Underwater target orientation estimation method, system and device based on four-order cumulant virtual array

Abstract

The invention provides an underwater target orientation estimation method, system and device based on a fourth-order cumulant virtual array, relates to the technical field of array signal processing, eliminates Gaussian colored noise by calculating the fourth-order cumulant output by an antenna array, is high in anti-noise capability, is more suitable for a complex underwater target orientation estimation scene, and is high in robustness. And through combination with the fourth-order cumulant, the array element number and the array aperture of the antenna array can be increased, a virtual array with a large aperture and a high degree of freedom is obtained, the limitation of the physical array element number on the degree of freedom estimation is broken through, and the degree of freedom and the estimation precision of underwater target orientation estimation are improved. Different noise subspace matrix calculation methods can be selected according to whether the number of underwater targets is known or not, underwater target orientation estimation can still be achieved when the number of the underwater targets is unknown, the number of the underwater targets does not need to serve as a parameter, eigenvalue decomposition calculation is not needed in the process of solving the noise subspace matrix, and the method is simple and convenient to implement. Compared with the prior art, the method has the advantages that the calculation complexity is reduced, the calculation expenditure is saved, the underwater target orientation estimation result is obtained through direct analysis by designing the polynomial, and compared with a spatial spectrum traversal mode, the calculation complexity and the calculation expenditure are reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of array signal processing, and more specifically, to an underwater target azimuth estimation method, system and device based on a fourth-order cumulant virtual array. Background Art

[0002] With the continuous advancement of science and technology, the exploration of underwater resources has become increasingly in-depth, whether in the civil, scientific research or military fields, and is gradually expanding to the deep sea. Deep-sea fishing operations, underwater resource detection, and underwater operations of ships and submarines all rely on advanced underwater working equipment. However, the underwater world has extremely low visibility and extreme and changeable environments, which poses great challenges to the use of these equipment. In this context, how to enable underwater working equipment to accurately estimate the target position has become an important topic of current research.

[0003] By using antenna arrays to receive radiation signals emitted by underwater equipment such as ships, submarines, and exploration equipment, the direction of arrival (DOA) of the received radiation signal can be estimated through an algorithm. The DOA of the radiation signal of an underwater target is the direction of the target.

[0004] DOA estimation refers to estimating the azimuth information of a single or multiple signal sources based on the received signal of the antenna array. Due to the Fourier relationship between the excitation signal and the directional pattern, DOA estimation can also be equivalent to a spectrum estimation problem. Array signal processing technology is the core of DOA estimation, focusing on processing the signals sensed or received by the radiation sensor array. At present, the most advanced and mature DOA estimation method based on subspace is the most representative one. Among them, the most representative one is the Multiple Signal Classification (MUSIC) algorithm proposed by Schmidt RO et al. The main idea of ​​this algorithm is to divide the covariance matrix of the array received data into a signal subspace and an orthogonal noise subspace based on the spectral decomposition theory of the matrix, and establish a spectral function based on the orthogonal characteristics of the signal subspace and the noise subspace. Then, the peak value is solved to obtain the angle estimation value of the signal, thereby improving the performance of the algorithm in terms of resolution and other aspects. At the same time, it also breaks through the physical aperture limit of the array for DOA estimation in the traditional spatial spectrum estimation algorithm, namely the Rayleigh limit, and promotes the development of research on subspace algorithms. However, this type of algorithm has the following disadvantages: (1) It is assumed that the noise in the environment is Gaussian additive white noise, and the impact on each antenna array element is the same. In the actual environment, the noise is mostly Gaussian colored noise. Under this noise, the accuracy of this type of algorithm is difficult to achieve the expected. (2) It is necessary to perform eigenvalue decomposition, and the eigenvalue decomposition process has high computational complexity and the computational cost is much greater than the general matrix operation. Underwater working equipment is generally mobile equipment. The large computational cost will bring great challenges to the power, endurance and cost of the equipment. (3) After the eigenvalue decomposition, the premise of using this algorithm is that the number of underwater targets is known or has been correctly estimated. However, in actual scenarios, especially in military exploration scenarios, the number of underwater targets is unknown. (4) This algorithm requires a certain number of antenna array elements, but in actual scenarios, underwater targets often appear in groups. When implementing this algorithm, more array elements are needed, which will greatly increase the hardware cost, computational cost and maintenance cost. (5) This algorithm requires a spatial spectrum search, and the search process is a traversal operation process. The DOA estimation accuracy is directly linked to the search step size. If the search step size is small, the number of traversals increases, and the computational complexity and computational time also increase. In short, this type of algorithm cannot take into account both accuracy and computational complexity.

[0005] High-order cumulants, especially fourth-order cumulants, have received extensive attention in DOA estimation because of their insensitivity to Gaussian noise and ability to expand the virtual array aperture. By utilizing high-order cumulants, the azimuth spectrum estimation of non-Gaussian signals can be realized under the background of Gaussian colored noise, thereby improving the accuracy and robustness of DOA estimation. For example, the prior art discloses a method for estimating the direction of arrival of a coprime array based on fourth-order cumulants. By constructing a one-layer coprime array and a two-layer coprime array, all fourth-order cumulants are calculated and a fourth-order cumulant matrix is ​​constructed, and finally the estimation of the direction of arrival is realized, which greatly increases the number of identifiable sources of the array under the condition of a limited number of array elements. However, in this method, eigenvalue decomposition is first required, which has a large computational complexity, and the number of source targets needs to be determined in advance, and the spatial spectrum needs to be calculated, and the spectrum peak needs to be found from the spatial spectrum according to the number of source targets, which cannot take into account both the computational complexity and the accuracy of azimuth estimation. Summary of the invention

[0006] In order to solve the problem that the current DOA estimation method based on fourth-order cumulants cannot take into account both computational complexity and azimuth estimation accuracy, the present invention proposes a method, system and device for underwater target azimuth estimation based on fourth-order cumulant virtual array. Based on fourth-order cumulants, the method, system and device have strong anti-noise ability, low overall computational complexity and low cost, and the number of targets to be estimated does not need to be known. By designing a special sparse array layout, the limitation of the number of physical array elements on the estimation freedom is broken, and the estimation accuracy of the underwater target azimuth is improved.

[0007] In order to achieve the above technical effects, the technical solution of the present invention is as follows:

[0008] In a first aspect, the present application proposes a method for estimating the underwater target azimuth based on a fourth-order cumulant virtual array, comprising the following steps:

[0009] S1: Construct the signal model of antenna array and antenna array receiving underwater target radiation signal;

[0010] S2: Calculate the fourth-order cumulant matrix of the antenna array based on the signal model;

[0011] S3: vectorizing the fourth-order cumulant matrix to obtain a virtual array output vector and a coordinate indication vector corresponding to the virtual array output vector, thereby increasing the number of array elements and the array aperture of the antenna array;

[0012] S4: calculating a selection matrix according to the coordinate indication vector corresponding to the virtual array output vector, and calculating an output vector of the virtual linear uniform array based on the selection matrix and the virtual array output vector;

[0013] S5: construct the Toeplitz matrix using the vector Toeplitzization function, take the output vector of the virtual linear uniform array as the object, and construct the signal covariance matrix using the Toeplitz matrix;

[0014] S6: When the number of underwater targets is known, the noise subspace matrix is ​​calculated based on the signal covariance matrix and orthogonal projection; when the number of underwater targets is unknown, the noise subspace matrix is ​​calculated based on the signal covariance matrix and quasi-orthogonal projection;

[0015] S7: Define a polynomial of the noise subspace matrix, and when the polynomial is equal to 0, solve the polynomial to obtain an underwater target azimuth estimation result.

[0016] Preferably, the antenna array includes an origin array element, a first subarray and a second subarray. When constructing the antenna matrix, mutually prime numbers M and mutually prime numbers d are set. The origin array element is an array element placed at the origin, and the coordinate is 0. The first array element of the first subarray is placed at the coordinate Nd, and then an array element is placed every 2Nd, and a total of The first element of the second subarray is placed at coordinate Md, and then an element is placed every 2Md, for a total of The array elements are arranged in a circle, where d is the unit distance between the array elements. Indicates rounding up; the physical array element coordinate set of the constructed antenna array It is expressed as:

[0017]

[0018] The array aperture of the constructed antenna array is MNd, and the number of physical array elements L is expressed as:

[0019]

[0020] Preferably, assume that there are K underwater targets, the wavelength of the underwater target radiation signal is denoted as λ, and the K signals emitted are denoted as {s1(t), s2(t), …, s K (t)}, the power of K signals is DOA is represented by {θ1,θ2,…,θ K}, then the signal model of the antenna array receiving the underwater target radiation signal is expressed as: x(t) = As(t) + n(t), where, represents the output vector, represents a plural set; represents the signal vector; represents the noise vector; represents the steering matrix, represents the steering vector, Represents the coordinates of the lth physical array element in the antenna array, arranged from small to large.

[0021] Preferably, based on the signal model, the process of calculating the fourth-order cumulant matrix of the antenna array is:

[0022] Define the fourth-order cumulant function cum4{·,·,·,·}, the fourth-order cumulant of ambient noise is The fourth-order cumulant of the underwater target signal is:

[0023] The fourth-order cumulant matrix C of the antenna array x The expression is:

[0024]

[0025] in, represents the Kronecker product; (·) H represents matrix transpose; (·) * represents matrix conjugation, and E{·} represents the expected calculation.

[0026] According to the above technical solution, due to the insensitivity of the fourth-order cumulant to Gaussian noise and interference, the fourth-order cumulant statistical operation is performed on the output of the antenna array, which has strong anti-noise ability and can remove Gaussian colored noise in the environment.

[0027] Preferably, the fourth-order cumulant matrix C x Vectorization, get the virtual array output vector, the expression is:

[0028] y=vec(C x )=Bc s

[0029] in, represents a single-snapshot virtual array output vector; Represents the fourth-order cumulant vector of underwater target signal; represents the virtual array steering matrix, represents the virtual array steering vector;

[0030] The elements in the virtual array output vector y are represented as:

[0031]

[0032] Where 1≤j,l,m,n≤L; the physical array element coordinate set of the virtual array is expressed as:

[0033] Defining vectors Defines the coordinate indicator vector of the physical array output vector Coordinate indicator vector v xThe value of the i-th element in the output vector x(t) of the physical array is the coordinate of the physical array element corresponding to the i-th element; then the coordinate indication vector of the virtual array output vector y is The calculation expression is:

[0034] Preferably, the virtual array includes a virtual linear uniform array ULA composed of L'=2(MN+M+N)-1 virtual array elements, and the array element spacing of the virtual linear uniform array ULA is d, so the array aperture of the virtual linear uniform array ULA reaches 2(MN+M+N-1)d;

[0035] The array output of the virtual linear uniform array ULA is but The coordinate indicator vector is in,

[0036] Selection Matrix The calculation expression is:

[0037] The expression for calculating the output vector of the virtual linear uniform array based on the selection matrix and the virtual array output vector is:

[0038] According to the above technical solution, by combining with the fourth-order cumulant, the array aperture of the virtual linear uniform array ULA is obtained to reach 2(MN+M+N-1)d. An array element can estimate a maximum of MN+M+N-1 underwater targets, greatly improving the degree of freedom and accuracy of DOA estimation.

[0039] Preferably, a vector Toeplitz function T(·) is defined, and a Toeplitz matrix is ​​constructed with the (N-1)M+1 elements after the vector as the first column elements and the reverse order of the (N-1)M+1 elements before the vector as the first row elements. The Toeplitz matrix is ​​used to construct the signal covariance matrix, and the expression is:

[0040] in, represents a diagonal matrix, represents the steering matrix of the virtual linear uniform array ULA, represents the steering vector of the virtual linear uniform array ULA;

[0041] When the number of underwater targets is known, the noise subspace matrix is ​​calculated based on the signal covariance matrix and orthogonal projection:

[0042] Select the first K columns of the signal covariance matrix R, where K represents the number of known underwater targets; the noise subspace matrix The calculation expression is:

[0043]

[0044] When the number of underwater targets is unknown, the noise subspace matrix is ​​calculated based on the signal covariance matrix and quasi-orthogonal projection:

[0045]

[0046] Among them, μ is the preset minimum value.

[0047] According to the above technical means, different noise subspace matrix calculation methods can be selected based on whether the underwater target is known, and the noise subspace matrix can be calculated using general matrix multiplication operations. Compared with the traditional method of extracting noise subspace by eigenvalue decomposition, the computational complexity is low and the cost is small. Moreover, when the number of underwater targets is unknown, the noise subspace matrix can still be calculated, avoiding the problem of needing to determine the number of underwater targets when extracting the noise subspace matrix in the traditional way.

[0048] Preferably, the noise subspace matrix and the steering vector of the virtual linear uniform array ULA Vertical, then Define polynomial Then the polynomial coefficients are:

[0049]

[0050] When the polynomial is equal to 0, solve the polynomial and record the solution of the polynomial as the symbol Get the underwater target position estimation result: express An estimate of ; where the polynomial can be solved Due to the conjugate symmetry of the polynomial coefficients, the solutions are mutually coupled, and we get The array aperture of the virtual linear uniform array ULA reaches 2(MN+M+N-1)d, and the estimated degree of freedom is An underwater target.

[0051] According to the above technical means, by designing and solving polynomials, the underwater target azimuth estimation result can be directly analyzed and obtained. Compared with the traditional method of spatial spectrum search and traversal, the calculation complexity is low and the estimation accuracy can be guaranteed.

[0052] In a second aspect, the present application proposes an underwater target azimuth estimation system based on a fourth-order cumulant virtual array, the system being used to implement the method described, comprising:

[0053] An antenna array construction unit, used to construct an antenna array and a signal model of the antenna array receiving radiation signals of underwater targets;

[0054] A fourth-order cumulant matrix construction unit, which calculates the fourth-order cumulant matrix of the antenna array based on the signal model;

[0055] A vectorization unit, used for vectorizing the fourth-order cumulant matrix to obtain a virtual array output vector and a coordinate indication vector corresponding to the virtual array output vector, thereby increasing the number of array elements and the array aperture of the antenna array;

[0056] An output vector calculation unit calculates a selection matrix according to a coordinate indication vector corresponding to the virtual array output vector, and calculates an output vector of the virtual linear uniform array based on the selection matrix and the virtual array output vector;

[0057] A signal covariance matrix construction unit, which constructs a Toeplitz matrix using a vector Toeplitzization function, takes the output vector of the virtual linear uniform array as an object, and constructs a signal covariance matrix using the Toeplitz matrix;

[0058] A noise subspace matrix calculation unit, when the number of underwater targets is known, calculates the noise subspace matrix based on the signal covariance matrix and orthogonal projection; when the number of underwater targets is unknown, calculates the noise subspace matrix based on the signal covariance matrix and quasi-orthogonal projection;

[0059] The estimation unit is used to define the polynomial of the noise subspace matrix. When the polynomial is equal to 0, the polynomial is solved to obtain the underwater target direction estimation result.

[0060] In a third aspect, the present application proposes an underwater target azimuth estimation device based on a fourth-order cumulant virtual array, wherein the device is equipped with the system.

[0061] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0062] The present invention proposes a method, system and device for estimating the underwater target azimuth based on a fourth-order cumulant virtual array. By calculating the fourth-order cumulant output by the antenna array, Gaussian colored noise is eliminated, the anti-noise ability is strong, and it is more suitable for complex underwater target azimuth estimation scenarios. In addition, by combining with the fourth-order cumulant, the number of array elements and the array aperture of the antenna array can be increased to obtain a virtual array with a large aperture and high degree of freedom, breaking through the limitation of the number of physical array elements on the estimation degree of freedom, and improving the degree of freedom and estimation accuracy of the underwater target azimuth estimation. The present invention can select different noise subspace matrix calculation methods according to whether the number of underwater targets is known. When the number of underwater targets is unknown, underwater target azimuth estimation can still be achieved without taking the number of underwater targets as a parameter, and the process of solving the noise subspace matrix does not require eigenvalue decomposition calculation, which reduces the computational complexity and saves computational expenses. The underwater target azimuth estimation result is obtained by directly analyzing the designed polynomial, which reduces the computational complexity and computational expenses compared with the spatial spectrum traversal method. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 A schematic diagram showing a flow chart of an underwater target azimuth estimation method based on a fourth-order cumulant virtual array proposed in an embodiment of the present invention;

[0064] Figure 2 A schematic diagram showing an antenna array proposed in an embodiment of the present invention;

[0065] Figure 3 A schematic diagram showing underwater target radiation signal acquisition proposed in an embodiment of the present invention;

[0066] Figure 4 A structural diagram of an underwater target azimuth estimation system based on a fourth-order cumulant virtual array proposed in an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0067] The drawings are for illustrative purposes only and should not be construed as limiting the present patent;

[0068] In order to better illustrate the present embodiment, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the actual size;

[0069] It is understandable to those skilled in the art that descriptions of certain well-known contents in the drawings may be omitted.

[0070] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0071] The positional relationships described in the drawings are only for illustrative purposes and should not be construed as limiting the present patent;

[0072] Example 1

[0073] This embodiment proposes a method for estimating the underwater target direction based on a fourth-order cumulant virtual array. The flowchart of the method is shown in FIG. Figure 1 , including the following steps:

[0074] S1: Construct the signal model of antenna array and antenna array receiving underwater target radiation signal;

[0075] S2: Calculate the fourth-order cumulant matrix of the antenna array based on the signal model;

[0076] S3: vectorizing the fourth-order cumulant matrix to obtain a virtual array output vector and a coordinate indication vector corresponding to the virtual array output vector, thereby increasing the number of array elements and the array aperture of the antenna array;

[0077] S4: calculating a selection matrix according to the coordinate indication vector corresponding to the virtual array output vector, and calculating an output vector of the virtual linear uniform array based on the selection matrix and the virtual array output vector;

[0078] S5: construct the Toeplitz matrix using the vector Toeplitzization function, take the output vector of the virtual linear uniform array as the object, and construct the signal covariance matrix using the Toeplitz matrix;

[0079] S6: When the number of underwater targets is known, the noise subspace matrix is ​​calculated based on the signal covariance matrix and orthogonal projection; when the number of underwater targets is unknown, the noise subspace matrix is ​​calculated based on the signal covariance matrix and quasi-orthogonal projection;

[0080] S7: Define a polynomial of the noise subspace matrix, and when the polynomial is equal to 0, solve the polynomial to obtain an underwater target azimuth estimation result.

[0081] In this embodiment, an antenna array is constructed, and the fourth-order cumulant of the antenna array output is calculated to eliminate Gaussian colored noise, and the anti-noise ability is strong, so that the method proposed in this embodiment is more suitable for complex underwater target position estimation scenarios, and the antenna array can increase the number of array elements and the array aperture by combining with the fourth-order cumulant to obtain a virtual array with a large aperture and high degree of freedom, breaking through the limitation of the number of physical array elements on the estimation degree of freedom, and improving the degree of freedom and estimation accuracy of the underwater target position estimation.

[0082] In this embodiment, different noise subspace matrix calculation methods can be selected according to whether the number of underwater targets is known. When the number of underwater targets is unknown, underwater target position estimation can still be achieved without taking the number of underwater targets as a parameter. The process of solving the noise subspace matrix does not require eigenvalue decomposition calculation, which reduces the computational complexity and saves computational expenses. The underwater target position estimation result is obtained by directly analyzing the designed polynomials, which reduces the computational complexity and computational expenses compared to the spatial spectrum traversal method.

[0083] Example 2

[0084] like Figure 2 As shown, the antenna array includes an origin array element, a first subarray and a second subarray. In this embodiment, when constructing the antenna matrix, the coprime numbers M and N are first set. The origin array element is an array element placed at the origin, and the coordinate is 0. Figure 2 The first element of the first subarray is placed at coordinate Nd, and then an element is placed every 2Nd. Array elements, see Figure 2 , the array element of the first subarray is represented by "●". The first array element of the second subarray is placed at coordinate Md, and then an array element is placed every 2Md, for a total of For the arrangement of array elements, see Figure 2 , the array elements of the second subarray are represented by “■”. Where d is the unit distance between array elements, Indicates rounding up. In an embodiment,

[0085] The physical element coordinate set of the constructed antenna array It is expressed as:

[0086]

[0087] The array aperture of the antenna array is MNd, and the number of physical array elements L is expressed as:

[0088]

[0089] In this embodiment, since the array element spacing of the first subarray and the second subarray is set to be a mutually prime number, this irregular spacing helps to reduce the spatial correlation between the array elements, thereby improving the array's ability to resolve underwater target radiation signals. The design of mutually prime numbers enables the array to more effectively capture and utilize signal information from different directions. Moreover, the combination of the origin array element and the two subarrays, as well as the arrangement of mutually prime number spacings, together constitute a diversified array element layout. This layout helps the array better identify radiation signals in complex environments, thereby improving the accuracy and reliability of signal processing. The synergy of the first subarray and the second subarray, and their mutual coordination with the origin array element, enables the entire antenna array to cover a wider spatial range.

[0090] like Figure 3 FIG. 1 is a schematic diagram of an antenna array collecting underwater target radiation signals. In this embodiment, a model of an antenna array receiving underwater radiation signals is first considered. It is assumed that there are K underwater targets, the wavelength of the underwater target radiation signal is denoted as λ, and the K transmitted signals are denoted as {s1(t), s2(t), …, s K(t)}, the power of K signals is DOA is represented by {θ1,θ2,…,θ K}, then the signal model of the antenna array receiving the underwater target radiation signal is expressed as: x(t) = As(t) + n(t), where, represents the output vector, represents a plural set; represents the signal vector; represents the noise vector; represents the steering matrix, represents the steering vector, Represents the coordinates of the lth physical array element in the antenna array, arranged from small to large.

[0091] Based on the above signal model, the process of calculating the fourth-order cumulant matrix of the antenna array is:

[0092] Define the fourth-order cumulant function cum4{·,·,·,·}, the fourth-order cumulant of ambient noise is The fourth-order cumulant of the underwater target signal is:

[0093] The fourth-order cumulant matrix C of the antenna array x The expression is:

[0094]

[0095] in, represents the Kronecker product; (·) H represents matrix transpose; (·) * represents matrix conjugation, and E{·} represents the expected calculation.

[0096] In a complex underwater environment, the propagation characteristics of the signal may be affected by many factors, such as multipath effect, scattering, attenuation, etc. By establishing a fourth-order cumulant matrix and vectorizing it, an output vector containing more useful information can be obtained, which is of great significance for improving the accuracy of underwater target azimuth estimation and realizing practical application requirements such as multi-target detection and tracking. x Vectorization, get the virtual array output vector, the expression is:

[0097] y=vec(C x )=Bc s

[0098] in, represents a single-snapshot virtual array output vector; Represents the fourth-order cumulant vector of underwater target signal; represents the virtual array steering matrix, represents the virtual array steering vector;

[0099] The elements in the virtual array output vector y are represented as:

[0100]

[0101] Where 1≤j,l,m,n≤L; the physical array element coordinate set of the virtual array is expressed as:

[0102] We define the vector Defines the coordinate indicator vector of the physical array output vector Coordinate indicator vector v x The value of the i-th element in the output vector x(t) of the physical array is the coordinate of the physical array element corresponding to the i-th element; then the coordinate indication vector of the virtual array output vector y is The calculation expression is:

[0103] In this embodiment, the virtual array includes a virtual linear uniform array ULA composed of L'=2(MN+M+N)-1 virtual array elements. The array element spacing of the virtual linear uniform array ULA is d, and the array aperture of the virtual linear uniform array ULA reaches 2(MN+M+N-1)d. By combining with the fourth-order cumulant, the array aperture of the virtual linear uniform array ULA reaches 2(MN+M+N-1)d. An array element can estimate a maximum of MN+M+N-1 underwater targets, greatly improving the degree of freedom and accuracy of DOA estimation.

[0104] The array output of the virtual linear uniform array ULA is but The coordinate indicator vector is in,

[0105] Selection Matrix The calculation expression is:

[0106] The expression for calculating the output vector of the virtual linear uniform array based on the selection matrix and the virtual array output vector is:

[0107] Define the vector Toeplitz function T(·), construct the Toeplitz matrix with the (N-1)M+1 elements after the vector as the first column elements and the reverse order of the (N-1)M+1 elements before the vector as the first row elements, and use the Toeplitz matrix to construct the signal covariance matrix. The expression is:

[0108] in, represents a diagonal matrix, represents the steering matrix of the virtual linear uniform array ULA, represents the steering vector of the virtual linear uniform array ULA;

[0109] When the number of underwater targets is known, the noise subspace matrix is ​​calculated based on the signal covariance matrix and orthogonal projection:

[0110] Select the first K columns of the signal covariance matrix R, where K represents the number of known underwater targets; the noise subspace matrix The calculation expression is:

[0111]

[0112] When the number of underwater targets is unknown, the noise subspace matrix is ​​calculated based on the signal covariance matrix and quasi-orthogonal projection:

[0113]

[0114] Among them, μ is the preset minimum value.

[0115] Noise Subspace Matrix and Steering Vector of Virtual Linear Uniform Array (ULA) Vertical, then

[0116] because Set variable It can be expressed as So we can get:

[0117]

[0118] Since the solution is non-zero, multiply the above equation by Make the degree of each term of the polynomial greater than or equal to 0, and get the polynomial The polynomial coefficients are:

[0119]

[0120] When the polynomial is equal to 0, solve the polynomial and record the solution of the polynomial as the symbol The solution obtained can be expressed according to the definition as in That is, the underwater target position estimation result is obtained: express An estimate of ; where the polynomial can be solved Due to the conjugate symmetry of the polynomial coefficients, the solutions obtained are mutually coupled (the mutually coupled solutions have the same complex argument), and we get The array aperture of the virtual linear uniform array ULA reaches 2(MN+M+N-1)d, and the estimated degree of freedom is An underwater target.

[0121] Example 3

[0122] like Figure 4 As shown, this embodiment proposes an underwater target direction estimation system based on a fourth-order cumulant virtual array, which is used to implement the method described, including: an antenna array construction unit, a fourth-order cumulant matrix construction unit, a vectorization unit, an output vector calculation unit, a signal covariance matrix construction unit, a noise subspace matrix calculation unit, and an estimation unit.

[0123] Among them, the antenna array construction unit is used to construct the antenna array and the signal model of the antenna array receiving the radiation signal of the underwater target. The fourth-order cumulant matrix construction unit calculates the fourth-order cumulant matrix of the antenna array based on the signal model; the vectorization unit is used to vectorize the fourth-order cumulant matrix to obtain the virtual array output vector and the coordinate indication vector corresponding to the virtual array output vector, thereby increasing the number of array elements and the array aperture of the antenna array. The output vector calculation unit calculates the selection matrix according to the coordinate indication vector corresponding to the virtual array output vector, and calculates the output vector of the virtual linear uniform array based on the selection matrix and the virtual array output vector. The signal covariance matrix construction unit constructs the Toeplitz matrix using the vector Toeplitz function, and constructs the signal covariance matrix using the Toeplitz matrix with the output vector of the virtual linear uniform array as the object. When the number of underwater targets is known, the noise subspace matrix calculation unit calculates the noise subspace matrix based on the signal covariance matrix and the orthogonal projection; when the number of underwater targets is unknown, the noise subspace matrix calculation unit calculates the noise subspace matrix based on the signal covariance matrix and the quasi-orthogonal projection. The estimation unit is used to define the polynomial of the noise subspace matrix. When the polynomial is equal to 0, the polynomial is solved to obtain the underwater target azimuth estimation result.

[0124] Example 5

[0125] This embodiment proposes an underwater target direction estimation device based on a fourth-order cumulant virtual array, and the device is equipped with the system. In a specific implementation, the underwater target direction estimation device can be an underwater working equipment, on which the system is installed, and the system includes: an antenna array construction unit, a fourth-order cumulant matrix construction unit, a vectorization unit, an output vector calculation unit, a signal covariance matrix construction unit, a noise subspace matrix calculation unit, and an estimation unit.

[0126] Among them, the antenna array construction unit is used to construct the antenna array and the signal model of the antenna array receiving the radiation signal of the underwater target. The fourth-order cumulant matrix construction unit calculates the fourth-order cumulant matrix of the antenna array based on the signal model; the vectorization unit is used to vectorize the fourth-order cumulant matrix to obtain the virtual array output vector and the coordinate indication vector corresponding to the virtual array output vector, thereby increasing the number of array elements and the array aperture of the antenna array. The output vector calculation unit calculates the selection matrix according to the coordinate indication vector corresponding to the virtual array output vector, and calculates the output vector of the virtual linear uniform array based on the selection matrix and the virtual array output vector. The signal covariance matrix construction unit constructs the Toeplitz matrix using the vector Toeplitz function, and constructs the signal covariance matrix using the Toeplitz matrix with the output vector of the virtual linear uniform array as the object. When the number of underwater targets is known, the noise subspace matrix calculation unit calculates the noise subspace matrix based on the signal covariance matrix and the orthogonal projection; when the number of underwater targets is unknown, the noise subspace matrix calculation unit calculates the noise subspace matrix based on the signal covariance matrix and the quasi-orthogonal projection. The estimation unit is used to define a polynomial of the noise subspace matrix, and when the polynomial is equal to 0, the polynomial is solved to obtain an estimation result of the underwater target position. The embodiments are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention.

[0127] For ordinary technicians in the field, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A method for underwater target azimuth estimation based on a fourth-order cumulant virtual array, characterized in that: The following steps are involved: S1: Construct the signal model of antenna array and antenna array receiving underwater target radiation signal; S2: Calculate the fourth-order cumulant matrix of the antenna array based on the signal model; S3: vectorizing the fourth-order cumulant matrix to obtain a virtual array output vector and a coordinate indication vector corresponding to the virtual array output vector, thereby increasing the number of array elements and the array aperture of the antenna array; S4: calculating a selection matrix according to the coordinate indication vector corresponding to the virtual array output vector, and calculating an output vector of the virtual linear uniform array based on the selection matrix and the virtual array output vector; S5: construct the Toeplitz matrix using the vector Toeplitzization function, take the output vector of the virtual linear uniform array as the object, and construct the signal covariance matrix using the Toeplitz matrix; S6: When the number of underwater targets is known, the noise subspace matrix is ​​calculated based on the signal covariance matrix and orthogonal projection; When the number of underwater targets is unknown, the noise subspace matrix is ​​calculated based on the signal covariance matrix and quasi-orthogonal projection; S7: Define a polynomial of the noise subspace matrix, and when the polynomial is equal to 0, solve the polynomial to obtain an underwater target azimuth estimation result.

2. The underwater target azimuth estimation method based on fourth-order cumulant virtual array according to claim 1 is characterized in that: The antenna array includes an origin array element, a first subarray and a second subarray. When constructing the antenna matrix, the coprime numbers M and N are set. The origin array element is the array element placed at the origin, with a coordinate of 0. The first array element of the first subarray is placed at the coordinate Nd, and then an array element is placed every 2Nd, with a total of The first element of the second subarray is placed at coordinate Md, and then an element is placed every 2Md, for a total of The array elements are arranged in a circle, where d is the unit distance between the array elements. Indicates rounding up; the physical array element coordinate set of the constructed antenna array It is expressed as: The array aperture of the constructed antenna array is MNd, and the number of physical array elements L is expressed as:

3. The underwater target azimuth estimation method based on fourth-order cumulant virtual array according to claim 2 is characterized in that: There are K underwater targets. The wavelength of the underwater target radiation signal is denoted as λ, and the K signals emitted are denoted as {s1(t),s2(t),…,s K (t)}, the power of K signals is DOA is represented by {θ1,θ2,…,θ K }, then the signal model of the antenna array receiving the underwater target radiation signal is expressed as: x(t) = As(t) + n(t), where, represents the output vector, represents a plural set; represents the signal vector; represents the noise vector; represents the steering matrix, represents the steering vector, Represents the coordinates of the lth physical array element in the antenna array, arranged from small to large.

4. The underwater target azimuth estimation method based on fourth-order cumulant virtual array according to claim 3 is characterized in that: Based on the signal model, the process of calculating the fourth-order cumulant matrix of the antenna array is: Define the fourth-order cumulant function cum4{·,·,·,·}, the fourth-order cumulant of ambient noise is The fourth-order cumulant of the underwater target signal is: The fourth-order cumulant matrix C of the antenna array x The expression is: in, represents the Kronecker product; (·) H represents matrix transpose; (·) * represents matrix conjugation, and E{·} represents the expected calculation.

5. The underwater target azimuth estimation method based on fourth-order cumulant virtual array according to claim 4 is characterized in that: The fourth-order cumulant matrix C x Vectorization, get the virtual array output vector, the expression is: y=vec(C x )=Bc s in, represents a single-snapshot virtual array output vector; Represents the fourth-order cumulant vector of underwater target signal; represents the virtual array steering matrix, represents the virtual array steering vector; The elements in the virtual array output vector y are represented as: Where, 1≤j,l,m,n≤L; the physical array element coordinate set of the virtual array is expressed as: Defining vectors Defines the coordinate indicator vector of the physical array output vector Coordinate indicator vector v x The value of the i-th element in the output vector x(t) of the physical array is the coordinate of the physical array element corresponding to the i-th element; then the coordinate indication vector of the virtual array output vector y is The calculation expression is:

6. The underwater target azimuth estimation method based on fourth-order cumulant virtual array according to claim 5 is characterized in that: The virtual array includes a virtual linear uniform array ULA composed of L'=2(MN+M+N)-1 virtual array elements, and the array element spacing of the virtual linear uniform array ULA is d, so the array aperture of the virtual linear uniform array ULA reaches 2(MN+M+N-1)d; The array output of the virtual linear uniform array ULA is but The coordinate indicator vector is in, Selection Matrix The calculation expression is: The expression for calculating the output vector of the virtual linear uniform array based on the selection matrix and the virtual array output vector is:

7. The underwater target azimuth estimation method based on fourth-order cumulant virtual array according to claim 6 is characterized in that: Define the vector Toeplitz function T(·), construct the Toeplitz matrix with the (N-1)M+1 elements after the vector as the first column elements and the reverse order of the (N-1)M+1 elements before the vector as the first row elements, and use the Toeplitz matrix to construct the signal covariance matrix. The expression is: in, represents a diagonal matrix, represents the steering matrix of the virtual linear uniform array ULA, represents the steering vector of the virtual linear uniform array ULA; When the number of underwater targets is known, the noise subspace matrix is ​​calculated based on the signal covariance matrix and orthogonal projection: Select the first K columns of the signal covariance matrix R, where K represents the number of known underwater targets; the noise subspace matrix The calculation expression is: When the number of underwater targets is unknown, the noise subspace matrix is ​​calculated based on the signal covariance matrix and quasi-orthogonal projection: Among them, μ is the preset minimum value.

8. The underwater target azimuth estimation method based on fourth-order cumulant virtual array according to claim 7 is characterized in that: Noise Subspace Matrix and Steering Vector of Virtual Linear Uniform Array (ULA) Vertical, then Define polynomial Then the polynomial coefficients are: When the polynomial is equal to 0, solve the polynomial and record the solution of the polynomial as the symbol Get the underwater target position estimation result: express An estimate of ; where the polynomial can be solved Due to the conjugate symmetry of the polynomial coefficients, the solutions are mutually coupled, and we get The array aperture of the virtual linear uniform array ULA reaches 2(MN+M+N-1)d, and the estimated degree of freedom is An underwater target.

9. An underwater target azimuth estimation system based on a fourth-order cumulant virtual array, characterized in that: The system is used to implement the method according to any one of claims 1 to 8, including: An antenna array construction unit, used to construct an antenna array and a signal model of the antenna array receiving radiation signals of underwater targets; A fourth-order cumulant matrix construction unit, which calculates the fourth-order cumulant matrix of the antenna array based on the signal model; A vectorization unit, used for vectorizing the fourth-order cumulant matrix to obtain a virtual array output vector and a coordinate indication vector corresponding to the virtual array output vector, thereby increasing the number of array elements and the array aperture of the antenna array; an output vector calculation unit, which calculates a selection matrix according to a coordinate indication vector corresponding to the virtual array output vector, and calculates an output vector of the virtual linear uniform array based on the selection matrix and the virtual array output vector; A signal covariance matrix construction unit, which constructs a Toeplitz matrix using a vector Toeplitzization function, takes the output vector of the virtual linear uniform array as an object, and constructs a signal covariance matrix using the Toeplitz matrix; A noise subspace matrix calculation unit, when the number of underwater targets is known, calculates the noise subspace matrix based on the signal covariance matrix and orthogonal projection; when the number of underwater targets is unknown, calculates the noise subspace matrix based on the signal covariance matrix and quasi-orthogonal projection; The estimation unit is used to define the polynomial of the noise subspace matrix. When the polynomial is equal to 0, the polynomial is solved to obtain the underwater target direction estimation result.

10. An underwater target azimuth estimation device based on a fourth-order cumulant virtual array, characterized in that: The device is equipped with the system of claim 9.

Images