A distributed source-aware approach

Abstract

The application relates to a distributed source sensing method and belongs to the technical field of array signal processing. The application firstly constructs a steering vector dictionary matrix and a power distribution matrix, then constructs an optimization problem model based on the above matrix, and finally obtains the power distribution of the distributed source through model solving, and the direction of arrival of the source is obtained through the mapping relationship between the power and the angle. The application can realize the direction finding sensing of the distributed source under the condition that the number of the source is unknown, and further improves the engineering applicability of the direction finding sensing algorithm.

Description

Technical Field

[0001] The present invention relates to the technical field of array signal processing, and in particular to a distributed information source perception method. Background Art

[0002] When performing direction finding perception for distributed sources, DOA estimation algorithms that support multiple sources, such as subspace fitting and MUSIC, are often used. These algorithms are all considered super-resolution direction finding technologies. By successfully overcoming the Rayleigh limit, they significantly improve spatial resolution compared to traditional direction finding methods, offering unique technical advantages.

[0003] However, when solving the above algorithm, the exact number of signal sources needs to be known in advance. Otherwise, information leakage will occur when spanning the signal subspace and the noise subspace, resulting in pseudo-peaks that interfere with the estimation of the source wave direction. Summary of the Invention

[0004] In view of this, the present invention proposes a distributed information source perception method, which can achieve direction finding perception of distributed information sources when the number of information sources is unknown.

[0005] The purpose of the present invention is achieved by the following technical solutions:

[0006] A distributed information source sensing method includes the following steps:

[0007] Step 1: Obtain the array received signal and calculate the time average estimation matrix of the covariance matrix using a finite number of sampling samples:

[0008] ,

[0009] in, is the time average estimation matrix of the covariance matrix R, N is the number of sampling points, represents the array receiving signal, and the superscript H represents the conjugate transpose;

[0010] Step 2: Construct the steering vector dictionary matrix and power distribution matrix respectively; the steering vector dictionary matrix is:

[0011]

[0012] The power distribution matrix is:

[0013]

[0014] in, is the directional vector dictionary matrix, is the power distribution matrix, Except for the diagonal elements, all other positions are 0, K is the number of airspace grids, that is, the reconnaissance airspace range Φ is divided into K airspace angles Ψ1, Ψ2,…, ΨK , is the steering vector of the kth spatial angle; M is the number of array elements; is an M×M-order identity matrix; the superscript T indicates the matrix transpose; is the signal power of the source corresponding to K spatial angles. If a spatial angle Ψ i If there is no signal source, then the corresponding is 0; is the received noise power corresponding to M array elements;

[0015] Step 3: Construct the optimization problem model based on the time-averaged estimation matrix of the covariance matrix, the steering vector dictionary matrix, and the power distribution matrix:

[0016] Step 4: Use the CVX toolkit to solve the optimization problem model, obtain the incoming wave angle and noise power of the distributed signal source, and complete distributed signal source perception.

[0017] Furthermore, the specific method of step 3 is:

[0018] Step 301: Construct the matrix G, the element in the i-th row and j-th column of the matrix G for:

[0019] ,

[0020] in, express For the element in row i and column j, |•| represents the modulo value;

[0021] Step 302: Construct vector q, the i-th element in vector q for:

[0022] ,

[0023] in, express The element in the i-th row and i-th column of , that is, the i-th diagonal element;

[0024] Step 303: Construct vector p, the i-th element of vector p for:

[0025] ,

[0026] in, Representation matrix The element in the i-th row and i-th column of , that is, the i-th diagonal element;

[0027] Step 304: Constructing an optimization problem model:

[0028] ,

[0029] in, Expressing a request Take the minimum value of p; 、 is a hyperparameter, a constant real number; To find the second-order norm; To find the first-order norm of y; To solve the condition, all elements in the vector p are required to be positive real numbers.

[0030] Furthermore, in step 4, the optimization problem model is solved by the cvx toolkit to obtain the vector p; each of the first K elements of the vector p The corresponding angle Ψ i That is, it is the angle of arrival of the i-th distributed signal source, and the last M elements of the vector p are the noise power of the corresponding array element.

[0031] Compared with the prior art, the present invention has the following advantages:

[0032] 1. Compared with the spatial spectrum direction finding algorithm, the present invention does not need to predict the number of signal sources.

[0033] 2. Compared with the traditional sparse direction finding algorithm, the present invention makes full use of the number of sampling snapshots and improves the robustness of fitting through statistical stability.

[0034] 3. The present invention can simultaneously estimate the received power of the noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a diagram of the solution results of the present invention when the number of information sources is unknown and the orientations of the three distributed information sources are 30°, 65°, and 98° respectively.

[0036] Figure 2 This is a diagram of the solution results of the present invention when the number of information sources is unknown and the orientations of the four distributed information sources are 30°, 65°, 98° and 140° respectively. DETAILED DESCRIPTION

[0037] The technical solution of the present invention is further described in detail below with reference to the accompanying drawings.

[0038] A distributed source sensing method, under the condition of unknown number of new sources, obtains an estimated covariance matrix from sampled snapshot data. First, a steering vector dictionary matrix and a power distribution matrix are constructed. Then, an optimization problem model is constructed based on these matrices. Finally, the power distribution of the distributed source is obtained by solving the model. The direction of the source wave is obtained from the power and angle mapping relationship. The specific steps include:

[0039] Step 1: Obtain the array received signal and calculate the time average estimation matrix of the covariance matrix using a finite number of sampling samples:

[0040] ,

[0041] in, is the time average estimation matrix of the covariance matrix R, N is the number of sampling points, represents the array receiving signal, and the superscript H represents the conjugate transpose.

[0042] Step 2: Construct the steering vector dictionary matrix and the power distribution matrix respectively; the steering vector dictionary matrix is:

[0043]

[0044] The power distribution matrix is:

[0045]

[0046] in, is the directional vector dictionary matrix, is the power distribution matrix, Except for the diagonal elements, all other positions are 0, K is the number of airspace grids, that is, the reconnaissance airspace range Φ is divided into K airspace angles Ψ1, Ψ2,…, Ψ K , is the steering vector of the kth spatial angle; M is the number of array elements; is an M×M-order identity matrix; the superscript T indicates the matrix transpose; is the signal power of the source corresponding to K spatial angles. If a spatial angle Ψ i If there is no signal source, then the corresponding is 0; is the received noise power corresponding to M array elements.

[0047] Step 3: Construct an optimization problem model based on the time-averaged estimation matrix of the covariance matrix, the steering vector dictionary matrix, and the power distribution matrix. The specific method is as follows:

[0048] Step 301: Construct a matrix G, where the element in the i-th row and j-th column of the matrix G is for:

[0049] ,

[0050] in, express For the element in row i and column j, |•| represents the modulo value;

[0051] Step 302: Construct vector q, the i-th element in vector q for:

[0052] ,

[0053] in, express The element in the i-th row and i-th column of , that is, the i-th diagonal element;

[0054] Step 303: Construct vector p, the i-th element of vector p for:

[0055] ,

[0056] in, Representation matrix The element in the i-th row and i-th column of , that is, the i-th diagonal element;

[0057] Step 304: Constructing an optimization problem model:

[0058] ,

[0059] in, Expressing a request Take the minimum value of p; 、 are hyperparameters, which are constant real numbers and can be set to 0.8 and 0.2 respectively; To find the second-order norm; To find the first-order norm of y; To solve the condition, all elements in the vector p are required to be positive real numbers.

[0060] Step 4: Use the cvx toolkit to solve the optimization problem model and obtain vector p; each of the first K elements of vector p The corresponding angle Ψ i That is, it is the angle of arrival of the i-th distributed signal source. The last M elements of the vector p are the noise power of the corresponding array element, completing the distributed signal source perception.

[0061] Under the condition of unknown number of new sources, this method obtains the estimated value of the covariance matrix based on the sampled snapshot data. By utilizing the sparsity of the spatial distribution of the information sources in the reconnaissance airspace, an over-complete steering vector dictionary matrix and a power distribution matrix are constructed to fit the sampled covariance matrix, thereby realizing the direction finding perception of the distributed information sources.

[0062] Here's a more concrete example:

[0063] A distributed information source sensing method includes the following steps:

[0064] Step 1: Get the array received signal and use a finite number of sampling samples to calculate the time average estimation matrix of the covariance matrix R , , where N is the number of sampling points, [·] H is the conjugate transpose.

[0065] Step 2: Construct the steering vector dictionary matrix separately and power distribution matrix :

[0066]

[0067]

[0068] In the above formula, K is the number of airspace grids, that is, the reconnaissance airspace range Φ is divided into K angles Φ=[Ψ1,Ψ2,…,Ψ K ]; M is the number of array elements; is an M×M unit matrix; [·] T is the matrix transpose symbol; is the signal power of the source corresponding to K spatial angles. If a spatial angle Ψ i If there is no signal source, then The value is 0; is the received noise power corresponding to M array elements.

[0069]

[0070] In the above formula: , A is the steering vector of the actual source, s(t) is the source vector, n(t) is the received noise vector, Indicates taking The conjugation of .

[0071] The above formula is:

[0072]

[0073] When the covariance matrix Estimated covariance matrix obtained from the sampled snapshots When substituted, the above formula becomes:

[0074]

[0075] It can be seen from the above formula that the theoretical covariance matrix can be re-described by the constructed steering vector dictionary matrix and power distribution matrix.

[0076] Step 3: Construct matrix G and vector q:

[0077] , that is, the element in the i-th row and j-th column of the matrix G is The square of the modulus of the element in row i and column j of the product matrix;

[0078] , that is, the i-th element of vector q is the matrix The i-th main diagonal element in the i-th row and i-th column.

[0079] Step 4: Construct vector p:

[0080] , that is, the i-th element of vector p is the matrix The i-th main diagonal element in the i-th row and i-th column.

[0081] Step 5: Build the optimization problem model:

[0082] .

[0083] The optimization problem model is further explained as follows:

[0084] because , so it is available The estimated covariance matrix obtained from the sampled snapshots Fitting is performed, so the optimization function can be constructed:

[0085]

[0086] When the above formula is minimum, that is, min (L) The solution is the power distribution of the distributed source.

[0087] Depend on It can be seen that:

[0088]

[0089] trace(·) is used to find the trace of the matrix.

[0090] Then by It can be seen that:

[0091]

[0092] Then we have:

[0093]

[0094] for Item, order , then:

[0095]

[0096] for Item, because is a real diagonal matrix, so ,make , then:

[0097]

[0098] Again Therefore:

[0099]

[0100] Then:

[0101]

[0102] Let Then:

[0103]

[0104] It is easy to know is a constant, so let

[0105] In summary:

[0106]

[0107] When L is the smallest, its derivative is 0, that is:

[0108]

[0109] Therefore

[0110] At the same time, considering the sparsity of p, it is required to minimize its 0-order norm, that is But because is non-convex and cannot be solved by convex optimization, it is relaxed to .

[0111] At the same time, considering the control of the fitting accuracy and sparsity of the optimization process, by setting two hyperparameters , the above solving requirements are unified into the model:

[0112] .

[0113] The above formula is the optimization problem model in step 5.

[0114] Step 6: Use the cvx toolkit to solve the model in step 5 to get the value of each element of the vector p, where the non-zero items in the first K items of the vector p correspond to the angle Ψ i is the angle of arrival of the distributed source i, and the last M items of the vector p are the noise power.

[0115] ​In order to verify the effectiveness of the method, simulation can be carried out. Simulation conditions: M=16 uniform linear array is adopted, the signal frequency is 800MHz, the bandwidth B=10MHz, the number of snapshots is N=1024, and the signal-to-noise ratio SNR=15dB.

[0116] Figure 1 is the solving result figure of the method under the condition of unknown number of sources, and the directions of the three distributed sources are 30°, 65° and 98° respectively. It can be seen from the figure that the directions of the sources solved by the method are 30°, 65° and 98° respectively.

[0117] Figure 2 is the solving result figure of the method under the condition of unknown number of sources, and the directions of the four distributed sources are 30°, 65°, 98° and 140° respectively. It can be seen from the figure that the directions of the sources solved by the method are 30°, 65°, 99° and 139° respectively.

[0118] It can be seen from the simulation that when the directions of the distributed sources are sensed under the condition of unknown number of sources, the method can obtain the accurate spatial distribution information of the sources.

[0119] In summary, under the condition of unknown number of sources, the method uses the sparsity of the spatial distribution of the sources in the reconnaissance space, constructs an over-complete steering vector dictionary matrix and a power distribution matrix, and through the re-description of the dictionary matrix and the power distribution matrix to the covariance matrix, the sampling covariance matrix is fitted, so that the direction finding sensing of the distributed sources under the condition of unknown number of sources is realized.

Claims

1. A distributed information source perception method, characterized in that: The following steps are involved: Step 1: Obtain the array received signal and calculate the time average estimation matrix of the covariance matrix using a finite number of sampling samples: ， in, is the time average estimation matrix of the covariance matrix R, N is the number of sampling points, represents the array receiving signal, and the superscript H represents the conjugate transpose; Step 2: Construct the steering vector dictionary matrix and power distribution matrix respectively; the steering vector dictionary matrix is: The power distribution matrix is: in, is the directional vector dictionary matrix, is the power distribution matrix, Except for the diagonal elements, all other positions are 0, K is the number of airspace grids, that is, the reconnaissance airspace range Φ is divided into K airspace angles Ψ1, Ψ2,…, Ψ K , is the steering vector of the kth spatial angle; M is the number of array elements; is an M×M-order identity matrix; the superscript T indicates the matrix transpose; is the signal power of the source corresponding to K spatial angles. If a spatial angle Ψ i If there is no signal source, then the corresponding is 0; is the received noise power corresponding to M array elements; Step 3: Construct an optimization problem model based on the time-averaged estimation matrix of the covariance matrix, the steering vector dictionary matrix, and the power distribution matrix. The specific method is as follows: Step 301: Construct a matrix G, where the element in the i-th row and j-th column of the matrix G is for: ， in, express For the element in row i and column j, |•| represents the modulo value; Step 302: Construct vector q, the i-th element in vector q for: ， in, express The element in the i-th row and i-th column of , that is, the i-th diagonal element; Step 303: Construct vector p, the i-th element of vector p for: ， in, Representation matrix The element in the i-th row and i-th column of , that is, the i-th diagonal element; Step 304: Constructing an optimization problem model: ， in, Expressing a request Take the minimum value of p; 、 is a hyperparameter, a constant real number; To find the second-order norm; To find the first-order norm of y; To solve the condition, all elements in the vector p are required to be positive real numbers; Step 4: Use the CVX toolkit to solve the optimization problem model, obtain the incoming wave angle and noise power of the distributed signal source, and complete distributed signal source perception.

2. A distributed information source perception method according to claim 1, characterized in that: In step 4, the optimization problem model is solved by the cvx toolkit to obtain vector p; each of the first K elements of vector p The corresponding angle Ψ i That is, it is the angle of arrival of the i-th distributed signal source, and the last M elements of the vector p are the noise power of the corresponding array element.

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