A method for estimating arrival angle of radar array based on Cauchy kernel adaptive filtering

Abstract

The present invention relates to a method for estimating the arrival angle of a radar using a Cauchy kernel graph adaptive filtering array, and belongs to the technical field of radar signal processing. The method comprises the following steps: 1) the time delay information of the radar array receiving signal is represented by a graph, and the graph adjacency matrix of each angle is constructed and stored; 2) the algorithm parameters are initialized; 3) the original echo signal is obtained, and the original array element signal is pulse compressed and the source number is estimated; 4) the graph adjacency matrix corresponding to the search angle in step 1) is extracted by grid search, and the graph Fourier transform matrix is ​​obtained; the current snapshot signal in step 3) is extracted for graph Fourier transform, and the signal is transformed into the graph domain; 5) the snapshot signal transformed into the graph domain in step 4) is filtered using the Cauchy kernel, and then the graph adaptive filtering iteration is performed, and then the signal is updated; 6) the spectrum peak search function is calculated. The present invention has the advantages of strong anti-noise ability and high estimation accuracy.

Description

Technical Field

[0001] The invention relates to a method for estimating the arrival angle of a Cauchy kernel image adaptive filtering array radar, which is suitable for estimating the angle of a radar target relative to a radar with high resolution and belongs to the technical field of radar signal processing. Background Art

[0002] Direction of Arrival (DOA) estimation is one of the important research directions in array signal processing. Conventional beamforming (CBF) is the most classic DOA estimation method, but it has disadvantages such as low resolution and high side lobes. In order to achieve angle super-resolution, multiple signal classification (MUSIC) based on subspace method and Estimation of Signal Parameters Via Rotational Invariance Techniques (ESPRIT) algorithm have been proposed.

[0003] In order to make full use of array information and solve the problem of low estimation accuracy of traditional methods under few snapshots, people apply graph signal processing (GSP) to subspace DOA estimation algorithms. The radar array is represented as a node of the graph, and the phase delay of the incident wave of the radar unit is represented as the edge of the graph. The most suitable adjacency matrix is ​​obtained by traversal, and the steering vector of the source signal is used as the eigenvector of the adjacency matrix of the graph. Therefore, it can be considered that the data of the array will be orthogonal to the remaining subspace after removing the eigenvector with the most target points, thereby completing the DOA estimation. The non-completely connected graph only uses the phase information of adjacent elements, and often ignores the phase difference information outside the adjacent elements, resulting in large errors when estimating DOA for multiple targets. To address this problem, Yu et al. proposed a DOA estimation method based on a fully connected graph, and adopted a multi-layer loop method to process the adjacency matrix in the case of multiple targets, solving the problem that the graph method has poor DOA estimation effect in the case of multiple targets, but it is only limited to the case of single snapshot estimation. For DOA estimation in the case of multiple snapshots, Li et al. proposed a spatiotemporal graph method, which uses a unit directed cyclic graph to represent the time series relationship, and then uses tensor product to combine the temporal adjacency matrix based on the graph shift operator and the spatial adjacency matrix based on the phase shift between sensors in the same array to construct a new adjacency matrix. However, this method is only applicable to narrowband signals, and the tensor product operation is large, which is not suitable for situations with more snapshots.

[0004] In order to solve the problems of the above-mentioned traditional graph methods, adaptive filtering methods were introduced. In 2016, Lorenzo et al. proposed an adaptive filtering strategy to adaptively estimate the signal defined on the graph. Under the assumption of limited bandwidth, it can reconstruct and track online from a limited number of observations on a vertex subset, allowing this subset to change over time in an adaptive manner. In addition, the least squares method was introduced, and a probability sampling strategy was set to design the sampling probability of each node in the graph to optimize the trade-off between the steady-state performance, graph sampling rate, and convergence speed of the adaptive algorithm. In order to further improve the convergence speed and reduce the computational complexity, Spelta et al. introduced a standardized minimum mean square algorithm in graph filtering and proposed two time-domain data selection methods for online reconstruction of band-limited graph signals. In order to solve the problem of poor reconstruction effect when the graph sampling signal is interfered by impulse noise, Zhao et al. introduced a generalized maximum entropy criterion that is robust to impulse noise in graph adaptive filtering, and introduced a data reuse strategy and a variable step size method to enhance the robustness of the graph filtering algorithm and reduce the impact of signal mutations on the estimation results. However, the current technology has not been applied to radar target angle estimation. The large number of snapshots in the array radar results in a large amount of computational effort in the construction of the space-time graph in the traditional graph signal processing method; while the adaptive filtering algorithm requires more snapshots to converge, and although the computational complexity is low, the accuracy is poor. How to combine the high accuracy and high information benefit rate of graph signal processing with the low computational complexity of adaptive filtering in arrival angle estimation is a difficult problem. Summary of the invention

[0005] The purpose of the present invention is to solve the problem of large computational complexity and poor stability of traditional methods when there are many snapshots of array radar signals and complex noise conditions of different targets. A Cauchy kernel graph adaptive filtering array radar arrival angle estimation method is proposed. This method uses a fully connected graph to represent the array in space, uses an adaptive filtering algorithm with low computational complexity in the time dimension to update each node on the graph structure separately, and uses the Cauchy kernel function as the filter kernel to adapt to complex noise conditions.

[0006] The present invention provides a method for estimating the angle of arrival of a Cauchy kernel image adaptive filtering array radar, which is characterized by comprising the following steps:

[0007] Step 1: The time delay information of the radar array receiving signal is represented by a graph, and the graph adjacency matrix of each angle is constructed and stored;

[0008] Step 2: Initialize the algorithm parameters;

[0009] Step 3: Obtain the original echo signal, perform pulse compression and source number estimation on the original array element signal;

[0010] Step 4: Extract the graph adjacency matrix corresponding to the search angle in step 1 through grid search, and calculate the graph Fourier transform matrix; extract the current snapshot signal in step 3, perform graph Fourier transform, and transform the signal into the graph domain;

[0011] Step 5: Filter the snapshot signal transformed into the image domain in step 4 using the Cauchy kernel, then perform image adaptive filtering iterations, and then update the signal;

[0012] Step 6: Calculate the peak search function.

[0013] Preferably, the specific steps of step 1 are as follows:

[0014] for A uniform linear array of array elements with an array element spacing of , the speed of light is , is the target direction, array element and The time delay is:

[0015] (1);

[0016] The steering vector is , then the echo signal received by the array element is expressed as:

[0017] (2);

[0018] in is the source signal, For noise, is the number of snaps;

[0019] Construct an edge to connect any two elements in the radar array, and construct a search angle of The adjacency matrix when for:

[0020] (3).

[0021] Preferably, the pulse compression of the original array element signal in step 3 is specifically performed as follows:

[0022] The linear frequency modulation LFM signal is used as the radar transmission signal, and its expression is:

[0023] (4);

[0024] in, represents the pulse width, Indicates the carrier frequency, represents the linear modulation frequency, Indicates the LFM signal bandwidth;

[0025] The expression of radar receiving echo is:

[0026] (5);

[0027] in represents the scattering coefficient of the target, Indicates slow time, represents the speed of light, For the purpose The distance of time, Indicates receiving noise;

[0028] After down-conversion processing, the baseband echo is obtained as:

[0029] (6);

[0030] in Indicates the wavelength of the transmitted signal;

[0031] Using the baseband transmission signal as the reference signal, the baseband echo is matched filtered to obtain the echo after pulse compression:

[0032] (7);

[0033] Combining all the array element signals of a single snapshot, we get .

[0034] Preferably, the source number estimation in step 3 is specifically:

[0035] The eigenvalues ​​of the data covariance matrix are arranged in descending order from large to small. ζ 1≥ ζ 1≥…≥ ζ M ,set up The MDL criterion based on information theory is described as the following function:

[0036] (8);

[0037] In the formula, S is the total number of snapshots, where:

[0038] (9);

[0039] The penalty function is:

[0040] (10);

[0041] The estimated number of information sources is:

[0042] (11);

[0043] Preferably, the specific steps of step 4 are:

[0044] When performing grid search, the graph adjacency matrix corresponding to the search angle is extracted, and the adjacency matrix feature decomposition is:

[0045] (12);

[0046] The subspace decomposition of the adjacency matrix is ​​defined as:

[0047] (13);

[0048] represents the direction vector of the signal subspace, represents the noise subspace, which are mutually orthogonal;

[0049] The graph Fourier transform and inverse Fourier transform are defined as:

[0050] (14);

[0051] The current snapshot signal can be transformed into the graph domain through graph Fourier transform.

[0052] Preferably, the Cauchy kernel in step 5 is specifically:

[0053] The residual of the graph signal is defined as:

[0054] (15);

[0055] in is the expected signal, set to the value of the graph node at the previous moment;

[0056] Representing the joint probability density of two random variables X and Y, the relevant entropy is a similarity measure and is defined as:

[0057] (16);

[0058] in represents the expectation operator, is the Cauchy kernel function, represents the kernel width, represents the error;

[0059] The cost function using the Cauchy kernel function as the optimization criterion is:

[0060] (17);

[0061] Where l is the kernel width of the Cauchy kernel, and the minimum value of the loss function in is obtained by using the gradient descent method. The derivative is expressed as:

[0062] (18).

[0063] Preferably, the image adaptive filtering in step 5) is specifically:

[0064] The value updated at each step according to the adaptive filtering is:

[0065] (19);

[0066] The adaptive step size is set to , then the graph signal is updated as:

[0067] (20);

[0068] The signal is updated to:

[0069] (twenty one);

[0070] For each search angle, a separate update of the snapshot signal is performed.

[0071] Preferably, the specific steps of step 6 are:

[0072] For the eigenvalue matrix , the noise subspace satisfies the covariance matrix that is time-independent and completely orthogonal to the steering vector. The expression for measuring the degree of orthogonality between the steering vector and the noise subspace is used as the spectrum peak search function:

[0073] (twenty two);

[0074] The eigenvector representing the eigenvalue corresponding to the deletion target, The angle corresponding to the maximum value is the result of DOA estimation.

[0075] Compared with the prior art, the Cauchy kernel graph adaptive filtering array radar arrival angle estimation method of the present invention has the following beneficial effects: the present invention proposes an adaptive filtering angle estimation algorithm based on graph structure, which combines the advantages of high precision of subspace-based graph signal processing DOA estimation algorithm and low computational complexity of adaptive filtering DOA estimation algorithm. First, the array is represented in space using a fully connected graph, and the snapshot signal is projected into the graph domain. Then, an adaptive filtering algorithm with low computational complexity is used in the time dimension to update the graph structure of each search angle, and a robust kernel function is used as the filtering kernel to cope with the interference of complex noise. The present invention has the advantages of strong anti-noise capability and high estimation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 It is a flow chart of the present invention;

[0077] Figure 2 is a uniform line array fully connected graph;

[0078] Figure 3 This is the angle estimation result diagram under Gaussian noise;

[0079] Figure 4 This is the angle estimation result diagram under impulse noise;

[0080] Figure 5 This is the angle estimation result under stable distributed noise. DETAILED DESCRIPTION

[0081] A method for estimating the angle of arrival of a radar array with a Cauchy kernel adaptive filtering array according to this embodiment is shown in the attached Figure 1 , including the following steps:

[0082] Set the Monte Carlo order to 200, the uniform linear array with 8 elements, the number of snapshots to 50, the signal-to-noise ratio to 5~20db, the target angle to -10 degrees, and use the root mean square error (RMSE) to measure the degree of deviation of the estimated angle. Set the noise to a Gaussian distribution noise with a mean of 0 and a standard deviation of 0.5; a pulse noise mixed with 90% Gaussian noise with a mean of 0 and a variance of 0.01 and 10% Gaussian noise with a mean of 0 and a variance of 100; the parameters are set to of Stable distributed noise, the characteristic function is:

[0083] (twenty three);

[0084] in,

[0085] (twenty four);

[0086] The comparison algorithms of graph adaptive filtering (GLMS) are multi-signal classification algorithm (music), graph signal processing algorithm (GSP), and adaptive filtering algorithm (LMS).

[0087] (1) For A uniform linear array of array elements with an array element spacing of , the speed of light is , is the target direction, array element and The time delay is:

[0088] (1);

[0089] The steering vector is , then the echo signal received by the array element can be expressed as:

[0090] (2);

[0091] in is the source signal, For noise, The number of snapshots.

[0092] When the number of elements in the adjacency matrix based on adjacent elements increases, the matrix will become sparse and the prediction results will be inaccurate. By constructing edges to connect any two elements in the radar array, a search angle of The adjacency matrix when for:

[0093] (3);

[0094] (2) Initialize the step size of the adaptive filter, the kernel width of the Cauchy kernel, and the reference vector value. The initial iteration step size is 0.0005, the Cauchy kernel width is 2.25, and the reference vector is the time delay vector ;

[0095] (3) Collect radar target echo data, perform preliminary pulse compression on the data, and estimate the number of sources;

[0096] The pulse compression is specifically:

[0097] The linear frequency modulation (LFM) signal is used as the radar transmission signal, and its expression is:

[0098] (4);

[0099] in, represents the pulse width, Indicates the carrier frequency, represents the linear modulation frequency, Indicates the LFM signal bandwidth.

[0100] The expression of radar receiving echo is:

[0101] (5);

[0102] in represents the scattering coefficient of the target, Indicates slow time, represents the speed of light, For the purpose The distance of time, Indicates receiving noise.

[0103] After down-conversion processing, the baseband echo is obtained as:

[0104] (6);

[0105] in Indicates the wavelength of the transmitted signal.

[0106] Using the baseband transmission signal as the reference signal, the baseband echo is matched filtered to obtain the echo after pulse compression:

[0107] (7);

[0108] Combining all the array element signals of a single snapshot, we get .

[0109] The source number estimation is as follows: the eigenvalues ​​of the data covariance matrix are arranged in descending order from large to small ζ 1≥ ζ 1≥…≥ ζ M， set up is the source variable, and the MDL criterion based on information theory can be described as the following function:

[0110] (8);

[0111] In the formula, S is the total number of snapshots, where:

[0112] (9);

[0113] The penalty function is:

[0114] (10);

[0115] The estimated number of information sources is:

[0116] (11).

[0117] (4) Perform a grid search to extract the graph adjacency matrix corresponding to the search angle. The adjacency matrix feature decomposition is:

[0118] (12);

[0119] The subspace decomposition of the adjacency matrix is:

[0120] (13);

[0121] represents the direction vector of the signal subspace, represents the noise subspace, which are mutually orthogonal.

[0122] The Fourier transform and inverse Fourier transform of the graph are:

[0123] (14).

[0124] (5) Adaptive filtering iteration: perform Fourier transform on the current snapshot signal and then filter it using the Cauchy kernel; then update the signal and perform inverse Fourier transform.

[0125] The Cauchy kernel is specifically: The residual of the image signal is:

[0126] (15);

[0127] in is the expected signal, set to the value of the graph node at the previous moment.

[0128] Representing the joint probability density of two random variables X and Y, the relevant entropy is a similarity measure and is defined as:

[0129] (16);

[0130] in represents the expectation operator, is the Cauchy kernel function, represents the kernel width, Represents error.

[0131] The cost function using the Cauchy kernel function as the optimization criterion is:

[0132] (17);

[0133] Where l is the kernel width of the Cauchy kernel, and the minimum value of the loss function in is obtained by using the gradient descent method. The derivative is expressed as:

[0134] (18).

[0135] Adaptive filtering signal update, specifically:

[0136] The value updated at each step of the adaptive filter is:

[0137] (19);

[0138] The adaptive step size is set to , then the graph signal is updated as:

[0139] (20);

[0140] The signal is updated to:

[0141] (twenty one);

[0142] For each search angle, a separate update of the snapshot signal is performed.

[0143] (6) Calculate the peak search function:

[0144] Ideally, the eigenvalue matrix is , however, due to the introduction of signal-to-noise ratio and the leakage of white noise, the other elements of the eigenvalue matrix are generally not 0. The noise subspace satisfies that the covariance matrix is ​​time-independent and completely orthogonal to the steering vector. An expression for measuring the degree of orthogonality between the steering vector and the noise subspace can be derived, The eigenvector representing the eigenvalue corresponding to the deletion target. The peak search function is defined as:

[0145] (twenty two);

[0146] if The same as the direction of arrival, then theoretically there is only one non-zero value, and the other values ​​are very close to zero. The value of is the largest. Therefore, The angle corresponding to the maximum value is the result of DOA estimation. Search each grid angle to obtain the angle-amplitude diagram. The angle with the larger amplitude is the location of the target.

[0147] Figure 2 The uniform linear array fully connected graph structure constructed for the algorithm. Figure 3 , 4 , 5 are the angle estimation results under three noise conditions respectively. Figure 3 For the Gaussian noise case, Figure 4 For the α noise case, Figure 5 For the case of impulse noise. It can be seen that the proposed algorithm is always better than the traditional graph algorithm, and it achieves the filtering of non-Gaussian noise on the graph structure with less computational cost, thus improving the accuracy of the graph DOA estimation method.

[0148] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is determined by the attached claims.

Claims

1. A method for estimating the angle of arrival of a radar array using a Cauchy kernel adaptive filter, characterized in that The following steps are involved: Step 1: The time delay information of the radar array receiving signal is represented by a graph, and the graph adjacency matrix of each angle is constructed and stored; Step 2: Initialize the algorithm parameters; Step 3: Obtain the original echo signal, perform pulse compression and source number estimation on the original array element signal; Step 4: Extract the graph adjacency matrix corresponding to the search angle in step 1 through grid search, and calculate the graph Fourier transform matrix; extract the current snapshot signal in step 3, perform graph Fourier transform, and transform the signal into the graph domain; Step 5: Filter the snapshot signal transformed into the image domain in step 4 using the Cauchy kernel, then perform image adaptive filtering iterations, and then update the signal; Step 6: Calculate the peak search function.

2. A method for estimating the angle of arrival of a radar using a Cauchy kernel adaptive filter array according to claim 1, characterized in that The specific steps of step 1 are as follows: For a uniform linear array with M array elements, the array element spacing is d, and the speed of light is c, is the target direction, and the time delay between array elements a and b is: The steering vector is Then the echo signal received by the array element is expressed as: Where u(s) is the source signal, n(s) is the noise, and s is the number of snapshots; Construct edges to connect any two elements in the radar array, and construct the adjacency matrix A when the search angle is θ: In the formula, w = 2πf, f is the frequency of the radar transmitting signal.

3. A method for estimating the angle of arrival of a radar using a Cauchy kernel adaptive filter array according to claim 1, characterized in that The pulse compression of the original array element signal in step 3 is specifically as follows: The linear frequency modulation LFM signal is used as the radar transmission signal, and its expression is: x T (s)=rect(s / T p )exp(j2πf c s+jπγt 2 ) (4) Among them, T p represents the pulse width, f c Indicates carrier frequency, γ = B / T p represents the linear modulation frequency, and B represents the LFM signal bandwidth; The expression of radar receiving echo is: Where σ0 represents the scattering coefficient of the target, s m represents slow time, c represents the speed of light, r s (s m ) is the target at t m The distance at the moment, n represents the received noise; After down-conversion processing, the baseband echo is obtained as: where λ = c / f c Indicates the wavelength of the transmitted signal; Using the baseband transmission signal as the reference signal, the baseband echo is matched filtered to obtain the echo after pulse compression: Combining all array element signals for a single snapshot yields x(s).

4. A method for estimating the angle of arrival of a radar using a Cauchy kernel adaptive filter array according to claim 1, characterized in that The source number estimation described in step 3 is specifically: The eigenvalues ​​of the data covariance matrix are arranged in descending order from large to small. ζ1≥ζ1≥…≥ζ M , set k as the source variable, and the MDL criterion based on information theory is described as the following function: Where S is the total number of snapshots and the penalty function is: p(k)=0.5k(2M-k)logS (9) The estimated number of information sources is:

5. A method for estimating the angle of arrival of a radar using a Cauchy kernel adaptive filter array according to claim 4, characterized in that The specific steps of step 4 are: When performing grid search, the graph adjacency matrix corresponding to the search angle is extracted, and the adjacency matrix feature decomposition is: A=FΛF H (11) The subspace decomposition of the adjacency matrix is ​​defined as: v(θ) represents the direction vector of the signal subspace, and N represents the noise subspace, which are orthogonal to each other; The graph Fourier transform and inverse Fourier transform are defined as: f(s)=F H x(s),x(s)=Ff(s) (13) The current snapshot signal can be transformed into the graph domain through graph Fourier transform.

6. A method for estimating the angle of arrival of a radar using a Cauchy kernel adaptive filter array according to claim 1, characterized in that The Cauchy kernel described in step 5 is specifically: The residual of the graph signal is defined as: e(s)=d(s)-F H x(s) (14) Where d(s) is the expected signal, which is set to the value of the graph node at the previous moment; p XY (x, y) represents the joint probability density of two random variables X and Y. The related entropy is a similarity measure and is defined as: V(X,Y)=E[κ σ (X,Y)]=∫∫κ σ (x,y)p XY (x,y)dxdy (15) where E[·] represents the expectation operator, is the Cauchy kernel function, l represents the kernel width, and e=xy represents the error; The cost function using the Cauchy kernel function as the optimization criterion is: Where l is the kernel width of the Cauchy kernel, and the gradient descent method is used to obtain the minimum value of the loss function in, and the derivative is expressed as .

7. A method for estimating the angle of arrival of a radar using a Cauchy kernel adaptive filter array according to claim 6, characterized in that The image adaptive filtering in step 5) is specifically as follows: The value updated at each step according to the adaptive filtering is: The adaptive step size is set to μ, and the graph signal is updated as: The signal is updated to: For each search angle, a separate update of the snapshot signal is performed.

8. The method for estimating the angle of arrival of a radar using a Cauchy kernel adaptive filter array according to claim 1, characterized in that The specific steps of step 6 are: For the eigenvalue matrix Λ=diag{1,0…,0}, the noise subspace satisfies the covariance matrix that is time-independent and completely orthogonal to the steering vector. The expression for measuring the degree of orthogonality between the steering vector and the noise subspace is used as the spectral peak search function: [] - The eigenvector representing the eigenvalue corresponding to the deleted target, and the angle corresponding to the maximum value of G is the result of DOA estimation.

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