Target orientation estimation method for resisting impulse noise interference based on adaptive zeroing array technology

Abstract

The invention provides a target orientation estimation method for resisting impulse noise interference based on an adaptive zeroing array technology. According to the method, the adaptive kernel width updating method is adopted, so that the algorithm is more suitable for the actually changing marine environment, and a higher convergence speed and a lower steady-state error can be achieved under the condition of limited snapshots. In addition, the adaptive zeroing array technology is adopted, complex operations such as eigenvalue solution and singular value decomposition are avoided, and prior conditions such as known information source number are not needed. The algorithm of the invention has the advantages of no prior, simple implementation and low calculation cost in engineering practical application. In a word, the algorithm provided by the invention can effectively resist the interference of impulse noise while ensuring the simplicity of the algorithm, and realizes accurate azimuth estimation.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater acoustic array signal processing, and in particular to a target azimuth estimation method based on adaptive nulling array technology to combat impulse noise interference. Background Art

[0002] In the field of underwater acoustic detection, Direction of Arrival (DOA) estimation algorithms based on array signal processing have attracted much attention due to their importance in signal parameter estimation. Beamforming-based DOA algorithms, such as conventional beamforming and minimum variance distortionless response (MVDR), have low angular resolution. Subspace-based DOA algorithms, such as the Multiple Signal Classification (MUSIC) algorithm and the Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT), can obtain high-resolution azimuth estimates, but they require the known number of signal sources as prior information and cannot avoid performing singular value decomposition of the covariance matrix, resulting in a large amount of computation and making it difficult to apply in practical systems. In recent years, adaptive nulling array technology has been gradually promoted and applied to the field of DOA estimation because it can maintain high resolution while maintaining algorithm simplicity.

[0003] However, in practical applications, arrays are often affected by impulse noise due to the influence of sounds such as aquatic biological activity, crustal movement, ice cracking or collision, which significantly reduces the performance of the above-mentioned DOA estimator. Hybrid correlation entropy has been proposed as a new robust statistic. Due to its inherent robustness to outliers, it is used to combat impulse noise interference. However, the performance of the algorithm based on the maximum hybrid correlation entropy criterion is very sensitive to the choice of kernel width value. The kernel width value can only be selected as a compromise between fast convergence speed and low steady-state deviation. Although there is currently an adaptive zeroing array technology based on maximum hybrid correlation entropy to combat impulse noise, the kernel width value is fixed and has weak adaptive dynamic adjustment capabilities in the face of fluctuations in the generalized signal-to-noise ratio of impulse noise and changes in the distribution characteristics of impulse noise. Therefore, it is impossible to achieve a lower estimation error under the condition of a limited number of snapshots. Summary of the Invention

[0004] The present invention aims to address the problems of the prior art by proposing a target bearing estimation method based on adaptive nulling array technology to combat impulse noise interference. While maintaining algorithmic simplicity, the method also enables high-resolution target bearing estimation in the presence of impulse noise and system input noise.

[0005] The present invention is achieved through the following technical solutions. The present invention proposes a target azimuth estimation method based on adaptive nulling array technology to resist impulse noise interference. The method comprises the following steps:

[0006] Step 1: Establish a mathematical model of the uniform linear array receiving signal;

[0007] Step 2: Construct a mathematical model of the adaptive zeroing array system output;

[0008] Step 3: Solve the cost function based on the maximum mixed correlation entropy criterion;

[0009] Step 4: Construct a kernel width adaptive update method;

[0010] Step 5: Use stochastic gradient descent method to iteratively solve the weight vector;

[0011] Step 6: Based on l=1,2,3...,L snapshots, perform iterative solution. According to step 4, the solution formula of the kernel width value is obtained. According to step 5, the iterative formula of the weight vector is obtained. The weight vector obtained by the last iterative solution is recorded as w end ; The output weight vector of the adaptive zeroing array system is

[0012] Step 7: Solve the spatial spectrum;

[0013] Step 8: Output the direction estimation result P(θ). The angle corresponding to the peak point in P(θ) is the direction of the target.

[0014] Furthermore, in step 1, it is assumed that there are Q far-field target narrowband sound sources incident on a uniform linear array with M array elements and an array element spacing of half a wavelength; the angles of the incident directions of the Q far-field targets relative to the array normal are θ1, θ2, ..., θ Q ; The number of snapshots of the received signal is L. In the lth snapshot, the array receives the signal vector

[0015]

[0016] in, is the narrowband source signal s of the qth far-field target q (l) direction vector, where q = 1, 2, ..., Q, is the additive noise received by the array. The noise is assumed to obey an α-stable distribution, satisfying that the noises of different array elements are independent and identically distributed with a mean of zero. is a noise-free signal.

[0017] Furthermore, in step 2, the first array sensor is set as the reference element, and the remaining M-1 elements form the auxiliary array; therefore, the received signal of the first reference element is x0(k)=u0(k)+n0(k), where u0(k) is the noise-free signal and n0(k) is the noise; the received signal of the auxiliary array is x(k)=u(k)+n(k); since the weight coefficient of the first element is constrained to be 1, the weight coefficients of all arrays are expressed as where w(l)=[w1(l),w2(l),...,w M-1 (l)] T ∈C (M-1)×1 ;

[0018] Therefore, the output of the adaptive zeroing array system, that is, the prediction error, is expressed as:

[0019]

[0020] Furthermore, in step three, the optimization condition based on the maximum mixed correlation entropy criterion is:

[0021]

[0022] Among them, σ1 and σ2 are the kernel width values ​​corresponding to two Gaussian kernel functions, satisfying σ1<σ2; a and b are mixing coefficients, satisfying 0≤a≤1, 0≤b≤1, a+b=1;

[0023] Using the instantaneous error to replace the expectation in the above formula, the cost function based on the maximum mixed correlation entropy criterion is approximately expressed as:

[0024]

[0025] Using Wirtinger Calculus to solve for J versus w * The derivative of (l) gives the gradient of the cost function:

[0026]

[0027] Among them, w * (l) is the conjugate of w(l).

[0028] Furthermore, in step 4, at the time of the lth iteration update, the slope is simplified as:

[0029]

[0030] To find its maximum value, calculate σ for the above formula respectively. 1l and σ 2l The derivative of , when the derivative function is 0, it is the extreme point:

[0031]

[0032] when When , the slope of the prediction error reaches its maximum value, and we can get:

[0033]

[0034] In this case, the exponent part is a constant.

[0035] Furthermore, the kernel width update rule is modified as follows:

[0036]

[0037] in, and To preset the kernel width, the adaptive kernel width value σ of the lth iteration is 1l and σ 2l Substitute the abbreviated formula Solve in .

[0038] Furthermore, in step five, the gradient descent method is used to iteratively solve the weight vector based on the hybrid correlation entropy criterion algorithm. The weight vector update formula is specifically expressed as:

[0039] w(l+1)=w(l)+μg(e(l))x(l)e * (l)

[0040] Where μ is the step size,

[0041] In order to compensate for the deviation caused by noise input, a bias compensation vector h(l) is introduced;

[0042] w(l+1)=w(l)+μg(e(l))x(l)e * (l)+h(l)

[0043] Under the following assumptions, Assumption 1: n0(l), u(l) and n(l) are uncorrelated; Assumption 2: The weight error vector Δw(l) is independent of the input vector x(l); the unbiased criterion is used to derive the calculation formula for the bias compensation vector h(l):

[0044]

[0045] Therefore, the weight vector update formula based on the maximum mixed correlation entropy criterion considering bias compensation is obtained:

[0046]

[0047] Furthermore, in step seven, the array pattern calculation formula output by the adaptive nulling array system is as follows:

[0048]

[0049] Where θ is the scanning angle vector, a(θ)=[1,e jπsinθ ,...,e j(M-1)πsinθ ] T is the direction vector corresponding to each scanning angle; the spatial spectrum is defined as the inverse of the array pattern:

[0050]

[0051] The present invention also proposes an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it implements the steps of a target azimuth estimation method based on adaptive zeroing array technology to combat pulse noise interference.

[0052] The present invention also proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of a target azimuth estimation method based on adaptive zeroing array technology to combat impulse noise interference.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] In view of the fluctuation of the generalized signal-to-noise ratio and the time-varying characteristics of the characteristic exponent of impulse noise, the algorithm with a fixed kernel width value cannot be dynamically adjusted during the iteration process, resulting in the problem that it is difficult to strike a balance between the convergence speed and the steady-state error. The present invention adopts an adaptive kernel width update method to make the algorithm more adaptable to the actual changing ocean environment, and can achieve faster convergence speed and lower steady-state error under the condition of a limited number of snapshots. In addition, the present invention adopts adaptive zeroing array technology to avoid complex operations such as eigenvalue solution and singular value decomposition, and does not require prior conditions such as the number of known signal sources. This makes the algorithm of the present invention have the advantages of no prior requirements, simple implementation and low computational cost in practical engineering applications. In short, the algorithm proposed in the present invention can effectively combat the interference of impulse noise while ensuring the simplicity of the algorithm, and achieve accurate azimuth estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0056] Figure 1 Schematic diagram of the array receiving signal.

[0057] Figure 2Schematic diagram of the principle of adaptive zeroing array considering offset compensation.

[0058] Figure 3 This is a flow chart of the direction estimation of the present invention.

[0059] Figure 4 These are the spatial spectra of the method of the present invention under different generalized signal-to-noise ratio conditions: (a) is the spatial spectrum under the condition of GSNR=0dB; (b) is the spatial spectrum under the condition of GSNR=20dB.

[0060] Figure 5 Schematic diagram of the normalized mean square deviation change curve of each method as the number of iterations changes;

[0061] Figure 6 Graph showing the comparison results between the method of the present invention and the other four methods: (a) is the root mean square error result of each method; (b) is the angle resolution probability result of each method. DETAILED DESCRIPTION

[0062] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0063] Combine Figures 1-6 The present invention proposes a target direction estimation method based on adaptive zeroing array technology to combat impulse noise interference, the method comprising the following steps:

[0064] Step 1: Establish a mathematical model of the uniform linear array receiving signal;

[0065] In step one, if Figure 1 As shown in the figure, assume that there are Q far-field target narrowband sound sources incident on a uniform linear array with M array elements and an array element spacing of half a wavelength; the angles of the incident directions of the Q far-field targets relative to the array normal are θ1, θ2, ..., θ Q ; The number of snapshots of the received signal is L. In the lth snapshot, the array receives the signal vector

[0066]

[0067] in, is the narrowband source signal s of the qth far-field target q (l) direction vector, where q = 1, 2, ..., Q, is the additive noise received by the array. The noise is assumed to obey an α-stable distribution, satisfying that the noises of different array elements are independent and identically distributed with a mean of zero. is a noise-free signal.

[0068] Step 2: Construct a mathematical model of the adaptive nulling array system output. The schematic diagram of the DOA estimation principle of the adaptive nulling array is as follows: Figure 2 shown.

[0069] In step 2, the first array sensor is set as the reference element, and the remaining M-1 elements form the auxiliary array. Therefore, the received signal of the first reference element is x0(k)=u0(k)+n0(k), where u0(k) is the noise-free signal and n0(k) is the noise. The received signal of the auxiliary array is x(k)=u(k)+n(k). Since the weight coefficient of the first element is constrained to 1, the weight coefficients of all arrays are expressed as where w(l)=[w1(l),w2(l),...,w M-1 (l)] T ∈C (M-1)×1 ;

[0070] Therefore, the output of the adaptive zeroing array system, that is, the prediction error, is expressed as:

[0071]

[0072] Step 3: Solve the cost function based on the maximum mixed correlation entropy criterion;

[0073] In step 3, the optimization condition based on the maximum mixed correlation entropy criterion is:

[0074]

[0075] Among them, σ1 and σ2 are the kernel width values ​​corresponding to two Gaussian kernel functions, satisfying σ1<σ2; a and b are mixing coefficients, satisfying 0≤a≤1, 0≤b≤1, a+b=1;

[0076] Using the instantaneous error to replace the expectation in the above formula, the cost function based on the maximum mixed correlation entropy criterion is approximately expressed as:

[0077]

[0078] Using Wirtinger Calculus to solve for J versus w * The derivative of (l) gives the gradient of the cost function:

[0079]

[0080] Among them, w * (l) is the conjugate of w(l).

[0081] Step 4: Construct a kernel width adaptive update method; the present invention will adaptively update the kernel width according to the prediction error, and select the kernel width corresponding to the maximum slope reduction of the prediction error, ensuring the fastest convergence speed of the algorithm in each iteration.

[0082] In step 4, at the lth iteration update, the slope is simplified as:

[0083]

[0084] To find its maximum value, calculate σ for the above formula respectively. 1l and σ 2l The derivative of , when the derivative function is 0, it is the extreme point:

[0085]

[0086] when When , the slope (gradient) of the prediction error reaches its maximum value, and we can get:

[0087]

[0088] At this point, the exponential part is a constant and it is no longer an algorithm based on mixed correlation entropy. More importantly, the algorithm will no longer converge. l ' increases as the error decreases. In order to solve this problem, the present invention revises the kernel width update rule as follows:

[0089]

[0090] in, and is the preset kernel width, calculated by Silverman rule or other methods. 1l and σ 2l Substitute the abbreviated formula Solve in .

[0091] Step 5: Use stochastic gradient descent method to iteratively solve the weight vector;

[0092] In step five, the gradient descent method is used to iteratively solve the weight vector based on the hybrid correlation entropy criterion algorithm. The weight vector update formula is specifically expressed as:

[0093] w(l+1)=w(l)+μg(e(l))x(l)e * (l)

[0094] Where μ is the step size,

[0095] In order to compensate for the deviation caused by noise input, a bias compensation vector h(l) is introduced;

[0096] w(l+1)=w(l)+μg(e(l))x(l)e * (l)+h(l)

[0097] Under the following assumptions, Assumption 1: n0(l), u(l) and n(l) are uncorrelated; Assumption 2: The weight error vector Δw(l) is independent of the input vector x(l); the unbiased criterion is used to derive the calculation formula for the bias compensation vector h(l):

[0098]

[0099] Therefore, the weight vector update formula based on the maximum mixed correlation entropy criterion considering bias compensation is obtained:

[0100]

[0101] Step 6: Based on l=1,2,3...,L snapshots, perform iterative solution. According to step 4, the solution formula of the kernel width value is obtained. According to step 5, the iterative formula of the weight vector is obtained. The weight vector obtained by the last iterative solution is recorded as w end ; The output weight vector of the adaptive zeroing array system is

[0102] Step 7: Solve the spatial spectrum;

[0103] In step 7, the array pattern calculation formula output by the adaptive nulling array system is as follows:

[0104]

[0105] Where θ is the scanning angle vector, a(θ)=[1,e jπsinθ ,...,e j(M-1)πsinθ ] T is the direction vector corresponding to each scanning angle; the spatial spectrum is defined as the inverse of the array pattern:

[0106]

[0107] Step 8: Output the direction estimation result P(θ). The angle corresponding to the peak point in P(θ) is the direction of the target. Figure 3 This is the overall flow chart of direction estimation.

[0108] Simulation experiment 1: The receiving array is a uniform linear array with 16 elements and an element spacing of half a wavelength. Three incoherent narrowband sound sources with a frequency of 300 Hz are incident on the array from -20°, 20° and 30° directions respectively, and the number of snapshots is 500. Each element is added with SαS pulse noise with a characteristic index α=1.2, and the spatial spectrum is plotted when the generalized signal-to-noise ratio (GSNR) is 0 dB and 20 dB respectively. The MCC, BC-MCC, MMCC and BC-MMCC methods are compared and analyzed with the method proposed in this invention (BC-AMMCC). Figure 4 As shown in (a), at high GSNR, all methods can distinguish the orientations of the three targets, but the spectrum peak of the method proposed in this invention is sharper; Figure 4 As shown in (b), when the GSNR is low, other methods cannot distinguish the target direction due to the presence of false peaks in the spatial spectrum caused by strong pulse interference, but the method proposed in the present invention can still distinguish the target direction.

[0109] Simulation experiment 2: The receiving array is a uniform linear array with 16 elements and a spacing of half a wavelength. A narrowband sound source is incident on the array from 0°. The normalized mean square error (NMSD) is used to reflect the degree of deviation between the estimated weight vector and the optimal weight vector, and is defined as NMSD = 10lg(E[||Δw|| 2 / ||w o || 2 ]). In this simulation experiment, the NMSD curves of different algorithms in each iteration process are plotted, which intuitively shows the convergence speed and steady-state performance of each algorithm. Figure 5 As shown in the figure, the proposed algorithm exhibits faster convergence speed and better steady-state performance.

[0110] Simulation Experiment 3: The receiving array is a uniform linear array with 16 elements and a spacing of half a wavelength. Three incoherent narrowband sound sources with a frequency of 300 Hz are incident on the array from directions of -20°, 20°, and 30°, respectively. The number of snapshots is 300. The GSNR is varied in the range of [-2:2:8] dB to compare and analyze the performance of different algorithms. Figure 6 (a) shows the Root Mean Square Error (RMSE) curves of various methods under impulse noise conditions as GSNR changes. Comparing the curves of various methods, it can be found that the method proposed in this paper has the lowest RMSE and is stable, with good estimation results under different GSNRs. However, as GSNR gradually increases, the advantage of the method proposed in this paper over other algorithms narrows. Figure 6(b) shows the angular resolution probability curves of each method as the GSNR changes in an impulse noise environment. A successful detection is defined as a target deviation within 3°. Comparing the curves of each method, it can be seen that the method proposed in this paper has the highest angular resolution probability.

[0111] In summary, the present invention provides a target azimuth estimation method based on zeroing array technology to combat impulse noise interference, which belongs to the field of underwater acoustic array signal processing. This application proposes a new DOA estimation algorithm that combines adaptive zeroing array technology based on bias compensation and adaptive kernel width update method, aiming to solve the problem of accurate DOA estimation under impulse noise interference and noisy input. The proposed method selects the kernel width value that reduces the prediction error along the maximum slope based on the maximum mixed correlation entropy criterion, thereby ensuring the fastest convergence speed of each iteration. This method combines the bias compensation strategy to make the DOA estimation have a lower steady-state error under the condition of a limited number of snapshots. Simulation experiments analyze the DOA estimation ability, convergence speed, root mean square error and resolution probability of the proposed improved algorithm. The results verify the effectiveness and feasibility of the present invention.

[0112] The present invention also proposes an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it implements the steps of a target azimuth estimation method based on adaptive zeroing array technology to combat pulse noise interference.

[0113] The present invention also proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of a target azimuth estimation method based on adaptive zeroing array technology to combat impulse noise interference.

[0114] The memory in the embodiments of the present application may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. The non-volatile memory may be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example and not limitation, many forms of RAM are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate synchronous DRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), and direct RAM bus RAM (DR RAM). It should be noted that the memory of the methods described herein is intended to include, but is not limited to, these and any other suitable types of memory.

[0115] In the above embodiments, all or part of the embodiments may be implemented by software, hardware, firmware, or any combination thereof. When implemented using software, all or part of the embodiments may be implemented in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present application are generated. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions may be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via a wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) method. The computer-readable storage medium may be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated therein. The available medium may be a magnetic medium (eg, a floppy disk, a hard disk, a magnetic tape), an optical medium (eg, a high-density digital video disc (DVD)), or a semiconductor medium (eg, a solid state disc (SSD)).

[0116] During implementation, each step of the above method can be completed by an integrated logic circuit of the hardware in the processor or by instructions in the form of software. The steps of the method disclosed in conjunction with the embodiments of the present application can be directly embodied as being executed by a hardware processor, or can be executed by a combination of hardware and software modules in the processor. The software module can be located in a storage medium mature in the art such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, etc. The storage medium is located in the memory, and the processor reads the information in the memory and completes the steps of the above method in conjunction with its hardware. To avoid repetition, it will not be described in detail here.

[0117] It should be noted that the processor in the embodiments of the present application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiment can be completed by an integrated logic circuit of the hardware in the processor or by instructions in the form of software. The above processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic device, a discrete gate or transistor logic device, or a discrete hardware component. The various methods, steps, and logic block diagrams disclosed in the embodiments of the present application can be implemented or executed. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor. The steps of the method disclosed in the embodiments of the present application can be directly embodied as being executed by a hardware decoding processor, or can be executed by a combination of hardware and software modules in the decoding processor. The software module can be located in a storage medium mature in the art, such as random access memory, flash memory, read-only memory, programmable read-only memory, or electrically erasable programmable memory, registers, etc. The storage medium is located in the memory, and the processor reads the information in the memory and completes the steps of the above method in combination with its hardware.

[0118] The above is a detailed introduction to the target azimuth estimation method based on adaptive zeroing array technology to combat pulse noise interference proposed in the present invention. Specific examples are used in this article to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea; at the same time, for general technical personnel in this field, according to the ideas of the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A target direction estimation method based on adaptive nulling array technology to combat impulse noise interference, characterized in that: The method comprises the following steps: Step 1: Establish a mathematical model of the uniform linear array receiving signal; Step 2: Construct a mathematical model of the adaptive zeroing array system output; Step 3: Solve the cost function based on the maximum mixed correlation entropy criterion; Step 4: Construct a kernel width adaptive update method; Step 5: Use stochastic gradient descent method to iteratively solve the weight vector; Step 6: Based on l=1,2,3...,L snapshots, perform iterative solution. According to step 4, the solution formula of the kernel width value is obtained. According to step 5, the iterative formula of the weight vector is obtained. The weight vector obtained by the last iterative solution is recorded as w end ; The output weight vector of the adaptive zeroing array system is Step 7: Solve the spatial spectrum; Step 8: Output the direction estimation result P(θ). The angle corresponding to the peak point in P(θ) is the direction of the target.

2. The method according to claim 1, characterized in that In step 1, assume that there are Q far-field target narrowband sound sources incident on a uniform linear array with M array elements and an array element spacing of half a wavelength; the angles of the incident directions of the Q far-field targets relative to the array normal are θ1, θ2, ..., θ Q ; The number of snapshots of the received signal is L. In the lth snapshot, the array receives the signal vector in, is the narrowband source signal s of the qth far-field target q (l) direction vector, where q = 1, 2, ..., Q, is the additive noise received by the array. The noise is assumed to obey an α-stable distribution, satisfying that the noises of different array elements are independent and identically distributed with a mean of zero. is a noise-free signal.

3. The method according to claim 2, characterized in that In step 2, the first array sensor is set as the reference element, and the remaining M-1 elements form the auxiliary array. Therefore, the received signal of the first reference element is x0(k)=u0(k)+n0(k), where u0(k) is the noise-free signal and n0(k) is the noise. The received signal of the auxiliary array is x(k)=u(k)+n(k). Since the weight coefficient of the first element is constrained to 1, the weight coefficients of all arrays are expressed as where w(l)=[w1(l),w2(l),...,w M-1 (l)] T ∈C (M-1)×1 ; Therefore, the output of the adaptive zeroing array system, that is, the prediction error, is expressed as:

4. The method according to claim 3, characterized in that In step 3, the optimization condition based on the maximum mixed correlation entropy criterion is: Among them, σ1 and σ2 are the kernel width values ​​corresponding to two Gaussian kernel functions, satisfying σ1<σ2; a and b are mixing coefficients, satisfying 0≤a≤1, 0≤b≤1, a+b=1; Using the instantaneous error to replace the expectation in the above formula, the cost function based on the maximum mixed correlation entropy criterion is approximately expressed as: Using Wirtinger Calculus to solve for J versus w * The derivative of (l) gives the gradient of the cost function: Among them, w * (l) is the conjugate of w(l).

5. The method according to claim 4, characterized in that In step 4, at the lth iteration update, the slope is simplified as: To find its maximum value, calculate σ for the above formula respectively. 1l and σ 2l The derivative of , when the derivative function is 0, it is the extreme point: when When , the slope of the prediction error reaches its maximum value, and we can get: In this case, the exponent part is a constant.

6. The method according to claim 5, characterized in that The core width update rule is modified as follows: in, and To preset the kernel width, the adaptive kernel width value σ of the lth iteration is 1l and σ 2l Substitute the abbreviated formula Solve in .

7. The method according to claim 6, characterized in that In step five, the gradient descent method is used to iteratively solve the weight vector based on the hybrid correlation entropy criterion algorithm. The weight vector update formula is specifically expressed as: w(l+1)=w(l)+μg(e(l))x(l)e * (L) Where μ is the step size, In order to compensate for the deviation caused by noise input, a bias compensation vector h(l) is introduced; w(l+1)=w(l)+μg(e(l))x(l)e * (l)+h(l) Under the following assumptions, Assumption 1: n0(l), u(l) and n(l) are uncorrelated; Assumption 2: The weight error vector Δw(l) is independent of the input vector x(l); the unbiased criterion is used to derive the calculation formula for the bias compensation vector h(l): Therefore, the weight vector update formula based on the maximum mixed correlation entropy criterion considering bias compensation is obtained:

8. The method according to claim 7, characterized in that In step 7, the array pattern calculation formula output by the adaptive nulling array system is as follows: Where θ is the scanning angle vector, is the direction vector corresponding to each scanning angle; the spatial spectrum is defined as the inverse of the array pattern:

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 8 are implemented.

10. A computer-readable storage medium for storing computer instructions, characterized in that: When the computer instructions are executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

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