Radiation source positioning method, storage medium and device based on covariance matrix reconstruction

Abstract

The present invention discloses a radiation source positioning method, storage medium, and device based on covariance matrix reconstruction. The radiation source positioning method includes: a drone equipped with a uniform linear array receives Q radiation source signals at K positions, and performs azimuth estimation on the Q radiation sources at each position of the drone; reconstructs the linear array manifold of the uniform linear array based on the azimuth estimation value of the radiation source, and reconstructs the receiving covariance matrix based on the reconstructed linear array manifold; performs eigenvalue decomposition based on the reconstructed receiving covariance matrix to obtain a reconstructed noise subspace, and constructs a spatial spectrum function by combining the orthogonality of the radiation source's steering vector and the noise subspace; and finds the extreme value of the spatial spectrum function through an exhaustive search method as the estimated value of the radiation source position. The present invention reconstructs the steering vector and the covariance matrix based on azimuth information, can fully utilize the azimuth information, and has higher positioning accuracy and performance.

Description

Technical Field

[0001] The present invention belongs to the technical field of passive positioning, and in particular relates to a radiation source positioning method, a storage medium and a device based on covariance matrix reconstruction. Background Art

[0002] The Global Positioning System (GPS) is the most important technology for providing location awareness worldwide via satellite, using at least 24 satellites for positioning. The most important features of the GPS system are its wide coverage, its ability to seamlessly provide navigation data to multiple vehicles, its relatively low power requirements, the miniaturization of its receivers, and its environmental friendliness, with GPS signals indeed not significantly interfering with ecosystems. However, GPS signals cannot penetrate most obstacles and their effectiveness is limited in harsh environments, such as buildings, urban canyons, under tree canopies, and in caves. Therefore, new positioning technologies are needed to meet the growing demand for precise positioning in such harsh environments.

[0003] Because of the aforementioned limitations of GPS, two-step positioning techniques based on sensor networks are gaining increasing attention. Sensor networks utilize several nodes with known locations for location awareness. For example, vehicular ad hoc networks (VANETs) have been proposed by the automotive research community in recent years as a means of achieving a connected road environment where vehicles and infrastructure components can communicate to improve positioning accuracy. However, these two-step positioning techniques use highly biased algorithms to obtain positioning results, resulting in unreliable results. Summary of the Invention

[0004] The purpose of the present invention is to address the deficiencies of the existing technology and provide a radiation source positioning method, storage medium and device based on covariance matrix reconstruction. The steering vector and covariance matrix are reconstructed through azimuth information, which can fully utilize the azimuth information and has higher positioning accuracy and performance than the traditional two-step positioning technology.

[0005] To achieve the above technical objectives, the present invention adopts the following technical solution: a radiation source positioning method based on covariance matrix reconstruction, specifically comprising the following steps:

[0006] Step S1: A UAV equipped with a uniform linear array receives signals from Q radiation sources at K locations, and estimates the azimuth angles of the Q radiation sources at each location of the UAV.

[0007] Step S2: reconstructing the linear array manifold of the uniform linear array according to the estimated azimuth angle of the radiation source, and reconstructing the receiving covariance matrix according to the reconstructed linear array manifold;

[0008] Step S3: Perform eigenvalue decomposition based on the reconstructed receiving covariance matrix to obtain the reconstructed noise subspace, and construct the spatial spectrum function by combining the orthogonality between the radiation source steering vector and the noise subspace;

[0009] Step S4: find the extreme point of the spatial spectrum function by exhaustive search as the estimated value of the radiation source position.

[0010] Furthermore, in step S1, the radiation source signal received by the UAV at the kth position is:

[0011] x k (t) = A k (θ)s k (t)+n k (t)

[0012] Among them, A k (θ) represents the linear array manifold of the uniform linear array, A k (θ)=[a(θ k1 ),...,a(θ kq ),...,a(θ kQ )],a(θ kq ) represents the guidance vector of the UAV at the kth position relative to the qth radiation source, θ kq represents the azimuth angle of the UAV at the kth position relative to the qth radiation source, θ kq =arctan((u ky -p qy ) / (u kx -p qx )), p q =[p qx ,p qy ] T Indicates the position coordinates of the qth radiation source, u k =[u kx ,u ky ] T represents the coordinates of the UAV at the kth position, j is the imaginary unit, λ represents the wavelength, d is the spacing between the elements of the uniform linear array, and M represents the number of elements of the uniform linear array; s k (t) represents the received signal of the UAV at the kth position relative to the radiation source, n k (t) represents zero-mean complex Gaussian stationary noise.

[0013] Furthermore, the process of estimating the azimuth angles of Q radiation sources at each position of the UAV in step S1 is as follows:

[0014] Step S1.1: Obtain the covariance matrix of the radiation source signal received by the UAV at the kth position in, represents the mean sign, H represents the conjugate transpose;

[0015] Step S1.2: covariance matrix Perform eigenvalue decomposition, Where Λ represents the eigenvalue matrix, Λ=diag{λ1,...,λ M}, the diagonal elements λ1,...,λ of Λ M is the covariance matrix The eigenvalue of λ1≥...≥ M ; represents the feature matrix, e1,...,e M is related to λ1,...,λ M One-to-one corresponding eigenvectors;

[0016] Step S1.3: Take the eigenvectors corresponding to the first K eigenvalues ​​to form the signal subspace E s =[e1,...,e K ], take the signal subspace E s The first M-1 rows and the last M-1 rows form the matrix E x and E y ;

[0017] Step S1.4: Matrix Perform eigenvalue decomposition to obtain the characteristic matrix E, and decompose the characteristic matrix E into K×K submatrices:

[0018]

[0019] Step S1.5: Calculate the auxiliary matrix And find the eigenvalue λ of the auxiliary matrix k , to the estimated azimuth

[0020] Furthermore, step S2 includes the following sub-steps:

[0021] Step S2.1: Determine the estimated value of the guidance vector of the UAV at the kth position relative to the qth radiation source based on the estimated value of the azimuth angle of the radiation source. Reconstruct the linear array manifold of the uniform linear array of the UAV at the kth position

[0022] Step S2.2: Reconstruct the covariance matrix of the received signal of the UAV at the kth position based on the reconstructed uniform linear array manifold of the UAV at the kth position. in, express The conjugate transpose of .

[0023] Furthermore, step S3 includes the following sub-steps:

[0024] Step S3.1, perform eigenvalue decomposition on the covariance matrix of the reconstructed UAV received signal at the kth position, sort the eigenvalues ​​from large to small, use the first Q eigenvalues ​​as the eigenvalues ​​of the reconstructed signal subspace, and use the last MQ eigenvalues ​​as the eigenvalues ​​of the reconstructed noise subspace;

[0025] The process of performing eigenvalue decomposition of the received signal covariance matrix is ​​as follows:

[0026]

[0027] Among them, U sk represents the reconstructed signal subspace, Σ sk represents the diagonal matrix consisting of the eigenvalues ​​corresponding to the reconstructed signal subspace, Σ sk =diag[σ M-Q+1,k ,...,σ M,k ]; U nk represents the reconstructed noise subspace, Σ nk represents the diagonal matrix consisting of the eigenvalues ​​corresponding to the reconstructed noise subspace, Σ nk =diag[σ 1,k ,...,σ M-Q,k ];

[0028] Step S3.2: Construct a spatial spectrum function based on the steering vector of the radiation source and the orthogonality of the reconstructed noise subspace:

[0029]

[0030] Where a(p) represents the steering vector of the search variable p,

[0031] Furthermore, the present invention also provides a computer-readable storage medium storing a computer program, wherein the computer program enables a computer to execute the radiation source positioning method based on covariance matrix reconstruction.

[0032] Furthermore, the present invention also provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and runnable on the processor. When the processor executes the computer program, the radiation source positioning method based on covariance matrix reconstruction is implemented.

[0033] Compared with the prior art, the present invention has the following technical effects: the radiation source positioning method based on covariance matrix reconstruction of the present invention integrates all azimuth information of the UAV at different positions. Compared with the traditional algorithm, there is no need to obtain the positioning result at the cost of bias, and the azimuth information can be fully utilized; secondly, the radiation source positioning method based on covariance matrix reconstruction of the present invention does not need to know the correspondence between the measured azimuth and the radiation source, eliminating the source matching step that the traditional algorithm relies on. Compared with the traditional two-step positioning method, the present invention utilizes the idea of ​​direct positioning and integrates all azimuth information of each measurement point. The mapping constructed is directly from the original azimuth data to the positioning result, and has higher positioning accuracy and performance. Using the UAV as a carrier, it fits the electronic countermeasure scenario and can identify the radiation source with high precision. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 This is a flow chart of a radiation source positioning method based on covariance matrix reconstruction according to the present invention;

[0035] Figure 2 The positioning scene graph of the present invention;

[0036] Figure 3 This is a comparison chart of the positioning performance of the radiation source positioning method based on covariance matrix reconstruction according to the present invention as the signal-to-noise ratio changes;

[0037] Figure 4 This is a comparison chart of the positioning performance of the radiation source positioning method based on covariance matrix reconstruction according to the present invention as the number of snapshots changes;

[0038] Figure 5 This is the positioning spectrum peak diagram of the radiation source positioning method based on covariance matrix reconstruction of the present invention. DETAILED DESCRIPTION

[0039] The technical solution of the present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0040] like Figure 1 This is a flow chart of a radiation source positioning method based on covariance matrix reconstruction according to the present invention, which specifically includes the following steps:

[0041] Step S1: The UAV equipped with a uniform linear array receives signals from Q radiation sources at K locations, and estimates the azimuth angles of the Q radiation sources at each location of the UAV, effectively reducing the computational complexity.

[0042] like Figure 2 This is the positioning scene diagram of the present invention. The radiation source signal received by the drone at the kth position in the present invention is:

[0043] x k (t) = A k(θ)s k (t)+n k (t)

[0044] Among them, A k (θ) represents the linear array manifold of the uniform linear array, A k (θ)=[a(θ k1 ),...,a(θ kq ),...,a(θ kQ )],a(θ kq ) represents the guidance vector of the UAV at the kth position relative to the qth radiation source, θ kq represents the azimuth angle of the UAV at the kth position relative to the qth radiation source, θ kq =arctan((u ky -p qy ) / (u kx -p qx )), p q =[p qx ,p qy ] T Indicates the position coordinates of the qth radiation source, u k =[u kx ,u ky ] T represents the coordinates of the UAV at the kth position, j is the imaginary unit, λ represents the wavelength, d is the spacing between the elements of the uniform linear array, and M represents the number of elements of the uniform linear array; s k )t) represents the received signal of the UAV at the kth position relative to the radiation source, n k (t) represents zero-mean complex Gaussian stationary noise.

[0045] The present invention uses a fast algorithm such as ESPRIT to estimate the azimuth angle of Q radiation sources at each position of the drone. The specific process is as follows:

[0046] Step S1.1: Obtain the covariance matrix of the radiation source signal received by the UAV at the kth position in, represents the mean sign, H represents the conjugate transpose;

[0047] Step S1.2: covariance matrix Perform eigenvalue decomposition, Where Λ represents the eigenvalue matrix, Λ=diag{λ1,...,λ M}, the diagonal elements λ1,...,λ of Λ M is the covariance matrix The eigenvalues ​​of λ1≥...≥λ M ; represents the feature matrix, e1,...,e M is related to λ1,...,λ M One-to-one corresponding eigenvectors;

[0048] Step S1.3: Take the eigenvectors corresponding to the first K eigenvalues ​​to form the signal subspace E s =[e1,...,e K ], take the signal subspace E s The first M-1 rows and the last M-1 rows form the matrix E x and E y ;

[0049] Step S1.4: Matrix Perform eigenvalue decomposition to obtain the characteristic matrix E, and decompose the characteristic matrix E into K×K submatrices:

[0050]

[0051] Step S1.5: Calculate the auxiliary matrix And find the eigenvalue λ of the auxiliary matrix k , to the estimated azimuth

[0052] Step S2: Reconstruct the linear array manifold of the uniform linear array based on the azimuth angle estimation value of the radiation source, reconstruct the receiving covariance matrix based on the reconstructed linear array manifold, and perform positioning using the reconstructed covariance matrix. This eliminates the need to consider the correspondence between the radiation source and the azimuth angle measurement value, and eliminates the source matching step required by the traditional azimuth angle positioning algorithm. The specific steps include the following:

[0053] Step S2.1: Determine the estimated value of the guidance vector of the UAV at the kth position relative to the qth radiation source based on the estimated value of the azimuth angle of the radiation source. Reconstruct the linear array manifold of the uniform linear array of the UAV at the kth position

[0054] Step S2.2: Reconstruct the covariance matrix of the received signal of the UAV at the kth position based on the reconstructed uniform linear array manifold of the UAV at the kth position. in, express The conjugate transpose of .

[0055] Step S3: Perform eigenvalue decomposition based on the reconstructed receiving covariance matrix to obtain the reconstructed noise subspace. Combined with the orthogonality of the radiation source's steering vector and the noise subspace, a spatial spectrum function is constructed. Since this method is a subspace-based algorithm, the constructed spatial spectrum has super-resolution. The method specifically includes the following substeps:

[0056] Step S3.1, perform eigenvalue decomposition on the covariance matrix of the reconstructed UAV received signal at the kth position, sort the eigenvalues ​​from large to small, use the first Q eigenvalues ​​as the eigenvalues ​​of the reconstructed signal subspace, and use the last MQ eigenvalues ​​as the eigenvalues ​​of the reconstructed noise subspace;

[0057] The process of eigenvalue decomposition of the received signal covariance matrix in the present invention is as follows:

[0058]

[0059] Among them, U sk represents the reconstructed signal subspace, Σ sk represents the diagonal matrix consisting of the eigenvalues ​​corresponding to the reconstructed signal subspace, Σ sk =diag[σ M-Q+1,k ,...,σ M,k ]; U nk represents the reconstructed noise subspace, Σ nk represents the diagonal matrix consisting of the eigenvalues ​​corresponding to the reconstructed noise subspace, Σ nk =diag[σ 1,k ,...,σ M-Q,k ];

[0060] Step S3.2: According to the orthogonality of the radiation source's steering vector and the reconstructed noise subspace, in an ideal case, we have Construct a spatial spectrum function:

[0061]

[0062] Where a(p) represents the steering vector of the search variable p,

[0063] Step S4: Since the orthogonality between the steering vector and the noise subspace is strongest at the extreme point, the extreme point of the spatial spectrum function is found by exhaustive search as the estimated value of the radiation source position; specifically, for each point in the spatial domain, the value of the spatial spectrum function of the point is calculated to obtain a three-dimensional spectrum graph, and the Q extreme points of the three-dimensional spectrum graph are found, which are respectively This is the final estimated value of the radiation source position, thereby realizing the positioning of the radiation source.

[0064] Example

[0065] According to the radiation source positioning method based on covariance matrix reconstruction of the present invention, the simulation parameters are set: the positions of the three sampling points of the UAV are [100 500] T , [300 200] T , and [400 0] T , the position coordinates of the radiation source are [0 0] Tand [100 0] T , unit is m.

[0066] Figure 3 This is a comparison chart of the positioning performance of the radiation source positioning method based on covariance matrix reconstruction as the signal-to-noise ratio changes. It can be seen that the present invention does not rely on pseudo-linear relationships to implement positioning and has lower bias. As the signal-to-noise ratio increases, the direct positioning error of the present invention decreases. Compared with the traditional two-step positioning algorithm, it has higher accuracy and better positioning performance. Figure 4 This is a comparison chart of the positioning performance of the radiation source positioning method based on covariance matrix reconstruction of the present invention as the number of snapshots changes. It can be seen that as the number of snapshots increases, the direct positioning error of the present invention decreases. Compared with the traditional two-step positioning algorithm, it has higher accuracy and better positioning performance.

[0067] Figure 5 This is a positioning spectrum peak diagram of the radiation source positioning method based on covariance matrix reconstruction of the present invention. When the signal-to-noise ratio is 10db and the number of snapshots is 100, the spectrum peak of the present invention is very obvious due to the high signal-to-noise ratio, and has better positioning performance.

[0068] In one technical solution of the present invention, a computer-readable storage medium is provided, which stores a computer program, and the computer program enables a computer to execute the radiation source positioning method based on covariance matrix reconstruction.

[0069] In another technical solution of the present invention, an electronic device is also provided, including: a memory, a processor, and a computer program stored in the memory and runnable on the processor. When the processor executes the computer program, the radiation source positioning method based on covariance matrix reconstruction is implemented.

[0070] In the embodiments disclosed herein, computer storage media can be tangible media that can contain or store programs for use by or in conjunction with an instruction execution system, device, or apparatus. Computer storage media can include, but are not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or equipment, or any suitable combination of the foregoing. More specific examples of computer storage media can include electrical connections based on one or more lines, portable computer disks, hard disks, random access memories (RAM), read-only memories (ROM), erasable programmable read-only memories (EPROM or flash memory), optical fibers, portable compact disk read-only memories (CD-ROMs), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0071] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0072] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person familiar with the technology can understand and think of any changes or replacements within the technical scope disclosed by the present invention, which should be included in the scope of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A radiation source positioning method based on covariance matrix reconstruction, characterized in that: The specific steps include: Step S1: A UAV equipped with a uniform linear array receives signals from Q radiation sources at K locations, and estimates the azimuth angles of the Q radiation sources at each location of the UAV. Step S2: reconstructing the linear array manifold of the uniform linear array according to the estimated azimuth angle of the radiation source, and reconstructing the receiving covariance matrix according to the reconstructed linear array manifold; Step S3: Perform eigenvalue decomposition based on the reconstructed receiving covariance matrix to obtain the reconstructed noise subspace, and construct the spatial spectrum function by combining the orthogonality between the radiation source steering vector and the noise subspace; Step S4: find the extreme point of the spatial spectrum function by exhaustive search as the estimated value of the radiation source position.

2. A radiation source positioning method based on covariance matrix reconstruction according to claim 1, characterized in that, In step S1, the radiation source signal received by the UAV at the kth position is: x k (t)=A k (θ)s k (t)+n k (t) Among them, A k (θ) represents the linear array manifold of the uniform linear array, A k (θ)=[a(θ k1 ),...,a(θ kq ),...,a(θ kQ )],a(θ kq ) represents the guidance vector of the UAV at the kth position relative to the qth radiation source, θ kq represents the azimuth angle of the UAV at the kth position relative to the qth radiation source, θ kq =arctan((u ky -p qy ) / (u kx -p qx )), p q =[p qx ,p qy ] T Indicates the position coordinates of the qth radiation source, u k =[u kx ,u ky ] T represents the coordinates of the UAV at the kth position, j is the imaginary unit, λ represents the wavelength, d is the spacing between the elements of the uniform linear array, and M represents the number of elements of the uniform linear array; s k (t) represents the received signal of the UAV at the kth position relative to the radiation source, n k (t) represents zero-mean complex Gaussian stationary noise.

3. A radiation source positioning method based on covariance matrix reconstruction according to claim 2, characterized in that, The process of estimating the azimuth angles of Q radiation sources at each position of the UAV in step S1 is as follows: Step S1.1: Obtain the covariance matrix of the radiation source signal received by the UAV at the kth position in, represents the mean sign, H represents the conjugate transpose; Step S1.2: covariance matrix Perform eigenvalue decomposition, Where Λ represents the eigenvalue matrix, Λ=diag{λ1,...,λ M }, the diagonal elements λ1,...,λ of Λ M is the covariance matrix The eigenvalue of λ1≥…≥λ M ; represents the feature matrix, e1,...,e M is related to λ1,...,λ M One-to-one corresponding eigenvectors; Step S1.3: Take the eigenvectors corresponding to the first K eigenvalues ​​to form the signal subspace E s =[e1,...,e K ], take the signal subspace E s The first M-1 rows and the last M-1 rows form the matrix E x and E y ; Step S1.4: Matrix Perform eigenvalue decomposition to obtain the characteristic matrix E, and decompose the characteristic matrix E into K×K submatrices: Step S1.5: Calculate the auxiliary matrix And find the eigenvalue λ of the auxiliary matrix k , to the estimated azimuth 4. A radiation source positioning method based on covariance matrix reconstruction according to claim 3, characterized in that: Step S2 includes the following sub-steps: Step S2.1: Determine the estimated value of the guidance vector of the UAV at the kth position relative to the qth radiation source based on the estimated value of the azimuth angle of the radiation source. Reconstruct the linear array manifold of the uniform linear array of the UAV at the kth position Step S2.2: Reconstruct the covariance matrix of the received signal of the UAV at the kth position based on the reconstructed uniform linear array manifold of the UAV at the kth position. in, express The conjugate transpose of .

5. A radiation source positioning method based on covariance matrix reconstruction according to claim 4, characterized in that, Step S3 includes the following sub-steps: Step S3.1, perform eigenvalue decomposition on the covariance matrix of the reconstructed UAV received signal at the kth position, sort the eigenvalues ​​from large to small, use the first Q eigenvalues ​​as the eigenvalues ​​of the reconstructed signal subspace, and use the last MQ eigenvalues ​​as the eigenvalues ​​of the reconstructed noise subspace; The process of performing eigenvalue decomposition of the received signal covariance matrix is ​​as follows: Among them, U sk represents the reconstructed signal subspace, Σ sk represents the diagonal matrix consisting of the eigenvalues ​​corresponding to the reconstructed signal subspace, Σ sk =diag[σ M-Q+1,k ,...,σ M,k ]; U nk represents the reconstructed noise subspace, Σ nk represents the diagonal matrix consisting of the eigenvalues ​​corresponding to the reconstructed noise subspace, Σ nk =diag[σ 1,k ,...,σ M-Q,k ]; Step S3.2: Construct a spatial spectrum function based on the steering vector of the radiation source and the orthogonality of the reconstructed noise subspace: Where a(p) represents the steering vector of the search variable p, 6. A computer-readable storage medium storing a computer program, characterized in that: The computer program enables a computer to execute the radiation source positioning method based on covariance matrix reconstruction as described in any one of claims 1 to 5.

7. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the radiation source positioning method based on covariance matrix reconstruction according to any one of claims 1 to 5 is implemented.

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