A method and device for low-speed target detection in reverberation background based on weighted sparse recovery

Abstract

The present invention belongs to the field of target detection technology, and in particular, relates to a method and device for detecting low-speed targets under a reverberation background based on weighted sparse recovery. For use in active sonar systems, the method includes: constructing an observation signal model under a reverberation background; estimating a weight vector for the spatial-temporal data of a detection distance unit using a sparse STAP method; constructing a norm-based sparse weighted optimization problem; iteratively solving the sparse weighted optimization problem by using a conjugate gradient method and an improved Newton method to obtain an optimal solution that satisfies the iteration termination condition, thereby determining the target angle, speed, and position estimation values ​​to achieve target detection. The present invention suppresses reverberation and enhances the target in solving the optimization problem, and can achieve low-speed target detection under conditions of strong reverberation and noise.

Description

Technical Field

[0001] The present invention belongs to the technical field of target detection, and in particular relates to a method and a device for detecting a low-speed target in a reverberation background based on weighted sparse recovery. Background Art

[0002] Active sonar transmits sound wave signals into the water. After the receiving array receives the echo signal formed by the superposition of the target's reflected sound waves, it analyzes whether the echo signal contains the target of interest to achieve the purpose of target detection. However, in addition to the echo reflected by the target, the echo signal is also mixed with reverberation signals. Especially in shallow water sonar detection, the sonar-transmitted sound waves are affected by the water surface, the bottom of the water, the mountain and other irregular scatterers, and the superposition of scattered echoes forms a reverberation signal. When the sonar carrier is in motion, the reverberation in different directions has different Doppler frequency shifts, which causes the power spectrum of the reverberation to be greatly broadened in the two-dimensional space-time plane. Non-cooperative moving targets, especially slow-moving targets, will be submerged by the reverberation with severe spectrum diffusion. The problem of reverberation suppression and target detection has become a daunting challenge in the field of underwater target detection.

[0003] Space time adaptive processing (STAP) technology is a joint filtering method that combines space and time domains, which can effectively suppress reverberation. With the continuous development of compressed sensing (CS) / sparse recovery theory, scholars have realized that the space-time coupled reverberation of the moving platform also has sparse characteristics in the space-time two-dimensional plane. Based on this characteristic, the covariance matrix can be reconstructed under very few samples. Therefore, a series of STAP methods based on sparse recovery are proposed to achieve high-resolution estimation of reverberation in the space-time domain. The relevant simulation and measured data processing results also show that the combination of this technology and STAP has great advantages. Among them, the zero-value weighted method based on sparse recovery performs zero-weighted optimization processing on the reverberation area to filter out the reverberation, and only uses test units instead of training data, thus avoiding the problem of large errors in the estimation of the reverberation covariance matrix caused by non-stationarity in the training data process.

[0004] In the sparse zero-weighted STAP method, it is usually assumed that the moving target can be well separated from the reverberation in the space-time spectrum, but the severe broadening of the reverberation space-time spectrum makes this assumption invalid. The low-speed target and the extended reverberation spectrum merge, which brings great challenges to the detection of low-speed targets. Therefore, it is impossible to directly apply the existing reverberation suppression method to the detection of low-speed targets in complex underwater environments. Summary of the invention

[0005] The purpose of the present invention is to overcome the defects of the prior art and propose a method and device for detecting low-speed targets in a reverberation background based on weighted sparse recovery.

[0006] In order to achieve the above object, the present invention proposes a low-speed target detection method in a reverberation background based on sparse weighting, which is used in an active sonar system. The method comprises:

[0007] Construct a model of the observed signal in a reverberant background;

[0008] The sparse STAP method is used to estimate the weight vector of the spatial-temporal data of the detection range unit;

[0009] Formulate norm-based sparse weighted optimization problems;

[0010] Iterative solution, through the conjugate gradient method and improved Newton method to solve the sparse weighted optimization problem, to obtain the optimal solution that meets the iteration termination conditions, and then determine the target angle, speed and position estimation value to achieve target detection.

[0011] Preferably, the active sonar system is an N-element uniform linear array distributed along the x-axis, with an element spacing of d=λ / 2, where λ is the signal wavelength, λ=c / f c , c and f c are the speed of sound and the carrier frequency respectively. Taking the array element at the origin as the reference point, K pulses are emitted, the pulse repetition period is T, and the kth pulse signal s k (t) is:

[0012] s k (t) = a(k)exp(j2πf c t)p(t)

[0013] Where a(k) is the amplitude of the kth pulse signal and p(t) is the waveform.

[0014] Preferably, the observation signal model under the reverberation background takes into account the influence of reverberation and noise, and the array received signal y is:

[0015] y=y tar +y rev +n

[0016] Among them, y tar is the target echo signal, y rev is the reverberation signal, n is the additive Gaussian white noise, with zero mean and variance σ 2 .

[0017] Preferably, the process of establishing the observation signal model under the reverberation background includes:

[0018] The angle-Doppler grid in the observation area is divided into M×K grids, where the discrete angle set is represented by θ = [θ0, θ1..., θ M-1 ], the discrete Doppler set is denoted as f d =[f d,0,f d,1 ,...,f d,K-1 ],

[0019] In the space-time spectrum, the d )'s target echo signal y tar for:

[0020] y tar =Ua tar

[0021] In the formula, space-time spectrum in Space-time Steering Vector for: m, k represent the row and column numbers of the grid, j represents the imaginary part, R and θ m represents the distance of the far-field point target and the angle of the mth grid row, a(k,R,θ m ) is the target reflection coefficient;

[0022] represents the spatial steering vector; u(θ)=[u(θ0),...,u(θ m ),...,u(θ M-1 )], represents the time domain steering vector, expressed as u(f d )=[u(f d,0 ),...,u(f d,k ),...,u(f d,K-1 )] T ,

[0023] u(f d,k )={exp(-j2πf d,k 0T),exp(-j2πf d,k 1T),...,exp(-j2πf d,k (K-1)T)}; [·] T represents the transpose of the vector; T represents the pulse repetition period;

[0024] The reverberation is modeled as the superposition of echoes from Q independent scatterers:

[0025]

[0026] Where q represents the number of independent scatterers, θ q represents the qth angle, represents the Kronecker product.

[0027] Preferably, the weight vector W is:

[0028] W=R revU -1

[0029] Where U represents the space-time steering vector [·] -1 Represents the inverse of the matrix, R rev =y rev y rev H , [·] H Represents the conjugate transpose of a vector.

[0030] Preferably, the norm-based sparse weighted optimization problem is:

[0031]

[0032]

[0033] In the formula, is the target space-time spectrum to be estimated, J(α) is the objective function, α is the space-time spectrum vector, (Wα) i represents the i-th element of the vector Wα, τ is a small positive number, ρ = 2σ 2 γ represents the regularization coefficient, which is the scale coefficient of the Laplace density function with respect to Wα.

[0034] Preferably, the iterative solution solves the sparse weighted optimization problem by using the conjugate gradient method and the improved Newton method to obtain the optimal solution that satisfies the iteration termination condition, and then determines the target angle, speed and position estimation value to achieve target detection, including:

[0035] Step 1) Let β be the iteration step value, traverse the set L iterations, and repeat the following steps:

[0036] Step 2) Solve the weight vector W using the sparse STAP method;

[0037] Step 3) The improved low-complexity algorithm based on Newton's method is used to solve the sparse weighted optimization problem. The conjugate method is used to solve the optimal solution α of the lth iteration through the following formula: l :

[0038]

[0039] Step 4) Update the Hessian matrix required for the l+1th iteration according to the following formula:

[0040]

[0041] Where diag[·] represents a diagonal matrix with vectors as diagonal elements,

[0042] Step 5) Determine whether the following iteration termination conditions are met, if yes, go to step 6); otherwise, go to step 2);

[0043]

[0044] In the formula, δ is the termination limit, α l-1 is the optimal solution of the l-1th iteration; ||·||2 represents the bi-norm;

[0045] Step 6) The optimal solution α l Convert to matrix form Determine target angle, velocity, and position estimates.

[0046] On the other hand, the present invention provides a low-speed target detection device in a reverberation background based on sparse weighting, which is used in an active sonar system, and the device comprises:

[0047] A model building module, used to build a model of the observed signal under the reverberation background;

[0048] A weight vector estimation module, used for estimating a weight vector for the spatial-temporal data of the detection range unit using a sparse STAP method;

[0049] The optimization building block for constructing norm-based sparse weighted optimization problems; and

[0050] The target detection module is used for iterative solution. It solves the sparse weighted optimization problem through the conjugate gradient method and the improved Newton method to obtain the optimal solution that meets the iteration termination conditions, and then determines the target angle, speed and position estimation value to achieve target detection.

[0051] Compared with the prior art, the advantages of the present invention are:

[0052] The low-speed target detection method under reverberation background based on weighted sparse recovery proposed in the present invention utilizes two-dimensional coupling information of spatial dimension and Doppler dimension to improve the target parameter estimation accuracy and reverberation suppression performance, and only uses the sparse weighted optimization problem to be designed using the distance data to be detected. Compared with the zero-weighted method, the present invention suppresses reverberation and enhances the target in solving the optimization problem, and can realize low-speed target detection under conditions of strong reverberation and noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a flow chart of the low-speed target detection method under reverberation background based on sparse weighting of the present invention;

[0054] Figure 2 is a comparison of space-time spectrum results under the condition of SNR = 0dB, where Figure 2(a) is the space-time spectrum of traditional beamforming, Figure 2(b) is the space-time spectrum of zero-value weighted processing, and Figure 2(c) is the space-time spectrum of sparse weighted processing;

[0055] FIG3 is a normalized target Doppler dimension and angle dimension cross-sectional diagram, wherein FIG3(a) is a normalized Doppler dimension cross-sectional diagram, and FIG3(b) is a normalized angle dimension cross-sectional diagram;

[0056] FIG4 is a comparison of space-time spectrum results under the condition of SNR = -20dB, where FIG4(a) is the space-time spectrum of traditional beamforming, FIG4(b) is the space-time spectrum of zero-value weighted processing, and FIG4(c) is the space-time spectrum of sparse weighted processing;

[0057] FIG. 5 is a normalized target Doppler dimension and angle dimension cross-sectional diagram, wherein FIG. 5( a ) is a normalized Doppler dimension cross-sectional diagram, and FIG. 5( b ) is a normalized angle dimension cross-sectional diagram. DETAILED DESCRIPTION

[0058] The present invention proposes a method for detecting low-speed targets under reverberation background based on sparse weighting. First, an observation signal model under reverberation background is constructed; then, the sparse STAP method is used to estimate the weight vector of the spatial-temporal data of the detection distance unit, and a sparse weighted optimization problem based on the norm is constructed; finally, a low-complexity optimization solution algorithm is derived, and the fast convergence of the algorithm is achieved through the conjugate gradient method and the improved Newton method. The proposed method realizes target enhancement and reverberation suppression through weighted sparse optimization, and the low-complexity solution method greatly improves the computational efficiency, thereby realizing low-speed target detection and high-resolution parameter estimation under reverberation background.

[0059] Principle description:

[0060] Assume that the sonar system is an N-element uniform linear array distributed along the x-axis with an element spacing of d = λ / 2, where λ = c / f c is the signal wavelength, c and f c Represents the speed of sound and carrier frequency. The array element at the origin is used as the reference point, K pulses are emitted, the pulse repetition period is T, and the kth pulse signal is:

[0061] s k (t) = a(k)exp(j2πf c t)p(t), (1)

[0062] Where a(k) is the amplitude of the k-th pulse signal and p(t) is the waveform. The k-th pulse echo received by the n-th array element can be expressed as:

[0063] y n,k (t|R,θ,f d )=a(k,R,θ)exp[j2πf c (t-τ n,k )]p(t-τ n,k ), (2)

[0064] Where R and θ represent the distance and angle of the far-field point target, a(k,R,θ) is the target reflection coefficient, and τ n,k is the time delay of the kth pulse received by the nth receiving element, which can be expressed as:

[0065]

[0066] Where v is the relative velocity between the platform and the target. Assuming a narrowband signal is transmitted, then The received signal can be expressed as:

[0067]

[0068] In the formula, f d =2v / λ is the Doppler frequency shift. After the echo signal is demodulated and matched filtered, the kth pulse signal of the nth receiving element becomes:

[0069]

[0070] Where psf(t)=IDFT[|p(f)| 2 ], psf(·) is the point spread function, IDFT[.] stands for inverse Fourier transform, and p(f) is the frequency spectrum of the baseband waveform p(t).

[0071] Divide the angle-Doppler in the observation area into M×K grids. The discrete angle set can be expressed as θ = [θ0, θ1..., θ M-1 ], the discrete Doppler set can be expressed as f d =[f d,0 ,f d,1 ,...,f d,K-1 ].

[0072] In the space-time spectrum, the d ) can be expressed as:

[0073] y tar =Ua tar , (6)

[0074] In the formula, the echo signal Space-time spectrum in Space-time Steering Vector for:

[0075]

[0076] In the formula, represents the spatial steering vector, which can be expressed as:

[0077] u(θ)=[u(θ0),...,u(θ m),...,u(θ M-1 )], (8)

[0078] In the formula, u(θ m ) can be expressed as:

[0079]

[0080] In the formula, [·] T represents the transpose of a vector, represents the time domain steering vector and can be expressed as:

[0081] u(f d )=[u(f d,0 ),...,u(f d,k ),...,u(f d,K-1 )] T , (10)

[0082] In the formula, u(f d,k )for:

[0083] u(f d,k )={exp(-j2πf d,k 0T),exp(-j2πf d,k 1T),...,exp(-j2πf d,k (K-1)T)},(11)

[0084] In active sonar systems, in addition to the target echo signal, there are also a large number of reverberation signals and background noise in the received signal, which seriously affects the sonar detection performance. Reverberation is generated when the transmitted signal is reflected and superimposed by a large number of irregular scatterers. After a large number of irregular scatterers are superimposed at the array receiving end, the reverberation component in the received signal is formed. Since the size, number, position and other factors of the scatterers in the water are uncertain, the reverberation is generally modeled as the superposition of the echoes of Q independent scatterers, which can be expressed as:

[0085]

[0086] In the formula, represents the Kronecker product. The noise n is additive Gaussian white noise with zero mean and variance σ 2 , the noise signal is uncorrelated with the echo signal, and the array elements are independent of each other. Considering the influence of reverberation and noise, the array receiving signal can be expressed as:

[0087] y=y tar +y rev +n=Ua tar +Ua rev +n=Ua+n, (13)

[0088] Since the number of array elements is usually much smaller than the number of grids divided by angles, that is, N<<M, the dimension of the measurement matrix y is smaller than the dimension of the matrix to be restored, that is, MK<HK. Therefore, recovering a from y is an ill-posed problem. Compressed sensing theory provides a method to recover high-dimensional sparse signals from low-dimensional measurement matrices. In sonar observation scenarios, the number of targets is much smaller than the number of grids divided by the space-time plane, and a has strong sparsity. High-resolution space-time spectrum can be obtained by the following l0 norm optimization:

[0089] min||α||0,st||y-Uα||2≤ε, (14)

[0090] The received signal contains reverberation signals, which appear as frequency domain interference. Its spectrum broadening will drown out the target, especially the low-speed target. In the case of strong reverberation, target signal detection becomes extremely challenging, especially when the radial relative speed of the target is low. The target signal and the reverberation signal are overlapped in the space-time spectrum, making it difficult to detect the low-speed target in the strong reverberation background. The traditional STAP reverberation suppression method requires a large number of unit samples to be detected, and the spatiotemporal changes of the underwater environment may lead to inaccurate prior knowledge, making it difficult for the existing reverberation suppression method to be applied in practice.

[0091] In order to suppress reverberation and noise, this paper proposes a low-speed target detection algorithm under reverberation background based on compressed sensing. The low-speed target detection under reverberation background is realized by using the unit data to be detected through weighted sparse optimization target enhancement and reverberation suppression method. In the distance unit to be detected, the space-time spectrum of the target can be obtained by the following weighted l0 norm optimization:

[0092] min||Wα||0,st||y-Uα||2≤ε. (15)

[0093] Since the reverberation is located in the Doppler frequency range near the relative velocity of zero, the data in this frequency range are selected as reverberation samples, and the reverberation space-time spectrum is solved by the sparse STAP method.

[0094] min||α rev ||0,st||y rev -Uα rev ||2≤ε. (16)

[0095] Its covariance matrix can be estimated as:

[0096] R rev =y rev y rev H =Gα rev α rev H G H , (17)

[0097] In the formula, [·] H represents the conjugate transpose of the vector. The weight vector in equation (15) can be obtained by the following equation:

[0098] W=R rev G -1 , (18)

[0099] In the formula, [·] -1 Represents the inverse of a matrix.

[0100] In practical applications, the estimation accuracy of the reverberation space-time spectrum has a great influence on the reverberation suppression performance. After estimating the weight vector using the sparse STAP method mentioned above, it is necessary to synchronously correct the reverberation spectrum estimation error in the subsequent optimization algorithm.

[0101] The l0-norm optimization problem in formula (15) is equivalent to the following weighted l1-norm optimization problem:

[0102]

[0103] where ρ = 2σ 2 γ represents the regularization coefficient, which is the scale coefficient of the Laplace density function with respect to Wα and can be expressed as

[0104]

[0105] The regularization coefficient ρ constrains the target estimation error term and target sparsity. If ρ is set too large, weak targets will be suppressed when reconstructing the target space-time spectrum, and only strong targets will be retained. If it is too small, noise and reverberation will remain in the space-time spectrum, resulting in false targets.

[0106] The weighted l1-norm optimization problem in equation (19) can be solved using a variety of optimization algorithms. Usually, it is necessary to call interior point solvers such as CVX and SEDUMI, which is not conducive to practical applications. In order to reduce the computational complexity and real-time performance of the algorithm, this paper proposes a low-complexity solution algorithm to solve the weighted l1-norm optimization problem in equation (19). In order to overcome the non-differentiability of the cost function at zero, we use the following smooth approximation

[0107]

[0108] Where, (Wα) i represents the i-th element of the vector Wα, τ is a small positive number. To reduce the impact of τ on the estimation result, it is usually taken as one thousandth of the noise variance. The optimization problem is transformed into:

[0109]

[0110] Derivation of the objective function J(α) with respect to the complex number α yields:

[0111]

[0112] In the formula, H(α) can be approximately regarded as the coefficient matrix of α, so H(α) can be approximately regarded as the Hessian matrix of the cost function, which can be expressed as:

[0113]

[0114] In the formula, diag[·] represents a diagonal matrix with vectors as diagonal elements. Newton's method or quasi-Newton's method will have convergence problems when solving non-quadratic optimization functions. At the same time, the cost function contains the weight vector W and the modulus of α, which increases the difficulty of solving. This paper derives an improved low-complexity algorithm based on Newton's method to solve the above optimization problem. From Newton's method, it can be seen that the lth iteration can be solved by the following formula:

[0115]

[0116] In the formula, β is the iteration step value. Substituting the conjugate gradient formula into the iteration formula, we can get

[0117] H(α l-1 )α l =(1-β)H(α l )α l +2βU H y. (26)

[0118] The revised formula of the Hessian matrix in the iteration is:

[0119]

[0120] Let β = 1, then the lth iteration can be solved by the following formula:

[0121]

[0122] From the above formula, we can know that solving the lth iteration α l The main point is that the Hessian matrix H(α l-1 ) is inverse, since H(α l-1 ) dimension is MK×MK, and the complexity of traditional matrix inversion operation is O(MK) 3 , the solution method requires multiple iterations, and the amount of calculation is very large. In order to avoid the problem of excessive amount of calculation caused by the inversion of the Hessian matrix, the conjugate gradient method is used to solve (28), thereby avoiding matrix operations and improving the solution rate. When the following iteration termination conditions are met, the iteration terminates and the estimated value is obtained

[0123]

[0124] In the above iterations, we obtain the target high-resolution space-time spectrum through sparse recovery, and at the same time, we achieve target enhancement and reverberation suppression through weighting in each iteration. After obtaining the estimate, we convert the vector Convert to matrix form matrix The non-zero coefficients in correspond to the coordinates in the space-time spectrum The target location. and The target's angle and velocity estimates are calculated, and the target position can be obtained by solving:

[0125]

[0126] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0127] Example 1

[0128] Embodiment 1 of the present invention proposes a method for detecting low-speed targets in a reverberation background based on weighted sparse recovery, comprising:

[0129] Construct a model of the observed signal in a reverberant background;

[0130] The weight vector is estimated by using the sparse STAP method to estimate the spatial-temporal data of the detection range unit;

[0131] Formulate norm-based sparse weighted optimization problems;

[0132] Iterative solution, through the conjugate gradient method and improved Newton method to solve the sparse weighted optimization problem, to obtain the optimal solution that meets the iteration termination conditions, and then determine the target angle, speed and position estimation value to achieve target detection.

[0133] The relevant algorithms for iterative solution are shown in Table 1.

[0134] Table 1 Flow chart of low-speed target detection under reverberation background based on weighted sparse recovery

[0135]

[0136] Example 2

[0137] Embodiment 2 of the present invention provides a low-speed target detection device in a reverberation background based on sparse weighting, which is implemented based on the method of embodiment 1 and is used in an active sonar system. The device includes:

[0138] A model building module, used to build a model of the observed signal under the reverberation background;

[0139] A weight vector estimation module, used for estimating a weight vector for the spatial-temporal data of the detection range unit using a sparse STAP method;

[0140] The optimization building block is used to construct norm-based sparse weighted optimization problems;

[0141] The target detection module is used for iterative solution. It solves the sparse weighted optimization problem through the conjugate gradient method and the improved Newton method to obtain the optimal solution that meets the iteration termination conditions, and then determines the target angle, speed and position estimation value to achieve target detection.

[0142] Simulation experiment:

[0143] Assume that the number of linear array elements in the sonar system is N = 20, the speed of sound is c = 1500 m / s, and the signal carrier frequency of the element at the origin is f c =1kHz, array element spacing d=0.75m, pulse repetition period T=0.1s, the transmitted signal is a linear frequency modulation signal with bandwidth B=100Hz and pulse width of 0.08s. The reverberation data consists of 200 scattering point echo signals located near the target observation angle and relative Doppler frequency of zero. The proposed algorithm is compared with beamforming and zero-value weighting methods.

[0144] Table 2 Comparison of algorithm running time

[0145]

[0146] First, the noise robustness of the algorithm is verified. The relative speed between the target and the sonar system is set to 4kn, Gaussian white noise is added to each receiving array element, and the signal-to-noise ratio (SNR) is 0dB. The space-time spectrum estimation results of the three algorithms are shown in Figure 2. Figure 2 (a) is the traditional beamforming space-time spectrum, Figure 2 (b) is the zero-value weighted space-time spectrum, and Figure 2 (c) is the sparse weighted space-time spectrum.

[0147] Due to the strong reverberation in the environment, the traditional beamforming processing cannot effectively suppress the reverberation, and the target is buried in the strong reverberation. However, the zero-value weighting and the proposed sparse weighting algorithm can effectively suppress the reverberation when SNR=0dB. The normalized profiles of the target point in the angle dimension and Doppler dimension are shown in Figure 3, where Figure 3(a) is the normalized Doppler dimension profile, and Figure 3(b) is the normalized angle dimension profile. The proposed method has the highest parameter estimation resolution in the angle dimension and Doppler dimension, and the sidelobe suppression is below -50dB, which is lower than the traditional beamforming and zero-value weighting methods, verifying the reverberation suppression and super-resolution parameter estimation performance of the proposed method.

[0148] Table 2 shows the average computing time comparison of 300 Monte Carlo experiments using traditional beamforming, zero-weighted processing, and sparse weighted processing methods. The results show that the traditional beamforming method has the lowest computational complexity due to the lack of optimized solution processing, and the computational complexity of zero-value weighted processing is higher than that of the beamforming method. Since the sparse weighted method uses the low-complexity solution algorithm proposed in this paper in the optimization solution process, the computational complexity is only slightly increased compared to the other two methods to achieve significant performance improvement.

[0149] Next, to further verify the noise robustness of the algorithm, Gaussian white noise is added to the data to make SNR = -20dB, and the space-time spectrum estimation results are shown in Figure 4. Figure 4 (a) is the space-time spectrum of traditional beamforming, Figure 4 (b) is the space-time spectrum of zero-value weighting processing, and Figure 4 (c) is the space-time spectrum of sparse weighting processing. In the traditional beamforming processing results, the target is masked in strong reverberation and strong noise, and the zero-value weighting algorithm also fails under low signal-to-noise ratio conditions, resulting in the target being unable to be detected. As shown in Figure 4 (c), the sparse weighting method proposed in this paper can still see clear target points under strong reverberation and strong noise conditions. Figure 5 is the normalized target Doppler dimension and angle dimension profile, where Figure 5 (a) is the normalized Doppler dimension profile, and Figure 5 (b) is the normalized angle dimension profile. The normalized profile diagram in Figure 5 shows that under the conditions of low signal-to-noise ratio and strong reverberation, the proposed method can still obtain high-resolution estimation results in the range dimension and Doppler dimension, verifying the noise robustness of the proposed algorithm.

[0150] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention is described in detail with reference to the embodiments, it should be understood by those skilled in the art that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention and should be included in the scope of the claims of the present invention.

Claims

1. A method for detecting low-speed targets in a reverberant background based on sparse weighting, for use in an N-element uniform linear array active sonar system, the method comprising: Construct a model of the observed signal in a reverberant background; The weight vector is estimated by using the sparse STAP method to estimate the spatial-temporal data of the detection range unit; Formulate norm-based sparse weighted optimization problems; Iterative solution, using the conjugate gradient method and improved Newton method to solve the sparse weighted optimization problem, obtain the optimal solution that meets the iteration termination conditions, and then determine the target angle, speed and position estimation values ​​to achieve target detection; The N-element uniform linear array is distributed along the x-axis, and the element spacing is d=λ / 2, where λ is the signal wavelength, λ=c / f c , c and f c are the speed of sound and the carrier frequency respectively. Taking the array element at the origin as the reference point, K pulses are emitted, the pulse repetition period is T, and the kth pulse signal s k (t) is: s k (t)=a(k)exp(j2πf c t)p(t) Where a(k) is the amplitude of the kth pulse signal, and p(t) is the waveform; The observation signal model under the reverberation background takes into account the influence of reverberation and noise, and the array received signal y is: y=y tar +y rev +n Among them, y tar is the target echo signal, y rev is the reverberation signal, n is additive Gaussian white noise, with zero mean and variance σ 2 ; The process of establishing the observation signal model under the reverberation background includes: The angle-Doppler grid in the observation area is divided into M×K grids, where the discrete angle set is represented by θ = [θ0, θ1..., θ M-1 ], the discrete Doppler set is denoted as f d =[f d,0 ,f d,1 ,...,f d,K-1 ], In the space-time spectrum, the d )'s target echo signal y tar for: yes tar =Do it tar In the formula, space-time spectrum in Space-time Steering Vector for: m, k represent the row and column numbers of the grid, j represents the imaginary part, R and θ m represents the distance of the far-field point target and the angle of the mth grid row, a(k,R,θ m ) is the target reflection coefficient; represents the spatial steering vector; u(θ)=[u(θ0),...,u(θ m ),...,u(θ M-1 )], represents the time-domain steering vector, expressed as u(f d )=[u(f d,0 ),...,u(f d,k ),...,u(f d,K-1 )] T , u(f d,k )={exp(-j2πf d,k 0T),exp(-j2πf d,k 1T),...,exp(-j2πf d,k (K-1)T)}; [·] T represents the transpose of the vector; T represents the pulse repetition period; The reverberation is modeled as the superposition of echoes from Q independent scatterers: Where q represents the number of independent scatterers, θ q represents the qth angle, represents the Kronecker product; The norm-based sparse weighted optimization problem is: In the formula, is the target space-time spectrum to be estimated, J(α) is the objective function, α is the space-time spectrum vector, (Wα) i represents the i-th element of the vector Wα, τ is a small positive number, ρ = 2σ 2 γ represents the regularization coefficient, γ is the scale coefficient of the Laplace density function with respect to Wα; The iterative solution solves the sparse weighted optimization problem by using the conjugate gradient method and the improved Newton method to obtain the optimal solution that meets the iteration termination condition, and then determines the target angle, speed and position estimation value to achieve target detection, including: Step 1) Let β be the iteration step value, traverse the set L iterations, and repeat the following steps: Step 2) Solve the weight vector W using the sparse STAP method; Step 3) The improved low-complexity algorithm based on Newton's method is used to solve the sparse weighted optimization problem. The conjugate method is used to solve the optimal solution α of the lth iteration through the following formula: l : H(a l-1 )a l =2U H y Step 4) Update the Hessian matrix required for the l+1th iteration according to the following formula: Where diag[·] represents a diagonal matrix with vectors as diagonal elements, Step 5) Determine whether the following iteration termination conditions are met, if yes, go to step 6); otherwise, go to step 2); In the formula, δ is the termination limit, α l-1 is the optimal solution of the l-1th iteration; ||·||2 represents the bi-norm; Step 6) The optimal solution α l Convert to matrix form Determine target angle, velocity, and position estimates.

2. The method for detecting low-speed targets in a reverberant background based on sparse weighting according to claim 1 is characterized in that: The weight vector W is: W=R rev U -1 Where U represents the space-time steering vector [·] -1 Represents the inverse of the matrix, R rev =y rev y rev H , [·] H Represents the conjugate transpose of a vector.

3. A device based on the method for detecting low-speed targets in a reverberation background based on sparse weighting according to claim 1, used in an N-element uniform linear array active sonar system, characterized in that: The device comprises: A model building module, used to build a model of the observed signal under the reverberation background; A weight vector estimation module, used for estimating a weight vector for the spatial-temporal data of the detection range unit using a sparse STAP method; The optimization building block for constructing norm-based sparse weighted optimization problems; and The target detection module is used for iterative solution. It solves the sparse weighted optimization problem through the conjugate gradient method and the improved Newton method to obtain the optimal solution that meets the iteration termination conditions, and then determines the target angle, speed and position estimation value to achieve target detection.

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