Reverberation suppression method based on adaptive meshless dictionary

Abstract

The invention discloses a reverberation suppression method based on a self-adaptive meshless dictionary, and the method comprises the steps: precisely selecting space-time atoms of a reverberation subspace in a continuous space-time plane through employing a particle swarm optimization algorithm, and constructing a self-adaptive space-time dictionary; sparse decomposition is carried out on sonar array observation data on a designed dictionary in combination with a sparse Bayesian learning algorithm, so that high-precision reverberation covariance matrix estimation is obtained, grid mismatch errors are eliminated, and the reverberation suppression effect and the target detection performance are improved.

Description

Technical Field

[0001] The invention belongs to the technical field of sonar, and in particular relates to a reverberation suppression method based on an adaptive gridless dictionary. Background Art

[0002] Reverberation is formed by the superposition of scattered signals generated by a large number of irregular scatterers in the ocean at the receiving point, and its spectral structure has certain similarities with the transmitted signal. When the active sonar platform moves at a certain speed, the scattered echoes incident from different spatial cone angles will show different Doppler frequencies, resulting in a significant expansion of the reverberation spectrum. This phenomenon makes the echo of stationary or low radial velocity targets may be completely masked by reverberation in the frequency domain. At this time, if the filtering method is simply relied on in the time domain or frequency domain, the reverberation suppression and target detection performance will be significantly reduced because the influence of array motion is not considered.

[0003] Space-time adaptive processing (STAP) technology can use the two-dimensional joint information of the spatial and temporal domains to achieve effective filtering of space-time coupled reverberation and target coherent accumulation, and improve the output signal-to-mixing ratio. Therefore, it is one of the key technologies for active sonar reverberation suppression and target detection on various mobile platforms. Existing studies have shown that STAP technology can suppress reverberation and enhance the ability of active sonar to effectively detect targets. However, the traditional STAP method requires a large number of independent and identically distributed (IID) samples to obtain ideal performance. The sparse recovery space-time adaptive processing (SR-STAP) method is based on compressed sensing (CS) theory, which breaks through the limitation of the traditional STAP method on IID samples and can reconstruct the reverberation power spectrum with the least samples. However, the SR-STAP method also has certain limitations. When the dictionary division is biased, the reverberation component is not located on the dictionary grid, and the mismatch between the reverberation ridge and the grid leads to a decrease in the accuracy of sparse recovery. Therefore, it is urgent to study the SR-STAP method under the influence of grid mismatch. Summary of the invention

[0004] In order to overcome the shortcomings of the prior art, the present invention provides a reverberation suppression method based on an adaptive gridless dictionary, which uses a particle swarm optimization algorithm to accurately select space-time atoms of the reverberation subspace in a continuous space-time plane to construct an adaptive space-time dictionary; and then combines the sparse Bayesian learning algorithm to perform sparse decomposition of the sonar array observation data on the designed dictionary, thereby obtaining a high-precision reverberation covariance matrix estimate, eliminating grid mismatch errors, and improving the reverberation suppression effect and target detection performance.

[0005] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0006] Step 1: Transmit a signal, divide the received data into frames according to the length of the transmitted pulse and perform sampling, and construct NM×1-dimensional data samples required for space-time adaptive processing based on the sampled data; the data samples include: samples to be detected and auxiliary samples; wherein the samples to be detected refer to data obtained from the distance unit RUT of the data to be detected, and the auxiliary samples refer to data obtained from the distance unit adjacent to the data to be detected, N is the spatial dimension, and M is the time dimension;

[0007] Step 2: Select the auxiliary reverberation samples for constructing the adaptive space-time dictionary. The specific steps of the selection are as follows:

[0008] (1) Based on the principle of sparse recovery technology, a traditional grid dictionary is constructed;

[0009] (2) performing sparse recovery on the unit to be detected and the L adjacent candidate units on both sides thereof, respectively, to obtain the sparse coefficient vector of the unit to be detected and the sparse coefficient vector of the candidate units;

[0010] (3) Calculate the similarity of the sparse coefficients of each candidate unit and the unit to be detected, and take the reverberation samples of the L distance units with the largest similarity as auxiliary reverberation samples;

[0011] Step 3: Use the particle swarm algorithm combined with the selected auxiliary reverberation samples to construct an adaptive space-time dictionary. The specific steps of the construction are as follows:

[0012] (1) constructing a reverberation covariance matrix based on the selected auxiliary reverberation samples;

[0013] (2) Initialize the parameters of the particle swarm algorithm and establish a fitness function model to measure the correlation between space-time atoms and reverberation subspace;

[0014] (3) The optimal reverberation space-time atoms searched during the particle swarm algorithm iteration are placed into the space-time steering vector set as the adaptive space-time dictionary for subsequent sparse recovery;

[0015] Step 4: Use the sparse Bayesian algorithm to reconstruct the reverberation samples based on the constructed space-time dictionary and estimate the reverberation covariance matrix. The specific steps are as follows:

[0016] (1) Based on the constructed space-time dictionary, update the iterative mean matrix μ and covariance matrix Σ.

[0017] (2) Based on the updated mean matrix μ and covariance matrix Σ, update the iterative sparse coefficient matrix γ and noise parameters

[0018] (3) Determine whether the iteration stop condition is met. If so, output the sparse coefficient matrix γ. If not, continue iterative update.

[0019] Step 5: Based on the output of the sparse Bayesian algorithm and the dictionary constructed by the particle swarm algorithm, the reverberation covariance matrix and the optimal filtering weights are determined and the space-time data is filtered.

[0020] Preferably, the step 1 is specifically:

[0021] The received data is divided into frames according to the transmission pulse length T and sampled. It is regarded as a distance unit. The received data is arranged according to the distance unit. The N array elements have M snapshot samplings in one distance unit. After sampling all the distance unit data, a KM×N data block is obtained, where K is the number of distance units. Represents the mth time domain data corresponding to the nth array element and the kth distance unit in the data matrix, and represents the data in the kth distance unit as in m=0,…,M-1X k Rearrange by columns to obtain a NM×1 space-time sample, that is:

[0022]

[0023] Preferably, the step 2 is specifically:

[0024] Step 2-1: Construct a dictionary to divide the space-time plane evenly into N along the spatial frequency axis and the Doppler frequency axis s ×N d grids, where N s =ρ s ×N,N d =ρ d ×M,ρ s >1,ρ d >1, parameter ρ s and ρ d are the resolutions along the spatial frequency axis and the Doppler frequency axis respectively; the space-time steering vector corresponding to each grid Considered as one atom, there are N s ×N d atoms; represent the normalized Doppler frequency and the normalized spatial frequency, respectively;

[0025] The amplitude of the reverberation component at each grid point is represented by α, and the reverberation is expressed as:

[0026] n=Φα (2)

[0027] Where Φ is a dictionary consisting of space-time steering vectors corresponding to grid points, and its expression is:

[0028]

[0029] The vector α is a sparse coefficient vector, written as:

[0030]

[0031] Then the space-time sparse representation model of the space-time sample x is:

[0032]

[0033] Step 2-2: Perform sparse recovery on the space-time samples of the unit to be tested and the L candidate units on both sides of it to obtain the sparse coefficient vector α of the unit to be tested rut and the sparse coefficient vector α of the candidate unit l ,l=1,2,3,…2L;

[0034] Based on the constructed dictionary Φ, the sparse coefficient vector α is solved through the following constrained optimization problem:

[0035]

[0036] Among them, ||·||0 represents the number of non-zero elements in α, ||·||2 represents taking the l2 norm of the vector, and ζ is the noise tolerance threshold;

[0037] Step 2-3: Calculate the similarity ξ between the sparse coefficients of each candidate unit and the unit to be detected l :

[0038]

[0039] Thus, the sparse coefficient vector similarity matrix z = [ξ1, ξ2, ξ3, …, ξ 2L ] T , take the space-time samples of the L distance units with the largest similarity as auxiliary reverberation samples.

[0040] Preferably, the s =ρ d =4.

[0041] Preferably, the step 3 is specifically:

[0042] Step 3-1: Based on the selected auxiliary reverb sample x l , the reverberation covariance matrix is ​​calculated using maximum likelihood estimation

[0043]

[0044] Step 3-2: Initialize the parameters of the particle swarm algorithm and construct a fitness function that measures the correlation between space-time atoms and reverberation subspace.

[0045] First, generate M random initial particles Each particle represents a solution with a maximum number of iterations T and is updated in the qth iteration as follows:

[0046]

[0047] in, and w q Respectively represent the search step and inertia weight of the ith particle; c1 and c2 are acceleration coefficients; r1 and r2 are random values ​​that obey uniform distribution (0, 1); a=1 is the convergence factor constant; and They represent the individual optimal position of the i-th particle and the global optimal position of the particle swarm respectively;

[0048] Iterate until T times to obtain convergence ability. After the iteration, all particles will converge to This particle has the maximum fitness and is considered the optimal solution of maxf(p);

[0049] Construct the objective function as the fitness function of the particle swarm algorithm, and set the function variable p = [f d ,f s ], the function expression is:

[0050]

[0051] in, is the residual in the current external iteration t, the initial residual At this time, R e is the space-time atomic space {S k} 0<k<t The projection on the complementary space of λ is the atomic weight factor; the fitness function represents the orthogonal projection of the residual from the atom, and in each iteration, the atom that best matches the residual after the previous iteration can be found in the continuous space-time plane according to the maximum inner product criterion;

[0052] Each particle has two dimensions, namely the normalized Doppler frequency and the normalized spatial frequency. After optimization, it converges to s t is the steering vector, and its normalized Doppler frequency and normalized spatial frequency are and The number of iterations q is the number of internal iterations of the particle swarm algorithm search once, and the number of iterations t is the number of external iterations to collect the optimal space-time atoms;

[0053] Step 3-3: Prepare an empty collection during the initialization of external iteration Used to collect selected atoms; the corresponding initial noise subspace where I is the unit matrix; the atoms s selected in the first t external iterations t join in The update method is Ct is the decomposition coefficient c t A collection of is the pseudo-inverse operation of the matrix; when When the residual energy of is reduced to the set threshold, the external iteration ends;

[0054]

[0055] in, represents the residual energy of the reverberant space, is the noise energy, η represents the preset threshold; after the iteration, the space-time atomic set Φ is obtained γ ;

[0056] All auxiliary samples are processed using the method from step 3-1 to step 3-3, and the space-time atoms obtained by L auxiliary samples are merged to obtain the adaptive overcomplete space-time dictionary matrix Φ S .

[0057] Preferably, the step 4 is specifically:

[0058] Step 4-1: Initialize the sparse Bayes algorithm hyperparameter γ 0 , Input training sample set X = [x1 x2… x L ];

[0059] Step 4-2: Based on the constructed space-time dictionary, update the iterative posterior mean matrix μ and covariance matrix Σ;

[0060] Using the known k-th iteration Γ(k) and Calculate the posterior distribution of Γ for the (k+1)th iteration and obtain the posterior mean matrix for the (k+1)th iteration and the covariance matrix Σ (k+1) ;

[0061]

[0062] in

[0063] Step 4-3: Based on the updated mean matrix μ and covariance matrix Σ, update the iterative sparse coefficient matrix γ and noise parameters through the expectation maximization EM algorithm

[0064]

[0065]

[0066] When the j+1th iteration Satisfy || γ j+1 -γ j ||2 / ||γ j ||2≤δ, δ is a sufficiently small positive threshold, then it is determined that the convergence condition is met;

[0067] Step 4-4: Determine whether the convergence condition is met. If so, output the sparse coefficient matrix γ, otherwise continue iterative update;

[0068] The final estimated reverberation covariance matrix for:

[0069]

[0070] Diagonal loading After that, the reverberation covariance matrix R is obtained r .

[0071] Preferably, the step 5 is specifically:

[0072] Under the minimum variance distortionless response (MVDR) criterion, the following constrained optimization problem is constructed:

[0073]

[0074] Among them, s t represents the space-time steering vector of the target direction; solving equation (17) to obtain the optimal filtering weight is:

[0075]

[0076] The output of the space-time filter is y = w H X represents the output power of each space-time channel of each distance unit sample after weighted space-time filtering. The optimal space-time filtering minimizes the output energy of the reverberation while ensuring the target energy is output without distortion.

[0077] The beneficial effects of the present invention are as follows:

[0078] (1) The adaptive space-time dictionary constructed by the present invention is more consistent with the distribution of reverberation in the space-time plane under non-uniform heterogeneous environments than the traditional grid dictionary, and can improve the estimation accuracy of the reverberation covariance matrix;

[0079] (2) The adaptive space-time dictionary constructed by the present invention can use fewer space-time atoms to represent the reverberation subspace, which has a lower dimension than the traditional dictionary, reduces the amount of calculation for sparse recovery, and saves computing resources;

[0080] (3) Compared with the traditional SR-STAP algorithm, the algorithm proposed in this invention has obvious improvements in reverberation suppression effect and target detection performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 The figure is a flow chart of the method of the present invention.

[0082] Figure 2 This is a diagram of the geometric structure of the active sonar array and the scattering model of the reverberation unit according to an embodiment of the present invention.

[0083] Figure 3 Schematic diagram of the adaptive dictionary construction process of an embodiment of the present invention, wherein (a) is a schematic diagram of the selected L auxiliary reverberation samples, (b) is a schematic diagram of the covariance matrix estimated for each auxiliary reverberation sample, (c) is a space-time atomic distribution diagram of each covariance matrix obtained by searching the particle swarm algorithm, and (d) is a space-time atomic distribution diagram of the space-time dictionary obtained by combining various space-time atomic sets.

[0084] Figure 4 The reverberation power spectra estimated by the method of the present invention and the comparative algorithm, where (a) is the LSMI-STAP algorithm, (b) is the MSBL-STAP algorithm, (c) is the traditional SR-STAP algorithm, and (d) is the method of the present invention.

[0085] Figure 5 It is the improvement factor curve of the method of the present invention and the comparison algorithm.

[0086] Figure 6 Filter output power curves of the method of the present invention and the comparison algorithm. DETAILED DESCRIPTION

[0087] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0088] The basic idea of ​​the present invention is to apply the particle swarm optimization algorithm to accurately select reverberation atoms in a continuous space-time plane and construct a gridless adaptive space-time dictionary; then combine the sparse Bayesian learning algorithm to perform sparse decomposition of the sonar array observation data on the designed dictionary, thereby obtaining a high-precision reverberation covariance matrix estimate, eliminating grid mismatch errors, and improving reverberation suppression and target detection performance.

[0089] Simulation test parameter settings:

[0090] Active sonar array as attached Figure 2 The deployment depth is 40m. The sonar platform uses a 16-element uniform linear array with half-wavelength array, emits continuous waves, and the sampling frequency is 5 times the transmission frequency. The moving platform has a moving speed of 15m / s, the target moves away from the sonar platform at a radial speed of 1m / s, the azimuth angle is 30°, the signal-to-noise ratio is -5dB, and the mixing-noise ratio is 30dB. The reverberation data is obtained by simulation of the point scattering model.

[0091] The flow chart of the method of the present invention is shown in the attached Figure 1 The specific implementation method is as follows:

[0092] Step 1. Frame the received data according to the transmission pulse length T = 20ms and sample it. Treat it as a distance unit. The received data is arranged according to the distance unit. The N = 16 array elements have M = 24 snapshots in one distance unit. After sampling all the distance unit data, KM × N data blocks can be obtained, where K is the number of distance units. Represents the mth time domain data corresponding to the nth array element and the kth distance unit in the data matrix, and represents the data in the kth distance unit as in X k By rearranging the columns, we can get a NM×1 space-time sample, namely:

[0093]

[0094] Step 2. Select auxiliary reverberation samples for building the adaptive space-time dictionary.

[0095] (1) First, we need to construct a dictionary to divide the space-time plane evenly into N parts along the spatial frequency axis and the Doppler frequency axis. s ×N d grids, where N s =ρ s ×N,N d =ρ d ×M,ρ s >1,ρ d >1, parameter ρ s and ρ d are the resolutions along the spatial frequency axis and the Doppler frequency axis respectively, and ρ s =ρ d =4. The gridded redundant dictionary is an extended form of the space-time steering vector. The space-time steering vector corresponding to each grid is Considered as one atom, there are N s ×N d atoms.

[0096] The amplitude of the reverberation component at each grid point is represented by α, and the reverberation can be expressed as:

[0097] n=Φα (2)

[0098] Where Φ is a dictionary consisting of space-time steering vectors corresponding to grid points, and its expression is:

[0099]

[0100] The vector α is a sparse coefficient vector and can be written as:

[0101]

[0102] Then the space-time sparse representation model of the space-time sample x is:

[0103]

[0104] (2) Perform sparse recovery on the space-time samples of the unit to be detected and L = 10 candidate units on both sides of it, and obtain the sparse coefficient vector α of the unit to be detected rut and the sparse coefficient vector α of the candidate unit l ,l=1,2,3,…2L.

[0105] Based on the constructed traditional dictionary Φ, the sparse coefficient vector α can be solved by the following constrained optimization problem:

[0106]

[0107] Among them, ||·||0 represents the number of non-zero elements in α, ||·||2 represents taking the l2 norm of the vector, and ζ is the noise tolerance threshold.

[0108] (3) Calculate the similarity ξ between the sparse coefficients of each candidate unit and the unit to be detected l :

[0109]

[0110] Thus, the sparse coefficient vector similarity matrix z = [ξ1, ξ2, ξ3, …, ξ 2L ] T , take the space-time samples of the L distance units with the largest similarity as auxiliary reverberation samples.

[0111] Step 3. Based on the particle swarm algorithm, an adaptive space-time dictionary is constructed according to the selected auxiliary reverberation samples. The specific steps of the construction are as follows:

[0112] (1) Based on the selected auxiliary reverberation sample x l , using maximum likelihood estimation to calculate the reverberation covariance matrix

[0113]

[0114] (2) Initialize the parameters of the particle swarm algorithm and construct a fitness function that measures the correlation between space-time atoms and the reverberation subspace.

[0115] First, generate M random initial particles Each particle represents a solution with a maximum number of iterations T and is updated in the qth iteration as follows:

[0116]

[0117] in, and w q Respectively represent the search step and inertia weight of the i-th particle; c1=2 and c2=2 are acceleration coefficients; r1 and r2 are random values ​​that obey uniform distribution (0, 1); a=1 is the convergence factor constant; and They represent the individual optimal position of the i-th particle and the global optimal position of the particle group. Iterate until T times to obtain convergence ability. After the iteration, all particles will converge to This particle has the maximum fitness and is considered the optimal solution of maxf(p).

[0118] Construct the objective function as the fitness function of the particle swarm algorithm, and set the function variable p = [f d ,f s ], the function expression is:

[0119]

[0120] in, is the residual in the current external iteration t, the initial residual At this time, R e is the space-time atomic space {S k} 0<k<t The projection on the complementary space of λ is the atomic weight factor; the fitness function represents the orthogonal projection of the residual from the atom, and in each iteration, the atom that best matches the residual after the previous iteration can be found in the continuous space-time plane according to the maximum inner product criterion.

[0121] Each particle has two dimensions, namely the normalized Doppler frequency and the normalized spatial frequency. After optimization, it converges to s t is the steering vector, and its normalized Doppler frequency and normalized spatial frequency are and Note that the above iteration number q is the number of internal iterations of the particle swarm algorithm search once, and the iteration number t is the number of external iterations for collecting the optimal space-time atoms.

[0122] (3) During the initialization of external iteration, prepare an empty collection Used to collect selected atoms. The corresponding initial noise subspace where I is the identity matrix. The atoms s selected in the first t external iterations are t join in The update method is C t is the decomposition coefficient c t A collection of is the pseudo-inverse operation of the matrix. When the residual energy of is reduced to a suitable threshold, the external iteration ends;

[0123]

[0124] in, represents the residual energy of the reverberant space, is the noise energy, η represents the preset threshold. After the iteration, the space-time atomic set Φ is obtained. γ .

[0125] All auxiliary samples are processed through the above steps, and the space-time atoms obtained by L auxiliary samples are merged to obtain the adaptive overcomplete space-time dictionary matrix Φ S .

[0126] The entire dictionary construction process is shown in the attached Figure 3 As shown, Figure 3 (a) is the time domain reverberation of a single array element. After sampling it in frames and arranging it according to the array elements, the space-time samples are obtained. Figure 3 (b) The estimated covariance matrix of the auxiliary reverberation samples selected in step 2, Figure 3 (c) is the space-time atomic distribution diagram of each covariance matrix obtained by searching the particle swarm algorithm. Figure 3 (d) is the space-time atom distribution diagram of the adaptive overcomplete space-time dictionary obtained by combining various space-time atom sets.

[0127] Step 4. Use the sparse Bayesian algorithm based on the space-time dictionary Φ constructed in step 3 S Reconstruct the auxiliary reverberation sample X and estimate the reverberation covariance matrix. The specific steps are as follows:

[0128] (1) Initialize the sparse Bayesian algorithm hyperparameter γ 0 =1, Input training sample set X = [x1x2…x L ].

[0129] (2) Based on the constructed space-time dictionary, update the iterative posterior mean matrix μ and covariance matrix Σ.

[0130] Using the known k-th iteration Γ(k) and Calculate the posterior distribution of Γ for the (k+1)th iteration and obtain the posterior mean matrix for the (k+1)th iteration and the covariance matrix Σ (k+1) .

[0131]

[0132] in

[0133] (3) Based on the updated mean matrix μ and covariance matrix Σ, the sparse coefficient matrix γ and noise parameters are updated through the expectation maximization (EM) algorithm.

[0134]

[0135]

[0136] When the k+1th iteration Satisfy || γ k+1 -γ k ||2 / ||γ k ||2≤δ, δ is a sufficiently small positive threshold, then the convergence condition is considered to be met.

[0137] (4) Determine whether the convergence condition is met. If so, output the sparse coefficient matrix γ; otherwise, continue iterative updating.

[0138] The final estimated reverberation covariance matrix for

[0139]

[0140] Diagonal loading After that, the reverberation covariance matrix R is obtained r .

[0141] Step 5: Based on the dictionary constructed by the particle swarm algorithm and the iterative results of the sparse Bayesian algorithm, the reverberation covariance matrix and the optimal filter weight are estimated, and the reverberation energy is minimized after filtering. The reverberation output power obtained after STAP processing of the space-time samples of each distance unit can be used as a test statistic.

[0142] Under the minimum variance distortionless response (MVDR) criterion, the following constrained optimization problem is constructed:

[0143]

[0144] Among them, s t Represents the space-time steering vector of the target direction. Solving the above problem, the optimal filter weight is

[0145]

[0146] The output of the space-time filter is y = w HX represents the output power of each space-time channel of each distance unit sample after weighted space-time filtering. The optimal space-time filtering can minimize the output energy of the reverberation while ensuring the target energy is output without distortion.

[0147] Example:

[0148] The embodiment of the present application performs a simulation experiment according to the above steps to evaluate the performance of the reverberation suppression method based on the adaptive gridless dictionary of the embodiment of the present application. In the simulation experiment, the algorithm proposed by the present invention is compared with the LSMI-STAP algorithm, the traditional SR-STAP algorithm and the MSBL-STAP algorithm.

[0149] The first experiment gives the estimated reverberation power spectrum of the algorithm proposed by the present invention and the comparison algorithm, and compares the estimation accuracy of the reverberation covariance matrix of each algorithm. The expression of the reverberation power spectrum is P = 1 / (S H R -1 S), where S is the steering vector and R is the estimated reverberation covariance matrix. Figure 4 In (a), the reverberation power spectrum formed by the LSMI-STAP algorithm is distributed on the reverberation ridge, but due to insufficient samples, the estimated reverberation energy is low, which is not conducive to subsequent reverberation suppression. Figure 4 As can be seen in (b), due to the off-grid effect, the reverberation power spectrum of the MSBL-STAP algorithm is severely broadened, and the target will be submerged by the reverberation. Figure 4 In (c), the reverberation power spectrum formed by the SR-STAP algorithm is distributed on the reverberation ridge, but it is not concentrated and has a certain degree of broadening, so the effect of suppressing reverberation is not good. Figure 4 In (d), the reverberation energy estimated by the algorithm proposed in the present invention is concentrated on the reverberation ridge. Compared with the MSBL-STAP and SR-STAP algorithms, the reverberation ridge has no obvious expansion, the reverberation power value is higher, and the reverberation suppression performance is better.

[0150] The second experiment compares the reverberation suppression performance of the proposed algorithm with that of the comparative algorithm. The expression of signal-to-mixture ratio loss is

[0151]

[0152] Where w represents the estimated space-time filter weight vector; R represents the reverberation plus noise covariance matrix; is the noise power; S t is the space-time steering vector of the target.

[0153] Attached Figure 5 SRNR of the algorithm proposed by the present invention and the comparison algorithm lossThe relationship between the LSMI-STAP algorithm and the normalized Doppler frequency. It can be seen that due to the insufficient number of samples used, the depth of the concave of the LSMI-STAP algorithm curve is shallow, and the suppression ability of the main reverberation area is insufficient. The traditional SR-STAP algorithm curve has a wide notch in the main reverberation area, which is easy to suppress the target energy at the same time. Compared with the SR-STAP and MSBL-STAP algorithms, the algorithm proposed in the present invention has the deepest concave in the main reverberation area, the narrowest notch, and the best reverberation suppression performance.

[0154] The third experiment compares the moving target detection performance of the proposed algorithm and the comparative algorithm. In the experiment, samples of 50 range cells are filtered, and the target is located in the 25th range cell. The experimental results obtained after calculating the output power are shown in the attached figure. Figure 6 As shown. It can be seen that all four algorithms can detect the target in the 25th distance unit. Among them, the target output power of the traditional SR-STAP algorithm and LSMI-STAP algorithm differs from the maximum reverberation output power by less than 5dB, and the target detection performance is poor. In comparison, the average output power of the algorithm proposed in the invention is lower than that of other algorithms outside the target distance unit, and the detection threshold is designed to be lower, which has better moving target detection capability.

[0155] In summary, the present invention proposes a novel sparse space-time dictionary construction method, which can accurately search for reverberation-related space-time atoms in a continuous space-time plane and construct a gridless sparse dictionary. Based on this, a sparse space-time adaptive processing method is designed to solve the problem of decreased reverberation suppression ability of the SR-STAP algorithm caused by traditional dictionary grid mismatch, so that this method has better reverberation suppression ability and target detection ability than the traditional SR-STAP algorithm.

Claims

1. A reverberation suppression method based on an adaptive gridless dictionary, characterized in that: The steps include: Step 1: Transmit a signal, divide the received data into frames according to the length of the transmitted pulse and perform sampling, and construct NM×1-dimensional data samples required for space-time adaptive processing based on the sampled data; the data samples include: samples to be detected and auxiliary samples; wherein the samples to be detected refer to data obtained from the distance unit RUT of the data to be detected, and the auxiliary samples refer to data obtained from the distance unit adjacent to the data to be detected, N is the spatial dimension, and M is the time dimension; Step 2: Select the auxiliary reverberation samples for constructing the adaptive space-time dictionary. The specific steps of the selection are as follows: (1) Based on the principle of sparse recovery technology, a traditional grid dictionary is constructed; (2) performing sparse recovery on the unit to be detected and the L adjacent candidate units on both sides thereof, respectively, to obtain the sparse coefficient vector of the unit to be detected and the sparse coefficient vector of the candidate units; (3) Calculate the similarity of the sparse coefficients of each candidate unit and the unit to be detected, and take the reverberation samples of the L distance units with the largest similarity as auxiliary reverberation samples; Step 3: Use the particle swarm algorithm combined with the selected auxiliary reverberation samples to construct an adaptive space-time dictionary. The specific steps of the construction are as follows: (1) constructing a reverberation covariance matrix based on the selected auxiliary reverberation samples; (2) Initialize the parameters of the particle swarm algorithm and establish a fitness function model to measure the correlation between space-time atoms and reverberation subspace; (3) The optimal reverberation space-time atoms searched during the particle swarm algorithm iteration are placed into the space-time steering vector set as the adaptive space-time dictionary for subsequent sparse recovery; Step 4: Use the sparse Bayesian algorithm to reconstruct the reverberation samples based on the constructed space-time dictionary and estimate the reverberation covariance matrix. The specific steps are as follows: (1) Based on the constructed space-time dictionary, update the iterative mean matrix μ and covariance matrix Σ; (2) Based on the updated mean matrix μ and covariance matrix Σ, update the iterative sparse coefficient matrix γ and noise parameters (3) Determine whether the iteration stop condition is met. If so, output the sparse coefficient matrix γ. If not, continue iterative update. Step 5: Based on the output of the sparse Bayesian algorithm and the dictionary constructed by the particle swarm algorithm, the reverberation covariance matrix and the optimal filtering weights are determined and the space-time data is filtered.

2. The reverberation suppression method based on an adaptive gridless dictionary according to claim 1, characterized in that: The step 1 is specifically as follows: The received data is divided into frames according to the transmission pulse length T and sampled. It is regarded as a distance unit. The received data is arranged according to the distance unit. The N array elements have M snapshot samplings in one distance unit. After sampling all the distance unit data, a KM×N data block is obtained, where K is the number of distance units. Represents the mth time domain data corresponding to the nth array element and the kth distance unit in the data matrix, and represents the data in the kth distance unit as in m=0,…,M-1X k Rearrange by columns to obtain a NM×1 space-time sample, that is:

3. The reverberation suppression method based on an adaptive gridless dictionary according to claim 2, characterized in that: The step 2 is specifically as follows: Step 2-1: Construct a dictionary to divide the space-time plane evenly into N along the spatial frequency axis and the Doppler frequency axis s ×N d grids, where N s =ρ s ×N,N d =ρ d ×M,ρ s >1,ρ d >1, parameter ρ s and ρ d are the resolutions along the spatial frequency axis and the Doppler frequency axis respectively; the space-time steering vector corresponding to each grid Considered as one atom, there are N s ×N d atoms; represent the normalized Doppler frequency and the normalized spatial frequency, respectively; The amplitude of the reverberation component at each grid point is represented by α, and the reverberation is expressed as: n=Φα (2) Where Φ is a dictionary consisting of space-time steering vectors corresponding to grid points, and its expression is: The vector α is a sparse coefficient vector, written as: Then the space-time sparse representation model of the space-time sample x is: Step 2-2: Perform sparse recovery on the space-time samples of the unit to be tested and the L candidate units on both sides of it to obtain the sparse coefficient vector α of the unit to be tested rut and the sparse coefficient vector α of the candidate unit l ,l=1,2,3,…2L; Based on the constructed dictionary Φ, the sparse coefficient vector α is solved through the following constrained optimization problem: Among them, ||·||0 represents the number of non-zero elements in α, ||·||2 represents taking the l2 norm of the vector, and ζ is the noise tolerance threshold; Step 2-3: Calculate the similarity ξ between the sparse coefficients of each candidate unit and the unit to be detected l : Thus, the sparse coefficient vector similarity matrix z = [ξ1, ξ2, ξ3, …, ξ 2L ] T , take the space-time samples of the L distance units with the largest similarity as auxiliary reverberation samples.

4. The reverberation suppression method based on an adaptive gridless dictionary according to claim 3, characterized in that: The s =ρ d =4.

5. The reverberation suppression method based on an adaptive gridless dictionary according to claim 3, characterized in that: The step 3 is specifically as follows: Step 3-1: Based on the selected auxiliary reverb sample x l , the reverberation covariance matrix is ​​calculated using maximum likelihood estimation Step 3-2: Initialize the parameters of the particle swarm algorithm and construct a fitness function to measure the correlation between space-time atoms and reverberation subspace; First, generate M random initial particles Each particle represents a solution with a maximum number of iterations T and is updated in the qth iteration as follows: in, and w q Respectively represent the search step and inertia weight of the ith particle; c1 and c2 are acceleration coefficients; r1 and r2 are random values ​​that obey uniform distribution (0, 1); a=1 is the convergence factor constant; and They represent the individual optimal position of the i-th particle and the global optimal position of the particle swarm respectively; Until iterates T times to obtain convergence ability, after the iteration, all particles will converge to This particle has the maximum fitness and is considered the optimal solution of maxf(p); Construct the objective function as the fitness function of the particle swarm algorithm, and set the function variable p = [f d ,f s ], the function expression is: in, is the residual in the current external iteration t, the initial residual At this time, R e is the space-time atomic space {S k } 0<k<t The projection on the complementary space of λ is the atomic weight factor; the fitness function represents the orthogonal projection of the residual from the atom, and in each iteration, the atom that best matches the residual after the previous iteration can be found in the continuous space-time plane according to the maximum inner product criterion; Each particle has two dimensions, namely the normalized Doppler frequency and the normalized spatial frequency. After optimization, it converges to s t is the steering vector, and its normalized Doppler frequency and normalized spatial frequency are and The number of iterations q is the number of internal iterations of the particle swarm algorithm search once, and the number of iterations t is the number of external iterations to collect the optimal space-time atoms; Step 3-3: Prepare an empty collection during the initialization of external iteration Used to collect selected atoms; the corresponding initial noise subspace where I is the unit matrix; the atoms s selected in the first t external iterations t join in The update method is C t is the decomposition coefficient c t A collection of is the pseudo-inverse operation of the matrix; when When the residual energy of is reduced to the set threshold, the external iteration ends; in, represents the residual energy of the reverberant space, is the noise energy, η represents the preset threshold; after the iteration, the space-time atomic set Φ is obtained γ ; All auxiliary samples are processed using the method from step 3-1 to step 3-3, and the space-time atoms obtained by L auxiliary samples are merged to obtain the adaptive overcomplete space-time dictionary matrix Φ S .

6. The reverberation suppression method based on an adaptive gridless dictionary according to claim 5, characterized in that: The step 4 is specifically as follows: Step 4-1: Initialize the sparse Bayes algorithm hyperparameter γ 0 , Input training sample set X = [x1 x2…x L ]; Step 4-2: Based on the constructed space-time dictionary, update the iterative posterior mean matrix μ and covariance matrix Σ; Using the known k-th iteration Γ(k) and Calculate the posterior distribution of Γ for the (k+1)th iteration and obtain the posterior mean matrix for the (k+1)th iteration and the covariance matrix Σ (k+1) ; in Step 4-3: Based on the updated mean matrix μ and covariance matrix Σ, update the iterative sparse coefficient matrix γ and noise parameters through the expectation maximization EM algorithm When the j+1th iteration Satisfy || γ j+1 -γ j ||2 / ||γ j ||2≤δ, δ is a sufficiently small positive threshold, then it is determined that the convergence condition is met; Step 4-4: Determine whether the convergence condition is met. If so, output the sparse coefficient matrix γ, otherwise continue iterative update; The final estimated reverberation covariance matrix for: Diagonal loading After that, the reverberation covariance matrix R is obtained r .

7. The reverberation suppression method based on an adaptive gridless dictionary according to claim 6, characterized in that: The step 5 is specifically as follows: Under the minimum variance distortionless response (MVDR) criterion, the following constrained optimization problem is constructed: Among them, s t represents the space-time steering vector of the target direction; solving equation (17) to obtain the optimal filtering weight is: The output of the space-time filter is y = w H X represents the output power of each space-time channel of each distance unit sample after weighted space-time filtering. The optimal space-time filtering minimizes the output energy of the reverberation while ensuring the target energy is output without distortion.

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