Tensor decomposition-based related information enhanced two-dimensional angle estimation method

Abstract

The invention relates to a related information enhanced two-dimensional angle estimation method based on tensor decomposition, which comprises the following steps: constructing tensor output of whole array receiving data, then obtaining a covariance tensor of the tensor output, and the covariance tensor is obtained on the whole array tensor output, so that the covariance tensor comprises cross-correlation and self-correlation information of array sub-area arrays. The method comprises the following steps: combining {1, 3} dimensions and {2, 4} dimensions of a covariance tensor to obtain a reconstructed matrix, rearranging elements in the reconstructed matrix to obtain an output matrix corresponding to a uniform array, synthesizing the matrix and a conjugate tensor of the matrix according to a third dimension to obtain a new combined tensor, performing spatial reconstruction on the combined tensor, performing tensor decomposition to obtain a combined factor of the tensor, and obtaining a final tensor. In conclusion, the method has the advantages that the spatial domain information and the time domain information of the received data are expressed in different dimensions, the angle estimation precision is improved, and the target radiation source is positioned more accurately.

Description

Technical Field

[0001] The invention belongs to the technical field of array signal processing, and in particular relates to a two-dimensional angle estimation method based on tensor decomposition-based correlation information enhancement. Background Art

[0002] In the fields of wireless communication, radar, sound processing, etc., determining the direction of the transmitting source or target is an important issue. Compared with uniform arrays, with the same number of array elements, non-uniform arrays have wider array element spacing, larger array aperture, and greater degrees of freedom, so they are less affected by mutual coupling, have higher angle estimation accuracy and more estimable signal sources, so they are more widely used. At the same time, the existing angle estimation algorithm based on non-uniform arrays obtains the corresponding difference covariance array by vectorizing the covariance of the array received data, and then uses spatial smoothing and subspace-based angle estimation algorithms to obtain the target angle.

[0003] However, the method based on the difference common array ignores the multi-dimensional structure of the array receiving data, and has the disadvantage of not being able to fully utilize the spatial and temporal information of the data. At the same time, because tensors are the generalization of vectors and matrices to dimensions, they can represent the spatial and temporal information of the array receiving data in different dimensions, thereby optimizing the data processing process. Therefore, compared with other angle estimation algorithms for non-uniform arrays, the tensor-based method has more advantages. However, the existing tensor-based method only considers the mutual correlation information between the array sub-arrays, but ignores the autocorrelation information of the sub-arrays, so the technology is not yet very mature.

[0004] In summary, the existing angle estimation methods based on non-uniform arrays have the following disadvantages: first, the method based on the difference common array cannot utilize the multi-dimensional information of the data and can only consider the spatial domain information and the time domain information in a mixed way; secondly, the existing tensor-based method is still imperfect. A patent named "Two-dimensional Direction of Arrival Estimation Method and Process for Mutually Prime Arrays Based on Structured Virtual Domain Tensor Signal Processing" mentions an immature tensor-based angle calculation method for non-uniform arrays, but it only considers the mutual correlation information between the array sub-arrays, and does not utilize the autocorrelation information of the sub-arrays, which affects the estimation accuracy. Therefore, there is an urgent need for a two-dimensional angle estimation method based on tensor decomposition with enhanced correlation information to solve the existing technical problems of being unable to utilize the multi-dimensional information of the received data, the mixed consideration of spatial domain information and time domain information, and the low estimation accuracy. Summary of the invention

[0005] In view of this, the present invention proposes a two-dimensional angle estimation method based on related information enhancement of tensor decomposition, which is applied to the field of array signal processing technology. It can make full use of the multi-dimensional information of the array received data, construct tensor output, and represent the spatial and time domain information of the received data in different dimensions, giving full play to the statistical characteristics of the array received data, improving the angle estimation accuracy, and solving the existing technical problems of being unable to utilize the multi-dimensional information of the received data, mixing the spatial and time domain information, and low estimation accuracy.

[0006] In order to achieve the above technical objectives, the specific technical solutions adopted by the present invention are:

[0007] S1: Received data matrix for the entire two-dimensional array Reconstruct and get the corresponding tensor output

[0008] S2: In order to use the mutual correlation information between sub-surface arrays and the autocorrelation information of the sub-surface arrays themselves, find the tensor The tensor related to

[0009] S3: Combine the dimensions with the same information in the matrix, that is, combine the {1,3} and {2,4} dimensions of the related tensors to obtain the matrix R;

[0010] S4: R is regarded as the output of the corresponding virtual array. However, the array elements in the corresponding virtual array are arranged in disorder. In order to obtain an ordered virtual array output, the elements in the matrix R are rearranged to obtain the output matrix Q of the corresponding virtual uniform array.

[0011] S5: extract the data from the first row to the second last row and the first column to the second last column of the output matrix Q to obtain a new matrix T; the data from the first row to the second last row and the first column to the second last column in Q are extracted here to weaken the correlation between T and its conjugate T*;

[0012] S6: Synthesize T and its conjugate T* in the third dimension to obtain the tensor

[0013] S7: Tensor Reconstruct the space and get a new tensor Here is The purpose of reconstruction is to increase the number of sources that can be estimated by the method.

[0014] S8: Tensor The dimensions carrying the same information in The {1,4}-dimensional and {2,5}-dimensional tensors are combined to obtain a new tensor

[0015] S9: Tensor Perform Canonical Polyadic decomposition to obtain its factor matrix C, G, V;

[0016] S10: Divide and add the elements in each column of the factor matrices C and G in turn to obtain parameters u and v;

[0017] S11: Merge the parameters u and v to obtain the final azimuth and elevation angle estimates θ and φ.

[0018] Furthermore, in step S1, the nested array is composed of two sub-arrays, where sub-array 1 is a uniform array, the array element spacing is d=λ / 2, λ is the wavelength of the incident signal, and the array element position set is

[0019]

[0020] Where N1 is the number of array elements in the x and y axes of sub-array 1. Sub-array 2 is a sparse array with an array element spacing of N1d and an array element position set of

[0021]

[0022] The element position set of the entire nested array is

[0023]

[0024] K far-field uncorrelated narrowband signals are injected into the array, and θ k ∈[-π / 2,π / 2] and φ k ∈[0,π] represents the azimuth and elevation angles of the kth signal, 1≤k≤K. The vector representation of the array receiving signal at time t based on the matrix model is in are the output vectors of the two sub-surface matrices of the nested surface at time t, and their expressions are:

[0025]

[0026] Among them, u k = sinφ k cosθ k , v k = sinφ k sinθ k ,s k (t) is the output of the kth signal at time t, t = 1, 2, ..., T, T is the total number of snapshots of the signal, is an independent and identically distributed additive white Gaussian noise vector, is the noise energy, I is the unit matrix, is the Kronecker product, and are the steering vectors of sub-array 1 along the x-axis and y-axis respectively, and their expressions are:

[0027]

[0028] Among them, u k = sinφ k cosθ k , v k = sinφ k sinθ k ; and are the steering vectors of sub-array 2 along the x-axis and y-axis respectively, and their expressions are:

[0029]

[0030] To avoid loss of structural information, the output signal of the array at time t is represented as two independent matrices:

[0031]

[0032] in, is an independent and identically distributed additive white Gaussian noise matrix. Connect the output matrices of the two sub-arrays to obtain the total output matrix of the entire array

[0033]

[0034] T snap X N (t) Connect through the time domain dimension to obtain a three-dimensional tensor

[0035]

[0036] in, represents the outer product of the vector, C3 represents the connection of the tensor along the third dimension (time domain dimension), s k =[s k (1),s k (2),...,s k (T)] T is the signal vector, is the noise tensor.

[0037] Furthermore, in step S2, the correlation tensor of the entire array output is obtained. At this time, not only the mutual correlation information between the sub-arrays can be used, but also the autocorrelation information of the sub-arrays themselves can be used to increase the amount of useful information. The correlation tensor of the entire array is

[0038]

[0039] in, is the energy of the kth signal, E{·} is the expected operation, is the noise tensor.

[0040] Further, in step S3, The {1, 3}th dimension is combined with the {2, 4}th dimension, and the reconstructed matrix is ​​as follows

[0041]

[0042] Where N is the reconstructed noise term, is the signal energy.

[0043] Furthermore, in step S4, R can be regarded as the output of the corresponding virtual array. However, at this time, the array elements in the corresponding virtual array are arranged in disorder. In order to obtain an ordered virtual array output, the elements in the reconstruction matrix R are rearranged to obtain the output matrix Q of the corresponding virtual uniform array. and It can be regarded as the guiding vector of the virtual array. The element position set of the virtual array is

[0044]

[0045] in addition, and The obtained elements and and The elements in are not completely consistent, so it is necessary to and Rearrange the elements in the matrix R to obtain the output of the corresponding uniform array

[0046]

[0047] in,

[0048]

[0049] for Steering vectors along the x- and y-axes, Reason and A uniform array composed of Z, where Z is the noise vector.

[0050] Furthermore, in step S5, the data from the first row to the second last row and the first column to the second last column of the output matrix Q are extracted to obtain a new matrix T. Here, the data from the first row to the second last row and the first column to the second last column of Q are extracted to weaken the correlation between T and its conjugate T*. The corresponding expression of T is:

[0051] T=Q(1:z x -1,1:z y -1)

[0052] Among them, z x is the number of rows in Q, z y is the number of columns of Q.

[0053] Further, in step S6, T and its conjugate T* are synthesized in the third dimension to obtain the tensor T* is the conjugate of T, and the expression can be written as

[0054]

[0055] in,

[0056]

[0057] Combined tensor The expression is

[0058]

[0059] Among them, υ(k)=[1,υ(u k ),υ(v k )] T is the symmetry factor, B x =[b(u1),b(u2),...,b(u K )],B y =[b(v1),b(v2),...,b(v K )], V = [υ(1),υ(2), ...,υ(K)] is the factor matrix, Signal energy The vector composed of 1≤k≤K, is the noise tensor.

[0060] Furthermore, in step S7, in order to increase the number of information sources that can be estimated by this method, the tensor Reconstruct the space and get a new tensor from Extract a sub-tensor from P x and P y is the length of the first and second dimensions of the subtensor, express The number of elements in express The number of elements in Finally, you can get L x L ysub-tensors, and the expression of the sub-tensor is

[0061]

[0062] Among them, 1≤l x ≤L x , 1≤l y ≤L y , and Represents the number of sub-tensors along the x-axis and y-axis respectively. Combine the obtained sub-tensors along the 4th dimension to obtain the tensor

[0063]

[0064] L y 4D tensor Connect along the 5th dimension to get a tensor

[0065]

[0066] in,

[0067]

[0068] C x =[c(u1),c(u2),...,c(u K )],C y =[c(v1),c(v2),...,c(v K )],G x =[g(u1),g(u1),...,g(u K )],G y =[g(v1),g(v1),...,g(v K )] is the tensor factor, is the noise tensor, υ(k)=[1,υ(u k ),υ(v k )] T .

[0069] Further, in step S8, the tensor Combine the dimensions that carry the same information in the tensor The {1,4}-dimensional and {2,5}-dimensional tensors are combined to obtain a new tensor Right now

[0070]

[0071] in,

[0072]

[0073]

[0074] is the noise tensor.

[0075] Furthermore, in step S9, the tensor Perform Canonical Polyadic decomposition (also called CP decomposition). CP decomposition can be performed using the existing toolbox tensor_toolbox or other tensor operation tools to obtain its factor matrices C, G, and V.

[0076] Furthermore, in step S10, the corresponding estimated parameters are obtained according to the obtained matrices C and G.

[0077]

[0078] Among them, ι1∈{[1,P x P y ],mod(ι1,P y )≠0}, ι1∈[1,P x P y -P x ],ι2∈[1,L x L y -L x ], ∠ is the phase operation, and mod(a,b) means the remainder of a / b.

[0079] In step S11, according to the obtained μ k and ν k , the final azimuth and elevation angles are estimated as

[0080] θ k =arctan(ν k / μ k )

[0081]

[0082] Among them, arctan(·) and arcsin(·) represent the inverse tangent and inverse sine operations.

[0083] By adopting the above technical solution, the present invention can also bring the following beneficial effects:

[0084] 1. The present invention mentions a two-dimensional angle estimation method based on tensor decomposition-related information enhancement. Different from the method of vectorizing the covariance matrix to obtain the difference covariance matrix and then performing angle estimation, it overcomes the defects of being unable to utilize the multi-dimensional information of the received data and only being able to consider the spatial and temporal domain information in a mixed manner. It can make full use of the multi-dimensional information of the array received data, construct a high-dimensional tensor output, and represent the spatial and temporal domain information of the received data in different dimensions.

[0085] 2. The two-dimensional angle estimation method based on tensor decomposition-based correlation information enhancement mentioned in the present invention is different from the existing tensor-based method in that it can only utilize the correlation information between sub-arrays of the array but cannot utilize the autocorrelation information of the sub-arrays. On the basis of utilizing the correlation information between the sub-arrays, it also utilizes the autocorrelation information of the sub-arrays, thereby giving full play to the statistical characteristics of the array received data and improving the angle estimation accuracy.

[0086] 3. The present invention makes the positioning of the target radiation source more accurate, thereby completing the tasks of searching, rescuing or attacking the target more accurately. In addition to being applicable to military fields such as radar electronic warfare, it can also be extended to civil and security fields, such as air traffic control, weather radar, marine ship monitoring, missing persons positioning and rescue, and unmanned driving, etc., and has broad application prospects and economic benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0088] Figure 1 A schematic flow chart of a two-dimensional angle estimation method based on tensor decomposition-related information enhancement provided in Example 1;

[0089] Figure 2 A schematic diagram of a nested array used in a two-dimensional angle estimation method for enhancing related information based on tensor decomposition provided in Example 1;

[0090] Figure 3 A schematic diagram of a uniform array corresponding to the matrix Q in a two-dimensional angle estimation method based on tensor decomposition-related information enhancement provided in Example 1; (where N1=N2=3 is set)

[0091] Figure 4 It is a performance diagram of the estimation of the azimuth angle θ under different signal-to-noise ratios (SNR) of a two-dimensional angle estimation method based on tensor decomposition-related information enhancement provided in Example 1;

[0092] Figure 5 A performance diagram of the pitch angle φ estimation method provided in Example 1 based on tensor decomposition and related information enhancement under different signal-to-noise ratios (SNRs);

[0093] Figure 6 This is a performance diagram of the estimation of the azimuth angle θ by a two-dimensional angle estimation method based on tensor decomposition and related information enhancement provided in Example 1 under different snapshot numbers;

[0094] Figure 7 This is a diagram showing the estimation performance of the pitch angle φ of a two-dimensional angle estimation method based on tensor decomposition and related information enhancement provided in Example 1 under different snapshot numbers. DETAILED DESCRIPTION

[0095] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0096] The following describes the embodiments of the present invention through specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the scope of protection of the present invention.

[0097] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on the present invention, it should be understood by those skilled in the art that an aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement the device and / or practice the method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this device and / or practice this method.

[0098] It should also be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention. The drawings only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0099] Additionally, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, it will be understood by those skilled in the art that the aspects described may be practiced without these specific details.

[0100] Example 1

[0101] In one embodiment of the present invention, see Figure 1-Figure 7 This embodiment provides a two-dimensional angle estimation method based on tensor decomposition-related information enhancement, including the following steps:

[0102] For the entire two-dimensional array receiving data matrix Reconstruct and get the corresponding tensor output

[0103] Find tensor The tensor related to

[0104] Combine the {1,3} and {2,4} dimensions of the relevant tensors to obtain the matrix R;

[0105] Rearrange the elements in the matrix R to obtain the output matrix Q corresponding to the uniform array;

[0106] Extract the data from the first row to the second to last row and the first column to the second to last column of the output matrix Q to obtain a new matrix T;

[0107] Synthesize T and its conjugate T* in the third dimension to get the tensor

[0108] For tensors Reconstruct the space and get a new tensor

[0109] The tensor The {1,4}-dimensional and {2,5}-dimensional tensors are combined to obtain a new tensor

[0110] The tensor Perform Canonical Polyadic decomposition to obtain its factor matrix C, G, V;

[0111] Divide and add the elements in each column of the factor matrix C and G in turn to obtain the parameters u and v;

[0112] The parameters u and v are combined to obtain the final azimuth and elevation angle estimates θ and φ.

[0113] In order to more clearly describe the method in this embodiment, a specific example is provided for illustration, which specifically includes:

[0114] Step 1: Consider a nested array such as Figure 1 As shown, it consists of two sub-arrays, where the sub-array is a 1-dimensional uniform array with an array element spacing of d = λ / 2, where λ is the wavelength of the incident signal. Assuming N1 = N2 = 3, the array element position set of the sub-array 1 is The element position set of sub-array 2 is The position set of the entire nested array is

[0115] Assume that three far-field uncorrelated signals are incident on the array, and the angles of the incident signals are (θ1, φ1) = (15.55°, 10.34°), (θ2, φ2) = (25.34°, 30.25°), (θ3, φ3) = (45.56°, 40.26°), where θ k is the azimuth, φ k is the pitch angle, k = 1, 2, 3. The vector representation of the array receiving signal at time t based on the matrix model is in

[0116]

[0117] Among them, u k = sinφ k cosθ k , v k = sinφ k sinθ k ,s k (t) is the output of the kth signal at time t, t = 1, 2, ..., T, T is the total number of snapshots of the signal, is an independent and identically distributed additive white Gaussian noise vector, is the noise energy, I is the unit matrix, is the Kronecker product,

[0118]

[0119] are the steering vectors of sub-array 1 along the x-axis and y-axis respectively, where u k = sinφ k cosθ k , v k = sinφ k sinθ k ,and

[0120]

[0121] are the steering vectors of sub-array 2 along the x-axis and y-axis respectively. To avoid loss of structural information, the output signal of the array at time t is represented as two independent matrices

[0122]

[0123] in, is the independent and identically distributed additive white Gaussian noise matrix, and I is the unit matrix. Connect the two matrices to get the total output matrix of the array

[0124]

[0125] T a quick shot Connect through the time domain dimension to obtain a three-dimensional tensor

[0126]

[0127] in, represents the outer product of the vector, C3 represents the connection of the tensor along the third dimension (time domain dimension), s k =[s k (1),s k (2),...,s k (T)] T is the signal vector, is the noise tensor.

[0128] Step 2: Obtain the correlation tensor of the entire array output. At this time, not only the mutual correlation information between the sub-arrays can be used, but also the autocorrelation information of the sub-arrays themselves can be used to increase the amount of useful information. The correlation tensor of the entire array output is

[0129]

[0130] in, is the energy of the kth signal, E{·} is the expected operation, is the noise tensor.

[0131] Step 3: The {1, 3}th dimension is combined with the {2, 4}th dimension, and the reconstructed matrix is ​​as follows

[0132]

[0133] Where N is the reconstructed noise term, is the signal energy.

[0134] Step 4: Rearrange the elements in the reconstruction matrix R to obtain the corresponding virtual array output. and It can be regarded as the guiding vector of the virtual array. The element position set of the virtual array is

[0135]

[0136] in addition, and The obtained elements and and The elements in are not completely consistent, so it is necessary to and Rearrange the elements in the matrix R to obtain the output of the corresponding uniform array

[0137]

[0138] in,

[0139]

[0140] for Steering vectors along the x- and y-axes, Reason and A uniform array composed of Z, where Z is the noise vector. Figure 3 The diagram shown is a schematic diagram of a virtual uniform array when N1=N2=3.

[0141] Step 5: Extract the data from the 1st to the 18th row and the 1st to the 18th column of Q to obtain the new matrix T, that is

[0142] T=Q(1:18,1:18) (12)

[0143] Among them, z x is the number of rows in Q, z y is the number of columns of Q.

[0144] Step 6: Synthesize T and its conjugate T* in the third dimension to obtain the tensor The expression of T* is

[0145]

[0146] in,

[0147]

[0148] Combined tensor The expression is

[0149]

[0150] Among them, υ(k)=[1,υ(u k ),υ(v k )] T is the symmetry factor, B x =[b(u1),b(u2),...,b(u K )],B y =[b(v1),b(v2),...,b(v K )], is a factor matrix, is the signal energy vector, is the noise tensor.

[0151] Step 7: Tensor Reconstruct the space and get a new tensor from A sub-tensor is proposed in Finally, 100 sub-tensors can be obtained, and the expression of the sub-tensor is

[0152]

[0153] Among them, 1≤l x ≤10 and 1≤l y ≤10 represents the number of sub-tensors along the x-axis and y-axis respectively. The obtained sub-tensors are combined along the fourth dimension to obtain the tensor

[0154]

[0155] Convert 10 4D tensors Connect along the 5th dimension to get a tensor

[0156]

[0157] in,

[0158]

[0159]

[0160] C x =[c(u1),c(u2),...,c(u K )],C y =[c(v1),c(v2),...,c(v K )],G x =[g(u1),g(u1),...,g(u K )],G y=[g(v1),g(v1),...,g(v K )] is the tensor factor, is the noise tensor, υ(k)=[1,υ(u k ),υ(v k )] T .

[0161] Step 8: Convert the tensor The {1,4}-dimensional and {2,5}-dimensional tensors are combined to obtain a new tensor ,Right now

[0162]

[0163] in,

[0164]

[0165] is the noise tensor.

[0166] Step 9: Convert the tensor Perform Canonical Polyadic decomposition using tensor_toolbox to obtain its factor matrices C, G, and V.

[0167] Step 10: According to the obtained matrices C and G, get the corresponding estimated parameters

[0168]

[0169] Among them, ι1∈{[1,100],mod(ι1,10)≠0}, ι1∈[1,90], ι2∈[1,90], ∠ is the phase operation, and mod(a,b) means the remainder of a / b.

[0170] Step 11: According to the obtained μ k and ν k , the final azimuth and elevation angles are estimated as

[0171] θ k =arctan(ν k / μ k )

[0172]

[0173] This embodiment carries out simulation experiment on the structure of this method. Figure 4-Figure 7 As shown, the specific simulation results are as follows: Figure 4 and Figure 5: This is a graph of the root mean square error (RMSE) of the azimuth angle θ and the elevation angle φ when the signal-to-noise ratio SNR changes with the embodiment method, where the angles of the incident target are (θ1, φ1) = (15.55°, 10.34°), (θ2, φ2) = (25.34°, 30.25°), (θ3, φ3) = (45.56°, 40.26°), the number of snapshots is 500, the signal-to-noise ratio changes from -10dB to 4dB, and the array parameters are N1 = N2 = 3.

[0174] It can be seen that for the azimuth angle θ, compared with the existing methods, the method of the present invention can obtain the best angle estimation accuracy, and for the pitch angle φ, the method of the present invention can obtain a better angle estimation structure.

[0175] Figure 6-Figure 7 The root mean square error (RMSE) of the azimuth angle θ and the pitch angle φ when the number of snapshots changes with the implementation method, the number of snapshots changes from 50 to 500, and the other parameters are Figure 4 Similarly, it can be seen that, for the azimuth angle θ, compared with the existing methods, the method of the present invention can always obtain the best angle estimation accuracy, and for the pitch angle φ, the method of the present invention can also obtain a better angle estimation result.

[0176] The results of the present invention significantly improve the estimation accuracy of the two-dimensional angle of the incident signal by the existing tensor decomposition method, and solve the problem that the existing tensor decomposition method can only use the mutual correlation information between the array sub-arrays but cannot use the autocorrelation information of the sub-arrays, so that the positioning of the target radiation source is more accurate, thereby more accurately completing the tasks of searching, rescuing or attacking the target.

[0177] In summary, the present invention proposes a two-dimensional angle estimation method based on tensor decomposition-related information enhancement, which mainly uses a two-dimensional non-uniform array to realize the two-dimensional angle estimation of the signal. It has the advantages of representing the spatial and temporal information of the received data in different dimensions, improving the angle estimation accuracy and locating the target radiation source more accurately.

[0178] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A two-dimensional angle estimation method based on tensor decomposition-related information enhancement, characterized in that: The following steps are involved: S1, for the entire two-dimensional array receiving data matrix Reconstruct and get the corresponding tensor output S2: In order to use the mutual correlation information between sub-surface arrays and the autocorrelation information of the sub-surface arrays themselves, find the correlation tensor of the tensor S3: Combine the dimensions with the same information in the matrix, that is, combine the {1,3} and {2,4} dimensions of the related tensors to obtain the matrix R; S4: Matrix R is the output of the corresponding virtual array. The elements of matrix R are rearranged to obtain the output matrix Q of the corresponding virtual uniform array. S5: extract the data from the first row to the second to last row and the first column to the second to last column of the output matrix Q to obtain a new matrix T; S6: Synthesize T and its conjugate T* in the third dimension to obtain the tensor S7: Tensor Reconstruct the space and get a new tensor S8: Tensor Combine the dimensions that carry the same information in the tensor The {1,4}-dimensional and {2,5}-dimensional tensors are combined to obtain a new tensor S9: Tensor Perform Canonical Polyadic decomposition to obtain its factor matrix C, G, V; S10: Divide and add the elements in each column of the factor matrices C and G in turn to obtain parameters u and v; S11: Merge the parameters u and v to obtain the final azimuth and elevation angle estimates θ and φ.

2. A two-dimensional angle estimation method based on tensor decomposition and related information enhancement as claimed in claim 1, characterized in that: In step S1, the nested array is composed of two sub-arrays, where sub-array 1 is a uniform array, the array element spacing is d=λ / 2, λ is the wavelength of the incident signal, and the array element position set is Among them, N1 is the number of array elements of sub-array 1 on the x and y axes, and sub-array 2 is a sparse array with an array element spacing of N1d. Its array element position set is The element position set of the entire nested array is K far-field uncorrelated narrowband signals are injected into the array, and θ k ∈[-π / 2,π / 2] and φ k ∈[0,π] represents the azimuth and elevation angles of the kth signal, 1≤k≤K, and the vector of the array receiving signal at time t based on the matrix model is expressed as in are the output vectors of the two sub-surface matrices of the nested surface at time t, and their expressions are: Among them, u k = sinφ k cosθ k , v k = sinφ k sinθ k ,s k (t) is the output of the kth signal at time t, t = 1, 2, ..., T, T is the total number of snapshots of the signal, is an independent and identically distributed additive white Gaussian noise vector, is the noise energy, I is the unit matrix, is the Kronecker product, and are the steering vectors of sub-array 1 along the x-axis and y-axis respectively, and their expressions are: Among them, u k = sinφ k cosθ k , v k = sinφ k sinθ k ; and are the steering vectors of sub-array 2 along the x-axis and y-axis respectively, and their expressions are: To avoid loss of structural information, the output signal of the array at time t is represented as two independent matrices: in, is an independent and identically distributed additive white Gaussian noise matrix. The output matrices of the two sub-arrays are connected to obtain the total output matrix of the entire array. T a quick shot Connect through the time domain dimension to obtain a three-dimensional tensor in, represents the outer product of the vector, C3 represents the connection of the tensor along the third dimension (time domain dimension), s k =[s k (1),s k (2),...,s k (T)] T is the signal vector, is the noise tensor.

3. A two-dimensional angle estimation method based on tensor decomposition and related information enhancement as claimed in claim 2, characterized in that: In step S2, the relevant tensor of the entire array is in, is the energy of the kth signal, E{·} is the expected operation, is the noise tensor.

4. A two-dimensional angle estimation method based on tensor decomposition and related information enhancement as claimed in claim 3, characterized in that: In step S3, The {1, 3}th dimension is combined with the {2, 4}th dimension, and the reconstructed matrix is ​​as follows Where N is the reconstructed noise term, is the signal energy.

5. A two-dimensional angle estimation method based on tensor decomposition and related information enhancement as claimed in claim 4, characterized in that: In the step S4, and is the guiding vector of the virtual array, and the element position set of the virtual array is Rearrange the elements in the matrix R to obtain the output Q corresponding to the uniform array in, for Steering vectors along the x- and y-axes, Reason and A uniform array composed of Z, where Z is the noise vector.

6. A two-dimensional angle estimation method based on tensor decomposition and related information enhancement as claimed in claim 5, characterized in that: In step S5, the expression of the new matrix T is: T=Q(1:z x -1,1:z y -1) Among them, z x is the number of rows in Q, z y is the number of columns of Q.

7. A two-dimensional angle estimation method based on tensor decomposition and related information enhancement as claimed in claim 6, characterized in that: In step S6, the conjugate of T is T*, and the expression of T* is: in, Combined tensor The expression is Among them, υ(k)=[1,υ(u k ),υ(v k )] T is the symmetry factor, B x =[b(u1),b(u2),...,b(u K )],B y =[b(v1),b(v2),...,b(v K )], V = [υ(1),υ(2), ...,υ(K)] is the factor matrix, Signal energy The vector composed of 1≤k≤K, is the noise tensor.

8. A two-dimensional angle estimation method based on tensor decomposition and related information enhancement as claimed in claim 7, characterized in that: In step S7, Extract a sub-tensor from P x and P y is the length of the first and second dimensions of the subtensor, express The number of elements in express The number of elements in Finally, you can get L x L y sub-tensors, and the expression of the sub-tensor is Among them, 1≤l x ≤L x , 1≤l y ≤L y , and Represents the number of sub-tensors along the x-axis and y-axis respectively. The obtained sub-tensors are combined along the fourth dimension to obtain the tensor L y 4D tensor Connect along the 5th dimension to get a tensor in, C x =[c(u1),c(u2),...,c(u K )],C y =[c(v1),c(v2),...,c(v K )],G x =[g(u1),g(u1),...,g(u K )],G y =[g(v1),g(v1),...,g(v K )] is the tensor factor, is the noise tensor, υ(k)=[1,υ(u k ),υ(v k )] T .

9. A two-dimensional angle estimation method based on tensor decomposition and related information enhancement as claimed in claim 8, characterized in that: In step S8, the new tensor The expression is in, is the noise tensor.

10. A two-dimensional angle estimation method based on tensor decomposition and related information enhancement as claimed in claim 9, characterized in that: In step S10, the expressions of parameters u and v are: Among them, ι1∈{[1,P x P y ],mod(ι1,P y )≠0}, In step S11, the final azimuth and pitch angles are i k =arctan(n k / m k ) Among them, arctan(·) and arcsin(·) represent the inverse tangent and inverse sine operations.

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