Method for estimating direction of arrival of coherent signal sources based on reconstruction of decorrelated covariance tensor

Abstract

The present invention discloses a method for estimating the direction of arrival (DOA) of coherent signal sources based on the reconstruction of a decorrelated covariance tensor, which mainly solves the problem of the sharp decline in the performance of tensor DOA estimation caused by the non-ideal scenario of coherent signals, as well as the problems of low decorrelation efficiency and poor effect of existing methods on the tensor statistics of multi-dimensional coherent signals. The implementation steps are as follows: constructing a uniform planar array symmetric about the origin of the coordinate system; tensor modeling of coherent signals; derivation of the covariance tensor of coherent signals and construction of the tensorized Hermitian Toeplitz mapping relationship; structured reconstruction of the decorrelated covariance tensor; obtaining the DOA estimation result through the canonical polyadic decomposition of the decorrelated covariance tensor. Without the need to introduce spatial smoothing, the present invention directly reconstructs the decorrelated covariance tensor by using the structured mapping of the covariance tensor of coherent signals, realizing high-efficiency and high-precision two-dimensional DOA estimation of coherent signals, and can be used for target direction finding and positioning in a multipath environment.

Description

Technical Field

[0001] The present invention belongs to the technical field of array signal processing, and particularly relates to the high-dimensional tensor statistical signal processing technology for coherent signal sources. Specifically, it is a method for estimating the direction of arrival (DOA) of coherent signal sources based on the reconstruction of the decorrelated covariance tensor, which can be used for target direction finding and positioning in multipath environments. Background Art

[0002] In various applications such as radar, sonar, wireless communication, medical imaging, and radio astronomy, DOA estimation is a core technology for target direction finding, positioning, navigation, and imaging. However, in the actual environment, due to path scattering during the propagation of target signal sources, the sensor array will receive multiple coherent signals generated after the target signal sources have undergone multipath attenuation. The statistical distributions corresponding to these coherent signals are not independent of each other, resulting in a rank deficiency problem in the high-order statistics of the signals received by the array. Therefore, traditional DOA estimation methods for incoherent signals, such as MUSIC, ESPRIT, etc., cannot effectively perform statistical processing on coherent signals. To decorrelate the statistics of coherent signals, methods such as spatial smoothing and Toeplitz matrix reconstruction are used to perform rank compensation on the statistics of coherent signals to construct a full-rank decorrelated covariance matrix, and then to estimate the DOA of coherent signals. However, with the innovation of application scenarios, the dimension of the signals sensed by the sensor array is continuously increasing, and the existing methods mainly use vectors and matrices for signal modeling and processing, which cannot retain the original features of multi-dimensional signals, resulting in performance loss in DOA estimation.

[0003] To retain the structural information of multi-dimensional received signals, tensors, as a multi-dimensional extension form of vectors and matrices, have begun to be applied to the field of array signal processing. By using tensors to model the received signals covering multi-dimensional spatio-temporal information and performing feature analysis and spatial information extraction on tensor signals, high-precision and high-resolution DOA estimation can be achieved. For the problem of DOA estimation of multi-dimensional coherent signals, the tensor spatial smoothing method extends the traditional spatial smoothing idea to the high-dimensional space, uses a smoothing window to sequentially translate and intercept the multi-dimensional coherent signals, and averages the high-order covariance tensors of the intercepted signals to solve the rank deficiency problem of the tensor statistics of coherent signals. However, this tensor decorrelation method needs to repeatedly introduce high-order tensor statistical calculations of multi-dimensional coherent signals, which not only brings higher computational complexity, but also introduces additional high-order statistical errors due to the accumulation of the high-order covariance tensors of the intercepted signals, and there are obvious performance defects in both the efficiency and accuracy of DOA estimation. Therefore, there is an urgent need to propose a more effective tensor decorrelation method to achieve high-precision and high-efficiency DOA estimation of multi-dimensional coherent signals. Summary of the Invention

[0004] The object of the present invention is to address the problems of low decoherence efficiency and poor effect in the statistical measures of multi-dimensional coherent signal tensors in existing methods, and to propose a method for estimating the direction of arrival (DOA) of coherent signal sources based on the reconstruction of decoherent covariance tensors. This method provides a feasible idea and an effective solution for directly reconstructing the decoherent covariance tensor by utilizing the prior structural characteristics of the statistical measures of coherent signal tensors, and achieving high-efficiency and high-precision two-dimensional DOA estimation of coherent signals.

[0005] The object of the present invention is achieved by the following technical solutions: A method for estimating the direction of arrival of coherent signal sources based on the reconstruction of decoherent covariance tensors, the method comprising the following steps:

[0006] (1) The receiving end uses (2M + 1)×(2N + 1) physical antenna elements to construct a uniform planar array symmetric about the origin of the coordinate system.

[0007] (2) Assume there are K far-field narrowband coherent signal sources from the directions of {(θ1, φ1), (θ2, φ2), …, (θ K , φ K )}, where θ k and φ k are respectively the azimuth angle and elevation angle of the k-th incident signal source, k = 1, 2, …, K; these K signal sources have coherence characteristics, that is, the statistical distributions of the signal waveforms they correspond to are not independent of each other. Specifically, the f snapshot sampling signal waveforms of the first signal source are expressed as and used as the reference signal source, then the signal waveform of the k-th signal source is expressed as:

[0008] S k = α k s1,

[0009] where the complex constant α k is the path attenuation factor corresponding to the k-th coherent signal source, and α1 = 1;

[0010] Stack the T snapshot sampling signals of the uniform planar array in the third dimension to obtain a three-dimensional coherent signal tensor which is modeled as:

[0011]

[0012] where, represents the vector outer product, is the noise tensor independent of each signal source, and a(μ k ) and a(v k ) are respectively the steering vectors of in the x-axis and y-axis directions, expressed as:

[0013]

[0014]

[0015] wherein, μ k = sin(φ k )cos(θ k ), v k = sin(φ k )sin(θ k ); [·]T represents the transpose operation;

[0016] (3) Calculate the autocorrelation statistic of the three-dimensional coherent signal tensor to obtain the second-order covariance tensor

[0017]

[0018] wherein, represents the power of the reference signal source, represents the noise power, represents the four-dimensional unit tensor, <·, ·> r represents the tensor contraction operation of two tensors along the r-th dimension, E[·] represents the mathematical expectation operation, (·) * represents the conjugate operation; The elements in

[0019]

[0020] are expressed as:

[0021]

[0022] represents the amplitude parameter, and m, m' ∈ [1, 2M + 1], n, n' ∈ [1, 2N + 1];

[0023] When the signal waveform statistical distributions of the signal sources are mutually independent, the corresponding incoherent signal covariance tensor is expressed in the form of a canonical polyadic tensor of rank K, that is, the accumulation of the outer product terms of the steering vectors corresponding to each of the K signals, and the elements therein satisfy the following tensorized Hermitian Toeplitz mapping relationship:

[0024]

[0025]

[0026] where However, due to the coherent characteristics of the K signal sources, the derived covariance tensor of coherent signals contains the cross outer product terms of the steering vectors corresponding to different signal sources, resulting in that this covariance tensor cannot be expressed in the form of a canonical polyadic tensor of rank K, and the elements in

[0027]

[0028]

[0029] (4) Arrange any slice with index (m, n, :, :) in according to the tensorized Hermitian Toeplitz mapping relationship, and directly reconstruct a structured tensor The reconstruction process is as follows:

[0030]

[0031] where i, i′ ∈ [1, M + 1], j, j′ ∈ [1, N + 1]; is expressed as:

[0032]

[0033] where Thus, the constructed structured tensor is equivalent to the decorrelated covariance tensor of a uniform planar array where d is half of the wavelength λ of the incident narrowband signal, i.e., and is expressed in the following canonical polyadic tensor form of rank K:

[0034]

[0035] where,

[0036]

[0037]

[0038] are respectively the steering vectors in the x-axis and y-axis directions, is the noise term, and its elements are expressed as:

[0039]

[0040] ​(5) Perform a canonical polyadic decomposition on the decorrelated covariance tensor to obtain the estimated values of the steering vectors q(μ k ) and q(v k ), denoted as and and extract the angle parameters from their exponential terms to obtain the two-dimensional direction-of-arrival estimation results of the coherent signals

[0041] Furthermore, the uniform planar array structure symmetric about the origin of the coordinate system described in step (1) is specifically described as: construct a uniform planar array symmetric about the origin of the coordinate system on the plane coordinate system xoy whose array element position coordinates on xoy are {(x, y)|x = [-M, M]d, y = [-N, N]d}, and the number of array elements is (2M + 1)×(2N + 1).

[0042] Furthermore, in step (3), the derivation of the covariance tensor of the coherent signals, in practice, is approximately obtained by calculating the autocorrelation statistic of the three-dimensional coherent signal tensor , that is, the sampling covariance tensor of the coherent signals

[0043]

[0044] Furthermore, in step (5), perform a canonical polyadic decomposition on the decorrelated covariance tensor to obtain the estimated values of the steering vectors q(μ k ) and q(v k ) and Then the parameters and are extracted from and as follows:

[0045]

[0046]

[0047] where, ∠(·) represents the operation of taking the argument of a complex number, and represent the m-th element of the steering vector and the n-th element of k , respectively; according to the parameters (μ k , v k , φ k) The relationship between them gives the two-dimensional direction of arrival (DOA) estimation The closed-form solution is:

[0048]

[0049]

[0050] Furthermore, in step (5), the canonical polyadic decomposition of the decorrelated covariance tensor needs to satisfy the Kruskal condition:

[0051]

[0052] where denotes the Kruskal rank of the matrix, and min(·) represents the minimum operation; the above Kruskal condition is transformed into:

[0053] 2min(M + 1, K)+2min(N + 1, K)≥2K + 3,

[0054] and then we get Thus, the maximum number of coherent signal sources that can be resolved by the method proposed in the present invention is M + N.

[0055] The present invention has the following advantages compared with the prior art:

[0056] (1) Based on the analysis of the structural characteristics of the multi-dimensional coherent signal tensor statistics, the present invention constructs a mapping relationship and a direct reconstruction method from the coherent signal covariance tensor to the decorrelated covariance tensor, avoiding the introduction of a complex tensor space smoothing calculation process, and providing a basis for realizing high-efficiency and high-precision coherent signal direction of arrival estimation;

[0057] (2) The present invention proposes an angle information extraction method for the decorrelated covariance tensor, and obtains the closed-form solution of the two-dimensional direction of arrival of the coherent signal through the decomposition of the decorrelated covariance tensor, realizing the two-dimensional direction of arrival estimation of the coherent signal, and having the performance advantages of low complexity and high precision. Brief Description of the Drawings

[0058] Figure 1 is the overall flow block diagram of the present invention.

[0059] Figure 2 is the schematic diagram of the uniform planar array structure symmetric about the origin of the coordinate system constructed by the present invention.

[0060] Figure 3 is the comparison diagram of the two-dimensional direction of arrival estimation accuracy performance of the coherent signal under different signal-to-noise ratio conditions of the method proposed by the present invention.

[0061] Figure 4 It is a comparison diagram of the coherent signal two-dimensional direction-of-arrival estimation accuracy performance of the method proposed by the present invention under different sampling snapshot numbers. Specific implementation manners

[0062] The technical solution of the present invention will be further described in detail with reference to the accompanying drawings below.

[0063] To solve the problems of low decoherence efficiency and poor effect of the multi-dimensional coherent signal tensor statistic in the existing methods, the present invention proposes a method for estimating the direction of arrival of coherent signal sources based on the reconstruction of the decoherence covariance tensor. Without introducing the tensor space smoothing process, the decoherence covariance tensor is directly reconstructed to achieve high-efficiency and high-precision two-dimensional direction-of-arrival estimation of coherent signals. Refer to Figure 1 The implementation steps of the present invention are as follows:

[0064] Step 1: Construct a uniform planar array symmetric about the origin of the coordinate system. At the receiving end, use (2M + 1)×(2N + 1) physical antenna elements to construct a uniform planar array symmetric about the origin of the coordinate system, as Figure 2 shown: Construct a uniform planar array symmetric about the origin of the coordinate system on the xoy plane of the planar coordinate system whose array element position coordinates on the xoy are {(x, y)|x = [-M, M]d, y = [-N, N]d}, and the number of array elements is (2M + 1)×(2N + 1); where the array element spacing d is taken as half of the wavelength λ of the incident narrowband signal, that is

[0065] Step 2: Tensor modeling of coherent signals. Assume that there are K far-field narrowband coherent signal sources from {(θ1, φ1), (θ2, φ2), …, (θ K , φ K )}, θ k and φ k are the azimuth angle and elevation angle of the k-th incident signal source respectively, k = 1, 2, …, K; since these K signal sources have coherent characteristics, the statistical distributions of the signal waveforms corresponding to them are not independent of each other; specifically, represent the T snapshot sampling signal waveforms of the first signal source as and use it as the reference signal source, then the signal waveform of the k-th signal source is represented as:

[0066] s k = α k s1,

[0067] where the complex constant α k is the path attenuation factor corresponding to the k-th coherent signal source, and α1 = 1.

[0068] Stack the T sampled snapshot signals of the uniform planar array in the third dimension to obtain a three-dimensional coherent signal tensor modeled as:

[0069]

[0070] where denotes the vector outer product, is the noise tensor independent of each signal source, a(μ k ) and a(v k ) are the steering vectors in the x-axis and y-axis directions respectively, expressed as:

[0071]

[0072]

[0073] where μ k = sin(φ k )cos(θ k ), v k = sin(φ k )sin(θ k ), [·]T represents the transpose operation;

[0074] Step 3: Coherent signal covariance tensor derivation and construction of the tensorized Hermitian Toeplitz mapping relationship. By finding the autocorrelation statistic of the three-dimensional coherent signal tensor obtain the second-order covariance tensor

[0075]

[0076] where represents the power of the reference signal source, represents the noise power, represents the four-dimensional identity tensor, <·,·> r represents the tensor contraction operation of two tensors along the r-th dimension, E[·] represents the mathematical expectation operation, (·) * represents the conjugate operation. The elements in can be expressed as:

[0077]

[0078] where

[0079]

[0080] denotes the amplitude parameter, and \(m, m'\in[1, 2M + 1]\), \(n, n'\in[1, 2N + 1]\). In practice, by calculating the autocorrelation statistic of the coherent signal tensor it is approximately obtained, that is, the coherent signal sampling covariance tensor

[0081]

[0082] When the statistical distributions of the signal waveforms of the signal sources are mutually independent, the corresponding incoherent signal covariance tensor can be expressed in the form of a canonical polyadic tensor of rank \(K\), that is, the accumulation of the outer product terms of the steering vectors corresponding to each of the \(K\) signals, and the elements in satisfy the following tensorized Hermitian Toeplitz mapping relationship:

[0083]

[0084]

[0085] where, However, due to the coherent characteristics of the \(K\) signal sources, the derived coherent signal covariance tensor contains the cross outer product terms of the steering vectors corresponding to different signal sources, resulting in that this covariance tensor cannot be expressed in the form of a canonical polyadic tensor of rank \(K\), having the problem of tensor rank deficiency. And, since does not have a canonical polyadic structure, the elements in do not satisfy the mapping relationship of tensorized Hermitian Toeplitz, that is:

[0086]

[0087]

[0088] Step 4: Solve the structured reconstruction of the decoherent covariance tensor. To solve the tensor rank deficiency problem of the coherent signal covariance tensor , arrange any slice with the index \((m, n, :, :)\) in according to the tensorized Hermitian Toeplitz mapping relationship, and directly reconstruct a structured tensor The specific operation is: arrange the elements in according to the following relationship to obtain

[0089] ​

[0090] Among them, \(i, i'\in[1, M + 1]\), \(j, j'\in[1, N + 1]\). According to the above arrangement form, It can be expressed as:

[0091]

[0092] Among them Thus, is equivalent to the decorrelation covariance tensor of a uniform planar array and can be expressed in the form of a canonical polyadic tensor of rank \(K\) as follows:

[0093]

[0094] Among them,

[0095]

[0096]

[0097] are the steering vectors of the uniform planar array in the \(x\)-axis and \(y\)-axis directions respectively, is the noise term, and the elements in it are expressed as:

[0098]

[0099] Thus, without introducing tensor space smoothing, the decorrelation covariance tensor of rank \(K\) is directly reconstructed,

[0100] Step 5: Obtain the direction-of-arrival estimation result through the canonical polyadic decomposition of the decorrelation covariance tensor. Since the decorrelation covariance tensor is a canonical polyadic tensor of rank \(K\), performing canonical polyadic decomposition on it can obtain the estimated values of the steering vectors \(q(\mu k )\) and \(q(v k )\), expressed as and Then the parameters and can be extracted from and as follows:

[0101]

[0102]

[0103] where ∠(·) represents the operation of taking the argument of a complex number, and represent the m-th element of the steering vector and the n-th element of k , v k ), respectively. According to the relationship between the parameters (μ k , φ k ) and the two-dimensional direction of arrival (θ ), the closed-form solution of the two-dimensional direction of arrival estimation is:

[0104]

[0105]

[0106] According to the Kruskal condition of the tensor canonical polyadic decomposition, the canonical polyadic decomposition of the decoherent covariance tensor needs to satisfy the following inequality:

[0107]

[0108] where represents the Kruskal rank of the matrix, and min(·) represents the operation of taking the minimum value. The above inequality condition can be transformed into:

[0109] 2min(M + 1, K) + 2min(N + 1, K) ≥ 2K + 3,

[0110] and then Thus, the maximum number of coherent signal sources that can be resolved by the method proposed in the present invention is M + N.

[0111] The following further describes the effect of the present invention in combination with simulation examples.

[0112] Simulation example: The incident signals are received by a uniform planar array symmetric about the origin of the coordinate system. The parameters are selected as M = 3 and N = 3, that is, the uniform planar array of the architecture contains 49 physical array elements in total. Assume that there are 2 incident coherent signal sources, and the azimuth angles and elevation angles of the incident directions are [25.4°, 30.4°] and [45.8°, 40.8°] respectively. The path attenuation factor α2 corresponding to the second signal source is randomly generated in the form of a Gaussian distribution, with a mean of 0 and a variance of 1. Compare the method for estimating the direction of arrival of coherent signal sources based on the reconstruction of the decoherent covariance tensor proposed in the present invention with the traditional tensor space smoothing method. Under the condition that the number of sampling snapshots T = 100, plot the performance comparison curve of the root-mean-square error (RMSE) varying with the signal-to-noise ratio SNR, as Figure 3 shown; Under the condition of SNR = 0dB, plot the performance comparison curve of RMSE varying with the number of sampling snapshots T, as Figure 4 shown.

[0113] From Figure 3 and Figure 4 the comparison results, it can be seen that the method proposed in the present invention has performance advantages in the accuracy of direction-of-arrival estimation, whether in different signal-to-noise ratio SNR scenarios or in different sampling snapshot number T scenarios. The performance advantage of the method proposed in the present invention comes from directly constructing the decoherent covariance tensor through structured tensor reconstruction, without the need to repeatedly calculate the tensor statistics of coherent signals and perform averaging processing, effectively avoiding the introduction of additional high-order statistical errors.

[0114] In summary, the present invention realizes the direct reconstruction of the decoherent covariance tensor by constructing a tensorized Hermitian Toeplitz mapping relationship, and further realizes the high-precision and high-efficiency two-dimensional direction-of-arrival estimation of coherent signal sources based on the decomposition of the decoherent covariance tensor.

[0115] The above is only the preferred embodiment of the present invention. Although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make many possible changes and modifications to the technical solution of the present invention, or modify it into an equivalent embodiment with equivalent changes, without departing from the scope of the technical solution of the present invention. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention still fall within the scope of the protection of the technical solution of the present invention.

Claims

1. A method for estimating the direction of arrival of coherent signal sources based on the reconstruction of de - correlated covariance tensors, characterized in that, including the following steps: (1) The receiving end uses (2M + 1) × (2N + 1) physical antenna elements to construct a uniform planar array symmetric about the origin of the coordinate system (2) Suppose there are K far-field narrowband coherent signal sources from {($\theta_1$, $\varphi_1$), ($\theta_2$, $\varphi_2$), …, ($\theta$ K , $\varphi$ K )}, where $\theta$ k and $\varphi$ k are the azimuth angle and elevation angle of the k-th incident signal source respectively, and k = 1, 2, …, K; these K signal sources have coherent characteristics, that is, the statistical distributions of the signal waveforms they correspond to are not independent of each other. Specifically, represent the T snapshot sampling signal waveforms of the first signal source as and use it as the reference signal source, then the signal waveform of the k-th signal source is represented as: s k = α k s1, where the complex constant α k is the path attenuation factor corresponding to the k-th coherent signal source, and α1 = 1; Stack the T snapshot sampling signals of the uniform planar array in the third dimension to obtain a three-dimensional coherent signal tensor which is modeled as: Among them, represents the vector outer product, is the noise tensor independent of each signal source, a(μ k ) and a(v k ) are respectively the steering vectors in the x-axis and y-axis directions, expressed as: where, μ k = sin(φ k )cos(θ k ), v k = sin(φ k )sin(θ k ), [·] T denotes the transpose operation; (3) Calculate the autocorrelation statistic of the three-dimensional coherent signal tensor to obtain the second-order covariance tensor Among them, represents the power of the reference signal source, represents the noise power, represents a four-dimensional unit tensor, <·,·> r represents the tensor contraction operation of two tensors along the r-th dimension, E[·] represents the mathematical expectation operation, (·) * represents the conjugate operation; The elements in are expressed as: wherein, Represents the amplitude parameter, and m, m′ ∈ [1, 2M + 1], n, n′ ∈ [1, 2N + 1]; When the signal waveform statistical distributions of the signal sources are mutually independent, the corresponding non-coherent signal covariance tensor is expressed in the form of a canonical polyadic tensor of rank K, that is, the accumulation of the outer product terms of the steering vectors corresponding to each of the K signals, and the elements therein satisfy the following tensorized Hermitian Toeplitz mapping relationship: Among them However, since the K signal sources have coherent characteristics, the derived covariance tensor of coherent signals contains the cross outer product terms of the steering vectors corresponding to different signal sources, resulting in that the covariance tensor cannot be expressed in the form of a canonical polyadic tensor of rank K, and the elements in do not satisfy the tensorized Hermitian Toeplitz mapping relationship, that is: (4) Take any slice with index (m, n, ∶, ∶) in and arrange it according to the tensorized Hermitian Toeplitz mapping relationship to directly reconstruct a structured tensor The reconstruction process is shown as follows: where \(i, i'\in[1, M + 1]\) and \(j, j'\in[1, N + 1]\); It is expressed as: Among them Thus, the constructed structured tensor is equivalent to the decorrelated covariance tensor of a uniform planar array where d is half of the wavelength λ of the incident narrowband signal, that is and is expressed in the following canonical polyadic tensor form of rank K: wherein, respectively the guiding vectors in the x-axis and y-axis directions is the noise term, and its elements are expressed as: (5) Perform canonical polyadic decomposition on the decorrelated covariance tensor to obtain the estimated values of the steering vectors q(μ k ) and q(ν k ), denoted as and and extract the angle parameters from their exponential terms to obtain the two-dimensional direction-of-arrival estimation result of the coherent signals 2. The method for estimating the direction of arrival of coherent signal sources based on the reconstruction of decoherent covariance tensor according to claim 1, characterized in that The specific description of the uniform planar array structure symmetric about the origin of the coordinate system in step (1) is as follows: A uniform planar array symmetric about the origin of the coordinate system is constructed on the plane coordinate system xoy. The coordinate positions of the array elements on xoy are {(x, y)|x = [-M, M]d, y = [-N, N]d}, and the number of array elements is (2M + 1) × (2N + 1).

3. The method for estimating the direction of arrival of coherent signal sources based on the reconstruction of decorrelated covariance tensors according to claim 1, characterized in that, The derivation of the covariance tensor of coherent signals described in step (3), in practice, is approximately obtained by calculating the autocorrelation statistic of the three-dimensional coherent signal tensor , that is, the sampling covariance tensor of coherent signals 4. The method for estimating the direction of arrival of coherent signal sources based on the reconstruction of de - correlated covariance tensors according to claim 1, wherein, In step (5), the decorrelated covariance tensor is subjected to canonical polyadic decomposition to obtain the estimated values of the steering vectors q(μ k ) and q(ν k ): and Then the parameters and are extracted from and as follows: where, ∠(·) represents the operation of taking the argument of a complex number, and represent the m-th element of the steering vector and the n-th element of respectively; according to the relationship between the parameters (μ k , v k ) and the two-dimensional direction of arrival (θ k , φ k ), the closed-form solution of the two-dimensional direction of arrival estimation is:

5. The method for estimating the direction of arrival of coherent signal sources based on the reconstruction of the decoherent covariance tensor according to claim 1, wherein In step (5), the canonical polyadic decomposition of the decorrelated covariance tensor needs to satisfy the Kruskal condition: Among them, represents the Kruskal rank of the matrix, and min(·) represents the minimum value operation; the above Kruskal condition is transformed into: 2min(M + 1, K)+2min(N + 1, K)≥2K + 3, Furthermore, we obtain Thus, the maximum number of coherent signal sources that can be resolved is M + N.

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