A method for estimating target parameters of echo signals of a wideband radar extended target

Abstract

The application discloses a target parameter estimation method of echo signals of a wideband radar extended target. The method is characterized in that: the echo signals are sparsely represented on an off-grid dictionary to form a sparse representation vector, the sparse representation vector is compressed, a sparse signal is reconstructed through a sparse recovery algorithm, and then target parameters including a time delay and a Doppler factor are jointly obtained. The method is based on a compression sensing technology, can effectively reduce the amount of data required for calculation and storage, and improve the resolution of a radar system. Meanwhile, the method can realize joint estimation of the time delay and the Doppler factor, and does not need to separately process the time delay and the Doppler factor, thereby meeting real-time requirements.

Description

Technical Field

[0001] This invention belongs to the field of radar echo signal processing, and specifically relates to a method for estimating target parameters of echo signals from broadband radar extended targets. Background Technology

[0002] A primary task of radar and sonar systems is to estimate target time delay and Doppler factor. In narrowband radar, the estimation of target time delay and Doppler factor has been well solved. However, with the increasing sophistication of applications, higher demands are being placed on radar performance (such as high resolution, low intercept, and strong countermeasures), which narrowband radar can no longer meet. This has led to increased research interest in broadband radar.

[0003] Wideband radar signal processing encompasses radar signal processing theories, methods, and techniques based on wideband target echo models. Its early development can be traced back to research on sonar detectors in the 1950s, and the subsequent development of wideband target echo processing methods based on fuzzy function theory and matched filtering theory in the 1960s. However, due to theoretical deficiencies and limitations in implementation technology, wideband radar signal processing did not see significant development in the following decades. Major progress in wideband radar signal processing occurred in the 1990s when narrowband signal processing was extended to the wideband scenario. Subsequently, methods for estimating wideband target time delay and Doppler factor, distinct from those for narrowband targets, were developed.

[0004] The Wideband Ambiguity Function (WAF) is the most commonly used method for estimating the time delay and Doppler factor of a wideband target. Its basic idea is to calculate the cross-correlation between the echo signal and the reference signal; the peak position of this cross-correlation is the estimated value of the wideband echo signal's time delay and Doppler factor. Here, the reference signal is obtained by time delaying and scaling the transmitted signal. Existing technology titled "A wavelet-based algorithm for time delay and Doppler measurements" is relevant. [1] Using wavelet transform to compute the WAF improves computational efficiency; this is an existing technique titled "Efficient wideband signal parameter estimation using aradon-ambiguitytransform slice". [2]Combining narrowband ambiguity functions, WAF (Wide-band Ambient Function), and Radon ambiguity functions to estimate the time delay and Doppler factor of wideband targets improves the WAF's ability to distinguish targets with different velocities; this existing technology, titled "JointParameters Estimation method based on Wide-Band Ambiguity Function,"... [3] Applying WAF (Wireless Array Response) to a broadband bistatic multiple-input multiple-output (MIMO) radar system, combined with the MUSIC and ESPRIT algorithms, enables the estimation of parameters such as target position, velocity, direction of arrival (AOA), and direction of departure (DOF). However, the amount of data required for storage and computation by these WAF-based methods remains substantial. Furthermore, as the bandwidth of the transmitted signal increases, the radar resolution also rises, making it difficult to model targets as single-point targets. In this case, the radar resolution is much smaller than the physical size of the target, and the target echo typically consists of multiple strong scattering points or consecutive scattering points. These types of targets are also known as extended targets.

[0005] When using a wave-based acoustic imagery (WAF) to estimate the extended target time delay and Doppler factor, interference from the side lobes of the echo ambiguity function at each scattering point prevents the formation of corresponding spikes on the ambiguity map, making it difficult for the WAF to distinguish the number and precise location of the extended target scattering points. Besides the WAF, an existing technique titled "Parameter estimation of wideband underwater acoustic multipath channels based on fractional Fourier transform" also exists. [4] The fractional Fourier transform method described in the document, known as "The Mellin Matched Filter," is an existing technique. [5] The prior art described in the document, which utilizes a Merlin matched filter and is titled "An Improved Merlin Matched Filter," is a method for using a Merlin matched filter. [6] The method described in the paper, which utilizes an improved Merlin matched filter, has also been used to estimate the time delay and Doppler factor of broadband targets. However, most of these methods process the time delay and Doppler factor separately, requiring the Doppler factor to be estimated before the time delay can be calculated, thus limiting their real-time performance. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention proposes a target parameter estimation method for the echo signal of a broadband radar extended target.

[0007] The technical solution of the present invention is as follows:

[0008] A method for estimating target parameters of echo signals from a broadband radar extended target, wherein the target parameters include time delay and Doppler factor, the method comprising:

[0009] Based on the time-delay Doppler domain of the extended target, a sparse representation dictionary is constructed;

[0010] Construct an off-grid dictionary based on the off-grid deviation of the target parameters from the sparse representation dictionary;

[0011] The echo signal is sparsely represented on the off-grid dictionary to form a sparse representation vector.

[0012] The sparse representation vector is compressed, and then the sparse signal is reconstructed by the sparse recovery algorithm. Finally, the target parameters of the extended target, including time delay and Doppler factor, are obtained together.

[0013] Furthermore, the method for constructing the sparse representation dictionary includes:

[0014] Based on the time delay Doppler domain of the extended target, the Doppler factor is geometrically sampled using Merlin transform to form a Doppler factor sampling vector, and the time delay is uniformly sampled using Fourier transform to form a time delay sampling matrix.

[0015] A sparse representation dictionary is formed based on the Doppler factor sampling vector and the time delay sampling matrix.

[0016] Furthermore, the specific steps of the method for constructing the sparse representation dictionary include:

[0017] Obtain the time-delay Doppler domain of the extended target [γ] min ,γ max ]×[τ min ,τ max ], where [γ min ,γ max ] represents the Doppler domain, γ min γ is the minimum value of the Doppler factor in the Doppler domain. max The maximum value of the Doppler factor in the Doppler domain; [τ min ,τ max ] represents the time delay domain, τ min τ is the minimum time delay in the time delay domain. max This represents the maximum delay value in the delay domain.

[0018] According to the Doppler domain [γ] min ,γ max Geometric sampling is performed on the Doppler factors to form the Doppler factor sampling vector γ = [γ1, γ2, ..., γ]. P ], where P is the total number of Doppler factor elements in the Doppler factor sampling vector;

[0019] According to the time delay domain [τ] min ,τ max The time delay is uniformly sampled to form a time delay sampling matrix, τ = [τ1, τ2, ..., τ]. P In the delay sampling matrix, each delay element is a vector of length Q. τ p Let p be the p-th array in the time delay sampling matrix, where p∈[1,P];

[0020] 4) Construct a sparse representation dictionary based on the formed Doppler factor sampling vector and the time delay sampling matrix.

[0021] Furthermore, the specific steps for geometric sampling of the Doppler factor include:

[0022] Set the geometric sampling step size γ0 is the geometric sampling basis. m is the sampling power; η0 is the bandwidth of the transmitted signal in the Merlin domain; This is the floor operator; This is the floor function operator;

[0023] Geometric sampling of the Doppler factor is performed using the set geometric sampling step size.

[0024] Furthermore, the specific steps for uniformly sampling the time delay include:

[0025] Set uniform sampling step size B is the bandwidth of the transmitted signal; Q discrete points are sampled at a set uniform sampling interval.

[0026] Furthermore, the specific steps for constructing the off-grid dictionary based on the off-grid deviation of the target parameter for the sparse representation dictionary include:

[0027] Let the actual time delay of the extended target scattering point be and actual Doppler factor It is not located on the two-dimensional discrete grid corresponding to the sparse representation dictionary, i.e. And order γ p These are the actual time delays. and actual Doppler factor The nearest lattice point is approximated by a first-order Taylor series expansion to the atoms in the lattice dictionary, expressed as:

[0028]

[0029] in, For atoms in the actual dictionary; and These are the sparse representation dictionary T and the Doppler factor bias dictionary T, respectively. B and delay deviation dictionary T C Atoms; n is the Nyquist sampling point number; N is the total number of Nyquist sampling points; Ts is the Nyquist sampling time interval; for First-order partial derivatives with respect to the grid parameter Doppler factor γ; yes First-order partial derivative with respect to the grid parameter delay τ;

[0030] The expression for the off-grid dictionary Ψ is:

[0031]

[0032] Among them, T D =[T B T C ]; δ=[δ1,δ2,…,δ P ] T , The doppler factor represents the deviation from the grid; θ = [θ1, θ2, ..., θ P ] T , The deviation from the grid represents the time delay; It is a vector whose elements are all 1s; It is the identity matrix; operators Represents the Kronecker product; when When, diag(g) represents generating a diagonal matrix with g as its diagonal elements; when When diag(G) is used, it means taking the diagonal elements of matrix G to form a column vector.

[0033] Furthermore, the specific steps of sparsely representing the echo signal on the off-grid dictionary to form a sparse representation vector include:

[0034] The echo signal is represented based on the off-grid dictionary:

[0035] u = Ψx + w

[0036] Where u is the echo signal; H is a sparse representation vector; H = P·Q; w is additive white Gaussian noise.

[0037] Furthermore, the specific steps for compressing the sparse representation vector include:

[0038] y = Φu = ΦΨx + Φw = Θx + n

[0039] in, To compress the measured values; Let M be the random measurement matrix and M << N; Θ = ΦΨ is the sensing matrix; n is the compressed noise, n = Φw.

[0040] Furthermore, the specific steps of reconstructing the sparse signal using a sparse recovery algorithm to obtain the target parameters of the extended target, which consist of time delay and Doppler factor, include:

[0041] The sparse representation vector is divided into two-layer block structures, which include a first-layer block structure based on the geometric sampling points of the Doppler factor and a second-layer block structure based on the uniform sampling points of the time delay.

[0042] Let the prior distribution of each block in the first-layer block structure be a Gaussian prior distribution. For block x in the first-layer block structure, the Gaussian prior distribution satisfies:

[0043] p(x;α,B)=N(0,Σ0)

[0044] Where B represents B1, ..., B P B is a block diagonal matrix of diagonal blocks; p It is a positive definite matrix. α is a non-negative hyperparameter vector, α = [α1, ..., α2] P ] T α p It is a non-negative hyperparameter; The operator ⊙ represents the Hadamard product;

[0045] Let the second-layer block structure corresponding to each block in the first-layer block structure follow a Gaussian prior distribution. For the second-layer block structure x corresponding to the p-th block in the first-layer block structure... p The Gaussian prior distribution it follows satisfies:

[0046] p(x p |b p )=N(0,B p )

[0047] in, For the weight vector b p The q-th element in control The parameter, b p It follows a gamma distribution: and λ is the control and The parameter representing the degree of correlation between them, where 0 ≤ λ ≤ 1;

[0048] After setting the Gaussian prior distribution, the improved structure-coupled sparse Bayesian learning algorithm is used to estimate the target parameters.

[0049] Furthermore, the specific method for estimating the target parameters using the improved structurally coupled sparse Bayesian learning algorithm includes:

[0050] 1) Initialization: Set the initial values: all elements in the non-negative hyperparameter vector are 1, i.e., α = 1; all elements in the weight vector are 1, i.e., b p =1, noise variance β=1;

[0051] 2) Iterate through the calculations until the convergence condition is met or the maximum number of iterations is reached:

[0052] 2.1) E-step: Mean μ = β -1 ΣΘ H y, covariance matrix

[0053] 2.2) M-step:

[0054] 2.3) Error value estimation:

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] 3) Output: Sparse vector recovery value The Doppler factor estimate is the sum of the Doppler factor grid point estimate and the Doppler factor bias estimate, i.e. The time delay estimate is the sum of the time delay grid point estimate and the time delay deviation estimate, i.e.

[0061] Where, matrix D = Σ + μμ H Divide matrix D into blocks, each with dimension Q×Q, (D) pp This represents its p-th diagonal block matrix; the matrix Σ is divided into blocks, each sub-matrix having a dimension of Q×Q, Σ ii This represents its i-th diagonal block matrix; the matrix Θ is divided into blocks, each sub-matrix having dimensions M×Q, Θi Represents its i-th submatrix; weights Representation matrix (D) pp The q-th diagonal element in the array, and has Operator The operator Tr(·) represents finding the conjugate of a matrix; the operator Re{·} represents finding the real part of a matrix.

[0062] Operator (·) Indicates: When hour,

[0063] when hour,

[0064]

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] This invention proposes a target parameter estimation method for echo signals of extended targets in broadband radar. This method sparsely represents the echo signal on a constructed off-grid dictionary, forming a sparse representation vector. This sparse representation vector is then compressed, and a sparse recovery algorithm is used to reconstruct the sparse signal. Finally, target parameters, including time delay and Doppler factor, are jointly obtained. This method is based on compressed sensing technology, which effectively reduces the amount of data required for computation and storage, and improves the resolution of the radar system. Furthermore, this method enables joint estimation of time delay and Doppler factor without separate processing, meeting real-time requirements.

[0067] In constructing the sparse representation dictionary, this invention also addresses the case where the target parameter is not located at a grid point (off-grid problem). It uses a first-order Taylor series expansion to estimate the off-grid deviation of the target parameter and obtains an off-grid dictionary based on this deviation. Then, this deviation value is used to correct the estimated value of the target parameter. Compared to conventional dense network methods for off-grid problems, this design does not increase grid density or data volume, effectively mitigating the impact of off-grid on estimation accuracy. Simultaneously, it avoids the problems associated with dense networks constructed by dense grid methods, which increase dictionary relevance and hinder sparse recovery processing.

[0068] The method of this invention makes full use of the two-layer block structure of sparse representation vectors. By combining BSBL with PC-SBL, this two-layer block structure is fully utilized to improve the recovery accuracy.

[0069] This invention utilizes Merlin transform for geometric sampling of the Doppler factor and Fourier transform for uniform sampling of the time delay when constructing the sparse representation dictionary. Compared to conventional two-dimensional uniform discretization methods, this invention's sampling method considers the influence of the Doppler factor on the waveform in the broadband echo model and appropriately adjusts the sampling interval. Therefore, even with a coarse grid, it can better adapt to the echo signal, improving computational efficiency. Attached Figure Description

[0070] Figure 1 This is a flowchart illustrating the target parameter estimation method for the echo signal of a broadband radar extended target in Example 1.

[0071] Figure 2 This is a schematic diagram of the two-layer block structure of the sparse representation vector in Example 8;

[0072] Figure 3(a) is a schematic diagram of the results of joint estimation of extended target delay and Doppler factor by WAF in Application Example 1;

[0073] Figure 3(b) is a schematic diagram of the results of joint estimation of extended target time delay and Doppler factor by MPC-SBL in Example 1.

[0074] Figure 4(a) is a schematic diagram of the root mean square error performance of the four methods in Example 2 for time delay estimation.

[0075] Figure 4(b) is a schematic diagram of the root mean square error performance of the four methods for Doppler factor estimation in Example 2. Detailed Implementation

[0076] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0077] Example 1:

[0078] This invention provides a method for estimating target parameters in the echo signal of a broadband radar extended target. The target parameters include time delay and Doppler factor, such as... Figure 1 As shown, the method includes:

[0079] Based on the time-delay Doppler domain of the extended target, a sparse representation dictionary is constructed;

[0080] Construct an off-grid dictionary based on the off-grid deviation of the target parameters from the sparse representation dictionary;

[0081] The echo signal is sparsely represented on the off-grid dictionary to form a sparse representation vector.

[0082] The sparse representation vector is compressed, and then the sparse signal is reconstructed by the sparse recovery algorithm. Finally, the target parameters of the extended target, including time delay and Doppler factor, are obtained together.

[0083] Example 2:

[0084] This embodiment, based on Embodiment 1, is further designed in that: the method for constructing the sparse representation dictionary in this example includes:

[0085] Based on the time delay Doppler domain of the extended target, the Doppler factor is geometrically sampled using Merlin transform to form a Doppler factor sampling vector, and the time delay is uniformly sampled using Fourier transform to form a time delay sampling matrix.

[0086] A sparse representation dictionary is formed based on the Doppler factor sampling vector and the time delay sampling matrix.

[0087] Example 3:

[0088] This embodiment, based on Embodiment 1, is further designed in that: the specific steps of the sparse representation dictionary construction method in this example include:

[0089] Obtain the time-delay Doppler domain of the extended target [γ] min ,γ max ]×[τ min ,τ max ], where [γ min ,γ max ] represents the Doppler domain, γ min γ is the minimum value of the Doppler factor in the Doppler domain. max The maximum value of the Doppler factor in the Doppler domain; [τ min ,τ max ] represents the time delay domain, τ min τ is the minimum time delay in the time delay domain. max This represents the maximum delay value in the delay domain.

[0090] According to the Doppler domain [γ] min ,γ max Geometric sampling is performed on the Doppler factors to form the Doppler factor sampling vector γ = [γ1, γ2, ..., γ]. P ], where P is the total number of Doppler factor elements in the Doppler factor sampling vector;

[0091] According to the time delay domain [τ] min ,τ max The time delay is uniformly sampled to form a time delay sampling matrix, τ = [τ1, τ2, ..., τ]. P In the delay sampling matrix, each delay element is a vector of length Q. τ pLet p be the p-th array in the time delay sampling matrix, where p∈[1,P];

[0092] 4) Construct a sparse representation dictionary based on the formed Doppler factor sampling vector and the time delay sampling matrix.

[0093] Example 4:

[0094] This embodiment, based on Embodiment 3, is further designed in that: the specific steps for geometric sampling of the Doppler factor in this example include:

[0095] Set the geometric sampling step size γ0 is the geometric sampling basis. m is the sampling power; η0 is the bandwidth of the transmitted signal (i.e., the signal corresponding to the echo signal) in the Merlin domain; This is the floor operator; This is the floor function operator;

[0096] Geometric sampling of the Doppler factor is performed using the set geometric sampling step size.

[0097] Example 5:

[0098] This embodiment, based on embodiment four, is further designed in that: the specific steps for uniformly sampling the time delay in this example include:

[0099] Set uniform sampling step size B is the bandwidth of the transmitted signal (in the frequency domain); Q discrete points are sampled at a set uniform sampling interval.

[0100] Example 6:

[0101] This embodiment, based on Embodiment 5, is further designed in the following way: The specific steps for constructing the off-grid dictionary according to the off-grid deviation of the sparse representation dictionary based on the target parameters include:

[0102] The target parameters are expanded using a first-order Taylor series, and the off-grid deviation of the target parameters is introduced into a sparse representation dictionary. A sparse Bayesian learning algorithm is then used to estimate the off-grid deviation, specifically by setting the actual time delay of the extended target scattering point. and actual Doppler factor It is not located on the two-dimensional discrete grid corresponding to the sparse representation dictionary, i.e. And order γ p These are the actual time delays. and actual Doppler factor The nearest lattice point is approximated by a first-order Taylor series expansion to the atoms in the lattice dictionary, expressed as:

[0103]

[0104] in, For the atoms of the actual dictionary (i.e., the actual delay) and actual Doppler factor (Corresponding column vectors of the dictionary); and These are the sparse representation dictionary T and the Doppler factor bias dictionary T, respectively. B and delay deviation dictionary T C Atoms; n is the Nyquist sampling point number; N is the total number of Nyquist sampling points; Ts is the Nyquist sampling time interval; for First-order partial derivatives with respect to the grid parameter Doppler factor γ; yes First-order partial derivative with respect to the grid parameter delay τ;

[0105] The expression for the off-grid dictionary Ψ is:

[0106]

[0107] Among them, T D =[T B T C ];

[0108] δ=[δ1,δ2,…,δ P ] T , This indicates the off-grid deviation of the Doppler factor;

[0109] θ = [θ1, θ2, ..., θ P ] T , The deviation from the grid represents the time delay; It is a vector whose elements are all 1s; It is the identity matrix;

[0110] Operators Represents the Kronecker product;

[0111] when When the diag(g) is used, it means generating a diagonal matrix with g as its diagonal element;

[0112] when When diag(G) is used, it means taking the diagonal elements of matrix G to form a column vector.

[0113] Example 7:

[0114] This embodiment, based on Embodiment Six, is further designed in that: the specific steps for sparsely representing the echo signal on the off-grid dictionary to form a sparse representation vector include:

[0115] Suppose there is an extended target in space, consisting of K spatially adjacent scattering points, moving radially along the detector at a constant velocity v. The detector's transmitted signal is... Where s(t) is the baseband complex envelope of the transmitted signal; f c It is the carrier frequency. The echo from the kth scattering point is α. k s(γ(t-τ k )). Among them, α k γ is the reflection coefficient at the k-th scattering point; γ = (cv) / (c+v) is the target Doppler factor; τ k Let be the time delay at the k-th scattering point. The extended target echo signal received by the detector is the superposition of the echoes from these K scattering points, and is contaminated with additive white Gaussian noise w(t):

[0116]

[0117] With T s By performing Nyquist sampling on the received signal u(t) at time intervals, we obtain:

[0118]

[0119] Where n = 0, ..., N-1. The above formula can be rewritten in the form of matrix multiplication:

[0120]

[0121] in, It is the observation vector; It is a vector composed of the reflection coefficients of the extended target scattering points; For the actual dictionary (the real dictionary, i.e., the actual latency) and actual Doppler factor (corresponding dictionary)

[0122] It is additive white Gaussian noise;

[0123] In this example, the echo signal is represented in the form of matrix product based on the off-grid dictionary:

[0124] u = Ψx + w

[0125] Where u is the echo signal; H is the sparse representation vector, i.e., the target reflection coefficient vector; H = P·Q. w is additive white Gaussian noise.

[0126] The specific steps for compressing the sparse representation vector in this example include:

[0127] y = Φu = ΦΨx + Φw = Θx + n

[0128] in, To compress the measured values; Let M be the random measurement matrix and M << N; Θ = ΦΨ is the sensing matrix; n is the compressed noise, n = Φw.

[0129] Example 8:

[0130] This embodiment, based on Embodiment Seven, is further designed in that: the specific steps for reconstructing the sparse signal using a sparse recovery algorithm to obtain the target parameters of the extended target, which consist of time delay and Doppler factor, include:

[0131] The sparse representation vector is divided into two-layer block structures, which include a first-layer block structure based on the geometric sampling points of the Doppler factor and a second-layer block structure based on the uniform sampling points of the time delay.

[0132] Since the grid dictionary Ψ is divided into P blocks based on discrete γ, the γ values ​​corresponding to different blocks are different. Correspondingly, x is also divided into P blocks based on γ, and each block x... p Both contain Q points, such as Figure 2 As shown. Because the scattering points of the extended target have the same velocity, these scattering points are within the same block. Therefore, there is only one block of x in x. p Not all values ​​are zero, corresponding to the Doppler factor of the extended target. p The number of non-zero elements represents the number of scattering points contained in the extended target, and their positions correspond to the time delays of these scattering points. Since the scattering points of the extended target are closely adjacent in the range space, their time delays are also closely adjacent. Therefore, within the corresponding blocks, these scattering points are clustered together, also exhibiting a blocky structure. Thus, the sparse vector x of the extended target echo signal can be divided into two layers of blocky structure.

[0133] Let the prior distribution of each block in the first-layer block structure be a Gaussian prior distribution. For block x in the first-layer block structure, the Gaussian prior distribution satisfies:

[0134] p(x;α,B)=N(0,Σ0)

[0135] Where B represents B1, ..., B P B is a block diagonal matrix of diagonal blocks; p It is a positive definite matrix. B p Reflects xp The correlation structure between inner elements; α is a non-negative hyperparameter vector, α = [α1, ..., α2]. P ] T α p Let α be a non-negative hyperparameter. p Used to control block x p The sparseness; The operator ⊙ represents the Hadamard product;

[0136] Let the second-layer block structure corresponding to each block in the first-layer block structure follow a Gaussian prior distribution. For the second-layer block structure x corresponding to the p-th block in the first-layer block structure... p The Gaussian prior distribution it follows satisfies:

[0137] p(x p |b p )=N(0,B p )

[0138] in, For the weight vector b p The q-th element in To control The parameter, b p It follows a gamma distribution: and λ is the control and The parameter represents the degree of correlation between elements, where 0 ≤ λ ≤ 1. This setting allows elements within the block to... There are connections between it and its neighboring elements, which can promote the aggregation of block signals.

[0139] After setting the Gaussian prior distribution, the target parameters are estimated using the Modified Pattern-Coupled Sparse Bayesian Learning (MPC-SBL) algorithm.

[0140] Example 9:

[0141] This embodiment, based on Embodiment 8, is further designed in the following way: The specific method for estimating the target parameters using the improved structure-coupled sparse Bayesian learning algorithm in this example includes:

[0142] 1) Initialization: Set the initial values: all elements in the non-negative hyperparameter vector are 1, i.e., α = 1; all elements in the weight vector are 1, i.e., b p=1, noise variance β=1;

[0143] 2) Iterative calculation continues until the convergence condition is met or the maximum number of iterations is reached. The convergence condition can be that the difference between the output of the previous iteration and the output of the next iteration is less than or equal to a set value, specifically including:

[0144] 2.1) E-step: The mean μ = β in the sparse Bayesian learning algorithm -1 ΣΘ H y, the covariance matrix in the sparse Bayesian learning algorithm

[0145] 2.2) M-step:

[0146] 2.3) Error value estimation:

[0147]

[0148]

[0149]

[0150]

[0151]

[0152] 3) Output: Sparse vector recovery value The Doppler factor estimate is the sum of the Doppler factor grid point estimate and the Doppler factor bias estimate, i.e. The time delay estimate is the sum of the time delay grid point estimate and the time delay deviation estimate, i.e.

[0153] Where, D=Σ+μμ H ;

[0154] Divide matrix D into blocks, each with dimension Q×Q, (D) pp This represents its p-th diagonal block matrix;

[0155] Divide the matrix Σ into blocks, each of which has a dimension of Q×Q. ii This represents its i-th diagonal block matrix;

[0156] Divide the matrix Θ into blocks, each of which has dimensions M×Q. i This represents its i-th submatrix;

[0157] weight Representation matrix (D) ppThe q-th diagonal element in the array, and has Operator The operator Tr(·) represents finding the conjugate of a matrix; the operator Re{·} represents finding the real part of a matrix.

[0158] Operator (·) express:

[0159] when hour,

[0160] when hour,

[0161] Application Example 1:

[0162] This example uses the target parameter estimation method of this invention to estimate the target parameters of a simulated echo signal of a broadband radar extended target, and compares it with the existing WAF method. The extended target contains four scattering points, and some simulation experimental parameters are as follows: The transmitted signal bandwidth B = 10kHz, and the geometric sampling basis γ0 = 1.01. The estimation results of the proposed method (referred to as the improved algorithm in the figure) and the WAF (wideband ambiguity function) method are shown in Figures 3(a) and 3(b), respectively. As can be seen from Figures 3(a) and 3(b), the wideband ambiguity function has poor resolution for extended targets. This is because when estimating the time delay and Doppler factor of an extended target using the wideband ambiguity function, it is affected by the side lobes of the ambiguity function of the echoes from each scattering point, preventing the formation of peaks corresponding to the scattering points on the ambiguity map. When the target is a point target, the time delay and Doppler factor can be estimated simply by finding the location of the maximum value. When the target is an extended target, although the location of the point corresponding to the maximum value on the time delay-Doppler plane can be found using the wideband ambiguity function, it is impossible to determine which points connected to the maximum value belong to the extended target when the number of scattering points of the extended target is unknown. Therefore, it is impossible to accurately estimate the target's time delay and Doppler factor. Even when the number of scattering points of the extended target is known, it is still impossible to effectively estimate the time delay and Doppler factor. Because the correspondence between the extended target scattering points and the maximum value of the broadband ambiguity function is unknown, it's impossible to determine the location of the maximum value within the extended target. Taking the extended target in the simulation as an example, this target contains four scattering points. If the maximum value corresponds to the first scattering point, then the following three points should be selected as the estimated time delay, and so on, resulting in four selection methods. The more scattering points the extended target contains, the more ways there are to select points, and the worse the estimation performance of time delay and Doppler factor becomes.

[0163] The sparse representation method of this invention effectively improves the resolution of extended targets. Even when the number and structure of the extended target's scattering points are unknown, this invention can still clearly determine the specific structural form of the extended target's scattering points from the estimation results of the improved structure-coupled sparse Bayesian learning algorithm (MPC-SBL). Taking simulation as an example, we can clearly see that the target contains 4 scattering points, and the position of each scattering point can be directly obtained. Therefore, compared with broadband fuzzy functions, the improved structure-coupled sparse Bayesian learning algorithm (MPC-SBL) has a higher resolution capability for extended targets.

[0164] Application Example 2:

[0165] This example uses the target parameter estimation method of this invention to estimate the target parameters of a simulated echo signal of another broadband radar extended target, and compares it with three other existing methods. The method of this invention is denoted as MPC-SBL (off-grid); the first existing method is the BSBL method, denoted as BSBL; the second existing method is the PC-SBL method, denoted as PC-SBL; the third method is largely the same as the target parameter estimation method of this invention, except that the third method does not construct an off-grid dictionary, but directly sparsely represents the echo signal on a sparse representation dictionary; this third method is denoted as MPC-SBL (on-grid).

[0166] In electromagnetic wave radar, since the transmitted signal propagates at the speed of light, the scale transformation amplitude of the target echo envelope relative to the transmitted signal envelope is extremely small. To accurately estimate the scale factor of the target echo, a large time-bandwidth product of the transmitted signal is required. Without distortion-free sampling, the amount of discrete sampled data at the radar receiver is too large, making it difficult for personal computer hardware to support such a large volume of computation and simulation. Therefore, the simulation parameters used in this example are those of an underwater sonar: a linear frequency modulated (LFM) signal as the transmitted signal, a time width T = 5ms, a bandwidth B = 10kHz, and a carrier frequency f... c =50kHz, sampling frequency f s =200kHz, and a Gaussian random matrix is ​​used as the measurement matrix. Assume there is one extended target in space containing four scattering points. These scattering points have the same Doppler factor, adjacent time delays, and a reflection coefficient of 1. The range of γ is 0.95≤γ≤1.05, and the range of τ is 0.011s≤τ≤0.0118s. γ is geometrically sampled based on the bandwidth η0 = 50 of the linear frequency modulated signal in the Merlin domain, i.e. m = [-9, ..., 10]. Then, τ is uniformly sampled in each discrete γ, i.e., the sampling interval is... For computational convenience, the number of discrete grid points for τ is kept constant at 30 for different γ values. The Monte Carlo experiment is performed 100 times, and the root mean square error (RMSE) is used to measure the estimation performance. r k It is the true value of the target parameter. These are the estimated values ​​of the target parameters.

[0167] Simulation results are shown in Figures 4(a) and 4(b). Based on Figures 4(a) and 4(b), the performance of the four methods for joint estimation of the extended target's time delay and Doppler factor can be analyzed and compared. Due to the non-uniform sampling of the time delay-Doppler factor plane, the resulting two-dimensional discrete plane is also non-uniform. Although each block has the same size, the spacing between atoms within different blocks is different, leading to greater differences between blocks. Since BSBL and PC-SBL cannot effectively handle this difference, their estimation performance is compromised. In contrast, the method of this invention effectively utilizes the two-layer block structure information contained in the extended target, resulting in a significant improvement in estimation performance compared to BSBL and PC-SBL. Figures 4(a) and 4(b) also show that the introduction of the off-mesh model effectively improves the algorithm's estimation performance.

[0168] References

[0169] [1]Niu XX,Ching PC,Chan Y TA wavelet-based algorithm for timedelay and Doppler measurements[C] / / Proceedings of ISSE'95-InternationalSymposium on Signals,Systems and Electronics.IEEE,1995:485-488.

[0170] [2]Sharif MR,Abeysekera S S.Efficient wideband signal parameter estimation using a radon-ambiguity transform slice[J].IEEE transactions onaerospace and electronic systems,2007,43(2):673-688.

[0171] [3]Li L.Joint Parameters Estimation method based on Wide-BandAmbiguity Function[C] / / 2018IEEE International Conference of Safety ProduceInformatization(IICSPI).IEEE,2018:605-609.

[0172] [4]Zhao Y, Yu H, Wei G, et al. Parameter estimation of widebandunderwater acoustic multipath channels based on fractional Fourier transform [J]. IEEE Transactions on Signal Processing, 2016, 64(20): 5396-5408.

[0173] [5]Monakov A.The mellin matched filter[J].IEEE Journal of SelectedTopics in Signal Processing,2015,9(8):1451-1459.

[0174] [6] Deng Wenli, Chen Shengyao. An improved Merlin matched filter [J]. Modern Radar, 2021, 43(1):21-29.

Claims

1. A method for estimating target parameters of echo signals from broadband radar extended targets, wherein the target parameters include time delay and Doppler factor, characterized in that: The method includes: Based on the time-delay Doppler domain of the extended target, a sparse representation dictionary is constructed; Construct an off-grid dictionary based on the off-grid deviation of the target parameters from the sparse representation dictionary; The echo signal is sparsely represented on the off-grid dictionary to form a sparse representation vector. The sparse representation vector is compressed, and then the sparse signal is reconstructed by the sparse recovery algorithm. Then, the target parameters of the extended target, including time delay and Doppler factor, are obtained in combination. The method for constructing the sparse representation dictionary includes: Based on the time delay Doppler domain of the extended target, the Doppler factor is geometrically sampled using Merlin transform to form a Doppler factor sampling vector, and the time delay is uniformly sampled using Fourier transform to form a time delay sampling matrix. A sparse representation dictionary is formed based on the Doppler factor sampling vector and the time delay sampling matrix; The specific steps of the method for constructing the sparse representation dictionary include: Obtain the delay Doppler domain of the extended target ,in For the Doppler region, This represents the minimum value of the Doppler factor in the Doppler domain. This represents the maximum value of the Doppler factor in the Doppler domain; For the time delay domain, This represents the minimum delay in the delay domain. This represents the maximum delay value in the delay domain. According to Doppler domain Geometric sampling is performed on the Doppler factor to form the Doppler factor sampling vector. , This represents the total number of Doppler factor elements in the Doppler factor sampling vector; According to the time delay domain The time delay is uniformly sampled to form a time delay sampling matrix. Each delay element in the delay sampling matrix is ​​a sequence of length . The vector, , The first element in the time delay sampling matrix arrays, ; 4) Construct a sparse representation dictionary based on the formed Doppler factor sampling vector and the time delay sampling matrix.

2. The target parameter estimation method for the echo signal of a broadband radar extended target according to claim 1, characterized in that: The specific steps for geometric sampling of the Doppler factor include: Set the geometric sampling step size , As a geometric sampling basis, ; m is the sampling power; ; The bandwidth of the transmitted signal in the Merlin domain; This is the floor operator; This is the floor function operator; Geometric sampling of the Doppler factor is performed using the set geometric sampling step size.

3. The target parameter estimation method for the echo signal of a broadband radar extended target according to claim 2, characterized in that: The specific steps for uniformly sampling the time delay include: Set uniform sampling step size , The bandwidth of the transmitted signal; sampled at a set uniform interval. Sampling of discrete points.

4. The target parameter estimation method for the echo signal of a broadband radar extended target according to claim 3, characterized in that: The specific steps for constructing the off-grid dictionary based on the off-grid deviation of the sparse representation dictionary according to the target parameters include: Let the actual time delay of the extended target scattering point be and actual Doppler factor It is not located on the two-dimensional discrete grid corresponding to the sparse representation dictionary, i.e. , and order , These are the actual time delays. and actual Doppler factor The nearest lattice point is approximated by a first-order Taylor series expansion to the atoms in the lattice dictionary, expressed as: ； in, For atoms in the actual dictionary; , and Sparse representation dictionary Doppler factor bias dictionary and delay deviation dictionary Atoms; , , n is the Nyquist sampling point number; N is the total number of Nyquist sampling points; Ts is the Nyquist sampling time interval; for Regarding grid parameters and Doppler factors The first-order partial derivative; yes Regarding the time delay of mesh parameters The first-order partial derivative; The off-grid dictionary The expression is: ; in, ; ; , This indicates the off-grid deviation of the Doppler factor; , , The deviation from the grid represents the time delay; It is a vector whose elements are all 1s; , It is the identity matrix; operators Represents the Kronecker product; when hour, Indicates the generation of a... A diagonal matrix with diagonal elements; when hour, Indicates taking the matrix The diagonal elements form a column vector.

5. The target parameter estimation method for the echo signal of a broadband radar extended target according to claim 4, characterized in that: The specific steps for sparsely representing the echo signal on the off-grid dictionary to form a sparse representation vector include: The echo signal is represented based on the off-grid dictionary: ; Where u is the echo signal; It is a sparse representation vector; w represents additive white Gaussian noise.

6. The target parameter estimation method for the echo signal of a broadband radar extended target according to claim 5, characterized in that: The specific steps for compressing the sparse representation vector include: ; in, To compress the measured values; It is a random measurement matrix, and ; For the perception matrix; This is the compressed noise. .

7. The target parameter estimation method for the echo signal of a broadband radar extended target according to claim 6, characterized in that: The specific steps for reconstructing the sparse signal using a sparse recovery algorithm, and then jointly obtaining the target parameters of the extended target, including time delay and Doppler factor, include: The sparse representation vector is divided into two-layer block structures, which include a first-layer block structure based on the geometric sampling points of the Doppler factor and a second-layer block structure based on the uniform sampling points of the time delay. Let the prior distribution of each block in the first-layer block structure be a Gaussian prior distribution. For block x in the first-layer block structure, the Gaussian prior distribution satisfies: ; in, For This is a block diagonal matrix representing the diagonal blocks; It is a positive definite matrix. ; A non-negative hyperparameter vector. , It is a non-negative hyperparameter; ; operator Represents the Hadamard product; Let the second-layer block structure corresponding to each block in the first-layer block structure follow a Gaussian prior distribution. For the second-layer block structure x corresponding to the p-th block in the first-layer block structure... p The Gaussian prior distribution it follows satisfies: ; in, ; For the weight vector b p The q-th element in , control The parameters, It follows a gamma distribution: , ,and ; , , To control and The parameters relating the degree of correlation between them, and ; After setting the Gaussian prior distribution, the improved structure-coupled sparse Bayesian learning algorithm is used to estimate the target parameters.

8. The target parameter estimation method for the echo signal of a broadband radar extended target according to claim 7, characterized in that: The specific method for estimating the target parameters using the improved structure-coupled sparse Bayesian learning algorithm includes: 1) Initialization: Set the initial values ​​of the non-negative hyperparameter vector to all 1s, i.e. The weight vector contains all 1s, that is... noise variance ; 2) Iterate through the calculations until the convergence condition is met or the maximum number of iterations is reached: 2-1) E-step: mean covariance matrix ; 2-2)M-step: , , ; 2-3) Error estimation: ; ; ; ; ; 3) Output: Sparse vector recovery value The Doppler factor estimate is the sum of the Doppler factor grid point estimate and the Doppler factor bias estimate, i.e. The time delay estimate is the sum of the time delay grid point estimate and the time delay deviation estimate, i.e. ; Among them, matrix For the matrix Divide the matrix into blocks, with each sub-matrix having a dimension of . , Indicates its first A diagonal block matrix; a pair of matrices Divide the matrix into blocks, with each sub-matrix having a dimension of . , Indicates its first A diagonal block matrix; a pair of matrices Divide the matrix into blocks, with each sub-matrix having a dimension of . , Indicates its first Submatrices; weights , Representation matrix The first in There are diagonal elements, and have Operator Indicates conjugate; operator Indicates finding the trace of a matrix; operator Indicates taking the real part; operator Indicates: When hour, ;when hour, .

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