenated into Y. l Its dimensions are M×N.

4. The passive radar undulating target detection method with joint tracking as described in claim 3, characterized in that: The implementation method for step S3 is as follows: The aforementioned dictionary of Doppler frequency upwards is specifically represented as follows: Θ=[a1 a2 … a m … a M ] in, j represents the imaginary unit; π represents pi; f represents the Doppler frequency; t m Indicates slow time; M is the number of Doppler frequency grids, and m is the column number of the dictionary.

5. The passive radar undulating target detection method with joint tracking as described in claim 4, characterized in that: The implementation method for step S4 is as follows: The initialization parameters include the initial motion state of the undulating target in the Cartesian coordinate system. Initial state covariance matrix P 0|0 and the initial support set range I1.

6. The passive radar undulating target detection method with joint tracking as described in claim 5, characterized in that: The implementation method for step S5 is as follows: S51: Initialization: Residual R = Y l,k Support set Signal to be recovered X0 = 0 M×N The number of iterations q = 1, so the number of iterations q is set. max ; where Y l,k It is the signal of the l-th element and the k-th frame echo after range compression; S52: Based on the target support set range I of the current frame k And the index is determined by equation (2): Where I k Let Θ be the range of the target support set in the current frame, Θ be the M×M observation matrix, and a q and b q They are respectively |Θ H R| within the support set range I k The row and column number of the largest element in the array, (·) H Represents transpose and conjugate; S53: Index set expansion: T(q,b) q ) = a q And K T =Ind{T[b q ]}, where Ind{·} represents a non-zero element in a vector, T[b q ] represents the b-th element of matrix T q List; S54: Perform vector estimation according to equations (3), (4), and (5): A=Θ[K T ] (3) X0[K T ,b q ]=x (5) in Represents the pseudo-inverse of a matrix; S55: Residual Iteration: R[b] q ] = Y l,k [b q ]-Ax; S56: Iteration: q = q + 1, if q ≤ q max If the result is positive, return to step S52; otherwise, end the iteration and output the final result X0. Thus, from S51 to S56, the dynamic extended orthogonal matching tracking of the range-compressed signals of each array element echo is completed, and the bistatic RD image of the current frame is output: in This represents the RD image of the l-th element and the k-th frame.

7. The passive radar undulating target detection method with joint tracking as described in claim 6, characterized in that: The implementation method for step S6 is as follows: S61: Perform constant false alarm rate (CFAR) detection on the bistatic distance-Doppler image of the current frame to obtain the current bistatic measurements, including the bistatic distance r. k With bistatic Doppler frequency f k ; S62: Based on the signal value x of each array element signal after two-dimensional correlation at the current range-Doppler unit. k Calculate the covariance matrix R DOA The approximate value is shown in equation (6). Where U is the number of snapshots; x k It is an L×1 dimensional vector. It is its complex conjugate signal; L is the number of antenna array elements; S63: Transform the covariance matrix R DOA Perform eigenvalue decomposition to obtain L-num smaller and equal eigenvalues, and construct a matrix from their corresponding eigenvectors. Where num represents the number of targets whose arrival direction is to be estimated; S64: Calculate the spectral estimation formula Ψ(θ), where the direction corresponding to the peak is the DOA estimate θ of the target in the current frame. k The spectral estimation formula is shown in equation (7): Where s e (θ t ) is the manifold matrix vector, as shown in equation (8), θ t This is represented as the entire angular observation interval. Perform t max When sampling uniformly at points, the angle corresponding to the t-th sampled value; Where j represents the imaginary unit; κ is the wave number, z l The coordinate distribution of array elements; Thus, from S61 to S64, the determination of the bistatic measurements for the current frame is complete, including r. k f k Compared with the DOA estimate θ k .

8. The passive radar undulating target detection method with joint tracking as described in claim 7, characterized in that: The implementation method for step S7 is as follows: S71: The predicted state volume point is obtained according to equation (9): in This represents the posterior state of the target in the Cartesian coordinate system of the previous frame. n x For the target posterior state vector The dimension of P; k-1|k-1 Let be the posterior state covariance matrix of the previous frame, and For P k-1|k-1 Cholesky decomposition can yield ξ i The volume point of the i-th standard Gaussian distribution is obtained from equation (10): in[·] i Represents the i-th column of the matrix; S72: The volume point is obtained through the target state transition matrix F: γ i kk-1 =Fα i According to equations (11) and (12), the variance between the state prediction estimate and the state prediction estimate is: Q k Here is the state covariance matrix; S73: The updated state volume point is obtained according to equation (13): in For P k|k-1 Cholesky decomposition can yield ξ i Let be the volume point of the i-th standard Gaussian distribution, obtained by equation (10); S74: The volume point is obtained through the measurement function h: Based on equations (14), (15), and (16), the one-step predicted value, prediction variance, and cross-covariance of the measurement can be obtained as follows: Where R k The measurement covariance matrix; S75: Calculate the filtering gain of the current frame according to equations (17), (18), and (19). Posterior state estimation And estimate the covariance P kk for: Where z k Based on the current frame bistatic measurement value r k f k And the target direction of arrival (DOA) estimate θ k composition; Thus, from S71 to S75, the determination of the target's posterior state is completed.

9. The passive radar undulating target detection method with joint tracking as described in claim 8, characterized in that: The implementation method for step S8 is as follows: S8 specifically includes the following sub-steps: S81: Based on the target's posterior state in the current frame The target state transition matrix F and the measurement function h are used to obtain the target's motion state in the Cartesian coordinate system in the next frame, as well as its corresponding measurement value in the bistatic coordinate system, as shown in equations (20) and (21): S82: Based on the predicted state r k+1k and f k+1k Centered on the target, determine the target support set range I for the next frame. k+1 As shown in equation (22): Where Δr and Δf are the target support set range parameters, which are set according to the target motion state; Thus, from S81 to S82, the determination of the target support set for the next frame is completed.

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