Radiation source direct positioning method based on random sampling

Abstract

The present application relates to a kind of radiation source direct positioning method based on random sampling, belong to radiation source direct positioning technical field, solve the problem of large amount of calculation of existing technology in radiation source direct positioning.It includes: using the receiving node arranged in dispersion to receive radiation source signal from different directions, the observation sample data of different time is obtained by sampling received data;Grid division is carried out to the coordinate system of radiation source sensing area;According to the grid point of pre-set quantity of uniform distribution, the likelihood ratio test statistic of time delay compensation is calculated based on observation sample data, selected grid point position as the matrix element of the position of grid point;Based on low-rank matrix completion method, complete the matrix element of entire radiation source sensing area, form the synchronization likelihood ratio test statistic matrix of sensing area received signal, the peak position in the synchronization likelihood ratio test statistic matrix of sensing area received signal is determined as the position of radiation source.Positioning method based on random sampling of radiation source is realized.

Description

Technical Field

[0001] This invention relates to the field of radiation source direct location technology, and in particular to a radiation source direct location method based on random sampling. Background Technology

[0002] For decades, passive radiation source localization based on electromagnetic signals emitted by radiation sources has been a significant concern for academic researchers and industry professionals. Radiation source localization is applied in radio surveillance, arrest support, search and rescue, and other fields. Most passive localization methods employ a two-step approach, such as Time Difference of Origin (TDOA), Frequency Difference of Origin (FDOA), and combined TDOA and FDOA localization. The first step extracts location-related signal parameters from the sampled signal. The second step uses the extracted parameters to estimate the location of the signal source. Two-step localization methods are often suboptimal because they ignore the inherent constraint that all extracted parameters should correspond to the signal source's location. Direct localization (DPD) can fully utilize the received raw data, overcoming the shortcomings of the two-step method. However, DPD requires traversing the sensing area, resulting in high computational costs; the more grids the sensing area is divided into, the greater the computational burden. Summary of the Invention

[0003] Based on the above analysis, the embodiments of the present invention aim to provide a method for direct location of radiation sources based on random sampling, so as to solve the problem of large computational load in existing direct location methods of radiation sources.

[0004] This invention provides a method for direct localization of radiation sources based on random sampling, comprising the following steps:

[0005] S1. Receive radiation source signals from different directions using I distributed receiving nodes, where I ≥ 3; sample the received data from the I receiving nodes to obtain observation sample data at different times;

[0006] S2. Establish a two-dimensional coordinate system for the radiation source sensing area and divide it into grids; randomly select a preset number of grid points according to a uniform distribution, and calculate the likelihood ratio test statistic after time delay compensation based on the observation sample data and the selected grid point locations as the matrix elements of the corresponding grid point locations.

[0007] S3. Based on the low-rank matrix completion method, complete the matrix elements of the unselected grid points in the entire radiation source sensing area to form the synchronous likelihood ratio test statistics matrix of the received signal in the sensing area. The position of the peak value in the synchronous likelihood ratio test statistics matrix of the received signal in the sensing area is determined as the position of the radiation source.

[0008] Furthermore, based on the observed sample data and the selected grid point locations, the likelihood ratio test statistic after time delay compensation is calculated as a matrix element representing the grid point locations, including:

[0009] Based on the positional relationship between the signal receiving node from which each observation sample data comes and the selected grid points, time delay compensation is performed on each observation sample data to generate a time delay compensated received data matrix;

[0010] The maximum likelihood ratio test statistic is calculated based on the received data matrix after time delay compensation and used as the matrix element for the selected grid point location.

[0011] Furthermore, iterative solution according to Calculate the maximum likelihood ratio test statistic; where, The estimated value of parameter U under the condition that U is the null hypothesis. The covariance matrix of the observed sample data; for The estimated value of parameter V under the condition; V is the value of parameter V under the alternative hypothesis. The covariance matrix of the observed sample data;

[0012] The iterative solution Includes the following steps:

[0013] S1. Initialize the iteration count k = 0, and randomly initialize... generate in, This is the estimated matrix of the noise power matrix Σ. Let H be the noise power of the i-th signal receiving node, i = 1, 2, ..., I, and H be the channel parameter matrix from the radiation source to each receiving node. In order to be in Assumption or Assume the estimated matrix of H;

[0014] S2, Updated Estimation in, right Eigenvalue decomposition yields the eigenvector matrix. and eigenvalue diagonal matrix For the thresholded eigenvalue matrix, Q is any orthogonal matrix;

[0015] S3. Determine whether the iteration has converged according to the following formula:

[0016]

[0017] If the above formula is true, and In order to be in Assuming the estimated matrix of H is given below, As If the above formula is true, and In order to be in Assuming the estimated matrix of H is given below, As If the above equation does not hold, return to step S2 to continue the iteration; where ε is the convergence accuracy.

[0018] Furthermore, the formula for calculating the maximum likelihood ratio test statistic of the received data matrix after time delay compensation is as follows:

[0019]

[0020] in, The estimated value of parameter U under the condition that U is the null hypothesis. The covariance matrix of the observed sample data; for The estimated value of parameter V under the condition; V is the value of parameter V under the alternative hypothesis. The covariance matrix of the observed sample data; det(·) is used to calculate the determinant of matrix ·, tr(·) is used to calculate the trace of matrix ·, and S is the covariance matrix of the received data matrix after time delay compensation. Let T be the received data matrix after time delay compensation, and let T be the number of samples corresponding to each receiving node in the observed sample data, t = 1, 2, ..., T.

[0021] Furthermore, time delay compensation is performed on the observation sample data of each signal receiving node, including: calculating the number of sampling points that need to be shifted forward or backward in the sampling time series of the observation sample data of each signal receiving node using the following formula:

[0022]

[0023] In the formula, Let be the data reception delay of the i-th signal receiving node. f is the data reception delay of the first signal receiving node. s Where Δn is the sampling frequency. i Let Δn be the number of sampling points that need to be shifted forward or backward in the sampling time series for the observation sample data of the i-th signal receiving node. i When the value is greater than 0, shift the time series backward by Δn. i Number of sampling points; Δn i When <0, shift forward by -Δn in the time series. i There are 1 sampling point; i = 2, 3, ..., 1; To perform rounding operation on ·.

[0024] Furthermore, the synchronization likelihood ratio test statistic matrix of the received signal in the entire sensing area is iteratively calculated to minimize the augmented Lagrangian function, and then completed to form the synchronization likelihood ratio test statistic matrix of the received signal in the sensing area; the iterative process includes:

[0025] S1. Initialize the entire matrix to be solved to obtain X. 0 This includes: initializing the selected preset number of grid points using the calculated likelihood ratio test statistic, and randomly initializing the remaining positions to be completed, Z... 0 =X 0 T 0 =X 0 , k = 0; where Z is the intermediate matrix and T is the augmented Lagrange multiplier matrix;

[0026] S2, Updated Estimation T k+1 =T k -ρ(Z k+1 -X k+1 Where D is the defined operator; P is the defined projection operator; ρ is the penalty factor; and Ω is the set of coordinates of elements in the matrix corresponding to a preset number of grid points. M is the set of coordinates of the matrix elements corresponding to the remaining grid points in the grid point matrix, excluding the preset number of grid points; M is a matrix initialized with the calculated likelihood ratio test statistic for the preset number of grid points.

[0027] S3, when ||X k+1 -X k || F Iteration stops when ||·|| is less than or equal to ε' or k is greater than K, where K is the preset number of iterations, ε' is the convergence precision, and ||·|| is the convergence precision. F To find the nuclear norm of F for ·.

[0028] Furthermore, operator D is obtained using the following formula:

[0029] W′=D τ (W)=U×S'×V H ,

[0030] Where [U,S,V]=svd(W), S'=max(abs(S)-τ,0), W is the input matrix of operator D, W' is the output matrix of operator D, svd is the singular value decomposition function, U is the matrix formed by the left singular value vectors of W, S is the singular value matrix of W, V is the matrix formed by the right singular value vectors of W, S' is the thresholded singular value matrix, abs(S) is the modulus of the complex number of the elements in matrix S, τ is the adjustment parameter, and H is the conjugate transpose.

[0031] Furthermore, the projection operator P is obtained using the following formula:

[0032]

[0033] Where X is the input matrix of the projection operator P, Ω' is the set of coordinate points of the matrix region mapped according to the elements in matrix X, and i,j are the coordinates of the elements in the matrix formed according to the projection operator P.

[0034] Furthermore, the augmented Lagrange function is expressed by the following formula:

[0035]

[0036] Where ρ > 0 is the penalty factor, and T is the augmented Lagrange multiplier matrix. m is the number of grid rows, and n is the number of grid columns.<X-Z,T> =trace((XZ) H T), ||·|| * This indicates the search for the nuclear norm of ·.

[0037] Furthermore, in When estimating H, we assume that the channel is a Ricean channel with parameters following a Ricean distribution, and that the radiation source signal is a narrowband signal.

[0038] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0039] 1. This invention randomly selects a preset number of grid points according to a uniform distribution. Based on the observed sample data and the selected grid point locations, a likelihood ratio test statistic after time delay compensation is calculated as the matrix element of the grid point location. A low-rank matrix completion method is used to complete the matrix elements of the unselected grid points in the entire radiation source sensing area, forming a synchronous likelihood ratio test statistic matrix of the received signal in the sensing area. The position of the peak value in this synchronous likelihood ratio test statistic matrix is ​​determined as the location of the radiation source. Compared with the direct positioning method in the prior art that traverses the entire sensing area for radiation source localization, this invention's distributed radiation source localization method based on random sampling significantly reduces the computational load while ensuring high positioning accuracy.

[0040] 2. The maximum likelihood ratio test statistic of the received data matrix after delay compensation in this invention is adopted. As an element in the matrix representing the location of the selected grid point, the calculation process is simple, while achieving high positioning accuracy.

[0041] 3. This invention proposes a new iterative algorithm to obtain the synchronization likelihood ratio test statistics matrix of the received signal in the entire sensing area. By minimizing the augmented Lagrangian function, the completed synchronization likelihood ratio test statistics matrix of the received signal in the sensing area is obtained. This method does not require sampling of the entire sensing area, and significantly reduces the required computational load while ensuring positioning performance.

[0042] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0043] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0044] Figure 1 This is a flowchart of the direct location method for radiation sources according to the present invention;

[0045] Figure 2 This is a schematic diagram showing the spatial relationship between the radiation source and the receiving node in the divided grid.

[0046] Figure 3 A comparison of the positioning accuracy between the direct positioning method based on the likelihood ratio test statistic, which involves traversing all grids, and the method described in this application.

[0047] Figure 4 The figure shows the numerical distribution of the log-likelihood ratio test statistic in the two-dimensional coordinate system of the radiation source sensing area when the average signal-to-noise ratio is -5.8 dB.

[0048] Figure 5 This is a distribution diagram of the log-likelihood ratio test statistic obtained using the method of this application in a two-dimensional coordinate system of the radiation source sensing area when the average signal-to-noise ratio is -5.8 dB. Detailed Implementation

[0049] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0050] A specific embodiment of the present invention discloses a method for direct localization of radiation sources based on random sampling, the flowchart of which is shown below. Figure 1 As shown, the specific steps include S1-S3.

[0051] S1. Receive radiation source signals from different directions using I distributed receiving nodes, where I ≥ 3; sample the received data from the I receiving nodes to obtain observation sample data at different times.

[0052] Each receiving node receives T samples within the observation time. The radiation source signal s(t) employs various modulation methods, including BPSK modulation and QPSK modulation. The signal received by the i-th receiving node within the observation time can be expressed as:

[0053]

[0054] In the formula, i = 1,...,I, t = 1,...,T, y i (t) The data received by the i-th receiving node at time t. i (t) represents the received noise of the i-th receiving node during the observation time, which follows a mean of 0 and a variance of . They follow a complex Gaussian distribution and are statistically independent of each other. i Let s(t) represent the channel parameters from the radiation source to the i-th receiving node, following a Ricean distribution. Let s(t) represent the radiation source signal, and τ... i This represents the propagation delay from the radiation source to the i-th receiving node. In this embodiment of the invention, the H0 assumption assumes that the radiation source has no radiation signal; the H1 assumption assumes that the radiation source has a radiation signal.

[0055] In distributed positioning, I distributed receiving nodes receive signals from a radiation source from different directions. The radiation source acts as the transmitter. When each transmitting node and each receiving node has only one antenna, and the transmitting and receiving nodes are relatively stationary, the channel model from the transmitting node to the i-th receiving node is as follows: is an unknown complex number that follows a Rice distribution, where α i φ i These are complex channel parameters, representing the influence of the channel on the signal amplitude and phase, respectively.

[0056] S2. Establish a two-dimensional coordinate system for the radiation source sensing area and divide it into grids; randomly select a preset number of grid points according to a uniform distribution, and calculate the likelihood ratio test statistic after time delay compensation based on the observed sample data and the selected grid point locations as the matrix elements of the corresponding grid point locations.

[0057] Specifically, the entire radiation source sensing area is divided into grids, and some grid points are randomly selected according to a uniform distribution; based on the multi-node receiving signal model, the receiving nodes sample the data to obtain the observation sample data matrix. Based on the selected grid point locations, time delay compensation is performed on the sample observation data matrix, and the corresponding log-likelihood ratio test statistic is calculated. The test statistic for the entire radiation source sensing area is completed using the low-rank matrix completion method. Based on the characteristic that the synchronous likelihood ratio test statistic is greater than that of asynchronous data, the location of the peak in the recovered matrix is ​​the location of the radiation source, thus completing the localization of the radiation source.

[0058] Construct the log-likelihood ratio test statistic and estimate it according to the maximum likelihood (ML) criterion. Assume the unknown parameters U and V in the joint conditional probability density function.

[0059] First, a channel model and a received signal model are established. The channel is modeled as a Ricean channel with parameters following a Ricean distribution. The radiating source signal is a narrowband signal, which is attenuated by the channel and then superimposed with Gaussian white noise at the receiving node, having a mean of 0 and a variance of 0. The complex Gaussian distribution.

[0060] Based on the observed sample data and the selected grid point locations, the likelihood ratio test statistic, after time delay compensation, is calculated as a matrix element representing the grid point locations, including:

[0061] Based on the positional relationship between the signal receiving node from which each observation sample data comes and the selected grid points, time delay compensation is performed on each observation sample data to generate a time delay compensated received data matrix;

[0062] The maximum likelihood ratio test statistic is calculated based on the received data matrix after time delay compensation and used as the matrix element for the selected grid point location.

[0063] Iterative solution according to Calculate the maximum likelihood ratio test statistic; where, for The estimated value of parameter U under the condition that U is the null hypothesis. The covariance matrix of the observed sample data; for The estimated value of parameter V under the condition; V is the value of parameter V under the alternative hypothesis. The covariance matrix of the observed sample data;

[0064] The iterative solution Including steps S21-S23:

[0065] S21. Initialize the iteration count k = 0, and randomly initialize... generate in, This is the estimated matrix of the noise power matrix Σ. Let be the noise power of the i-th signal receiving node, i = 1, 2, ..., I; H is the channel parameter matrix from the radiation source to each receiving node; In order to be in Assumption or Assume the estimated matrix of H;

[0066] Specifically, in When estimating H, we assume that the channel is a Ricean channel with parameters following a Ricean distribution, and that the radiation source signal is a narrowband signal.

[0067] S22, Updated Estimation in, right Eigenvalue decomposition yields the eigenvector matrix. and eigenvalue diagonal matrix For the thresholded eigenvalue matrix, Q is any orthogonal matrix;

[0068] S23. Determine whether the iteration has converged according to the following formula:

[0069]

[0070] If the above formula is true, and In order to be in Assuming the estimated matrix of H is given below, As If the above formula is true, and In order to be in Assuming the estimated matrix of H is given below, As If the above equation does not hold, return to step S2 to continue the iteration; where ε is the convergence accuracy.

[0071] The formula for calculating the maximum likelihood ratio test statistic of the received data matrix after time delay compensation is:

[0072]

[0073] in, for The estimated value of parameter U under the condition that U is the null hypothesis. The covariance matrix of the observed sample data; for The estimated value of parameter V under the condition; V is the value of parameter V under the alternative hypothesis. The covariance matrix of the observed sample data; det(·) is used to calculate the determinant of matrix ·, tr(·) is used to calculate the trace of matrix ·, and S is the covariance matrix of the received data matrix after time delay compensation. Let T be the received data matrix after time delay compensation, and let T be the number of samples corresponding to each receiving node in the observed sample data, t = 1, 2, ..., T.

[0074] Specifically, based on the constructed multi-node signal reception model, in and Under the assumption that the joint conditional probability density functions of I receiving nodes and all observed samples are as follows:

[0075]

[0076] In the formula, express Assume the joint conditional probability density function value of the observed samples. express Assume the joint conditional probability density function value of the observed samples. U is Assume the covariance matrix of the observation data from the next I nodes is V. Suppose we have the covariance matrix of the observation data from the next I nodes. The determinant is represented by det(·).

[0077] exist and Under the assumptions, the log-likelihood ratio (GLR) test statistic is constructed based on the joint conditional probability density function of I receiving nodes and all observed samples.

[0078] The process of simplifying the log-likelihood ratio test statistic is as follows:

[0079]

[0080] In the formula, This represents the sample covariance matrix of the observed data.

[0081] consider Assuming all nodes receive data synchronously, the distributed signal reception model is as follows:

[0082] y(t)=Hs(t)+n(t)

[0083] In the formula, This indicates that there are p signal sources, each independent of the others, and the mean of s(t) is generally zero. Let p represent the channel parameters, where p is less than I. Assume there is one radiation source, i.e., p = 1. The I-dimensional noise vector n(t) is assumed to follow a complex Gaussian distribution with zero mean, i.e., n(t) ~ CN(0,Σ), where the covariance matrix Σ is a diagonal matrix. Therefore, the received signal vector follows a zero-mean Gaussian distribution, and its covariance matrix is ​​R.

[0084] R = HH H +Σ,

[0085] The covariance matrix of the received signal is a matrix of rank p plus a diagonal matrix. in,

[0086] The maximum likelihood estimation problem can be transformed into the following optimization problem:

[0087]

[0088] In the formula, R is the covariance matrix to be solved (in this embodiment, it represents U under the H0 assumption and V under the H1 assumption). t represents time, t = 1, 2, ..., T. Let represent the power of the noise received by the i-th receiving node, det() represent the determinant of the matrix, and tr(·) represent the trace of the matrix; Assuming H = 0, Under the assumption Let represent the channel parameters from the radiation source to each receiving node, and I represent the number of receiving nodes. The above equation has no closed-form solution, but a local maximum can be found through an alternating optimization method.

[0089] Time delay compensation is performed on the observation sample data of each signal receiving node, including: calculating the number of sampling points that need to be shifted forward or backward in the sampling time series of the observation sample data of each signal receiving node using the following formula:

[0090]

[0091] In the formula, Let be the data reception delay of the i-th signal receiving node. f is the data reception delay of the first signal receiving node. s Where Δn is the sampling frequency. i Let Δn be the number of sampling points that need to be shifted forward or backward in the sampling time series for the observation sample data of the i-th signal receiving node. i When the value is greater than 0, shift the time series backward by Δn. i Number of sampling points; Δn i When <0, shift forward by -Δn in the time series. i There are 1 sampling point; i = 2, 3, ..., 1; To perform rounding operation on ·.

[0092] According to the received signal model, y(t) = [y1(t),...,y I (t)] T ,t=1,...,T. The data after time delay compensation is The time-delay-compensated data is then substituted into the log-likelihood ratio test statistic to calculate the value of the log-likelihood ratio test statistic.

[0093] S3. Based on the low-rank matrix completion method, complete the matrix elements of the unselected grid points in the entire radiation source sensing area to form the synchronous likelihood ratio test statistics matrix of the received signal in the sensing area. The position of the peak value in the synchronous likelihood ratio test statistics matrix of the received signal in the sensing area is determined as the position of the radiation source.

[0094] The synchronization likelihood ratio test statistic matrix of the received signal in the entire sensing area is iteratively calculated to minimize the augmented Lagrangian function, and then completed to form the synchronization likelihood ratio test statistic matrix of the received signal in the sensing area. The iterative process includes:

[0095] S31. Initialize the entire matrix to be solved to obtain X. 0 This includes: initializing the selected preset number of grid points using the calculated likelihood ratio test statistic, and randomly initializing the remaining positions to be completed, Z... 0 =X 0 T 0 =X 0 , k = 0; where Z is the intermediate matrix and T is the augmented Lagrange multiplier matrix.

[0096] The augmented Lagrange function is expressed by the following formula:

[0097]

[0098] Where ρ > 0 is the penalty factor, and T is the augmented Lagrange multiplier matrix. m is the number of grid rows, and n is the number of grid columns.<X-Z,T> =trace((XZ) H T), ||·|| * This indicates the search for the nuclear norm of ·.

[0099] Specifically, in the specific embodiments of the present invention, ρ = 0.05 is used.

[0100] S32, Updated Estimation

[0101] T k+1 =T k -ρ(Z k+1 -Xk+1 Where D is the defined operator; P is the defined projection operator; ρ is the penalty factor; and Ω is the set of coordinates of elements in the matrix corresponding to a preset number of grid points. M is the set of coordinates of the matrix elements corresponding to the remaining grid points in the grid point matrix, excluding the preset number of grid points; M is a matrix initialized with the calculated likelihood ratio test statistic for the preset number of grid points.

[0102] Operator D is obtained using the following formula:

[0103] W′=D τ (W)=U×S'×V H ,

[0104] Where [U,S,V]=svd(W), S'=max(abs(S)-τ,0), W is the input matrix of operator D, W' is the output matrix of operator D, svd is the singular value decomposition function, U is the matrix formed by the left singular value vectors of W, S is the singular value matrix of W, V is the matrix formed by the right singular value vectors of W, S' is the thresholded singular value matrix, abs(S) is the modulus of the complex number of the elements in matrix S, τ is the adjustment parameter, and H is the conjugate transpose.

[0105] The projection operator P is obtained using the following formula:

[0106]

[0107] Where X is the input matrix of the projection operator P, Ω' is the set of coordinate points of the matrix region mapped according to the elements in matrix X, and i,j are the coordinates of the elements in the matrix formed according to the projection operator P.

[0108] S33, when ||X k+1 -X k || F Iteration stops when ||·|| is less than or equal to ε' or k is greater than K, where K is the preset number of iterations, ε' is the convergence precision, and ||·|| is the convergence precision. F To find the nuclear norm of F for ·.

[0109] The sampled observation data is time-delayed based on the randomly selected grid points, and the log-likelihood ratio test statistic at the randomly selected grid points is calculated to obtain M. Steps S31-S33 are then used to complete the matrix elements for the entire radiation source sensing area.

[0110] Figure 2 This represents the spatial relationship between the radiation source and the receiving node.

[0111] In a specific embodiment of the present invention, the modulation method of the signal emitted by the radiation source is BPSK modulation, the carrier frequency is 1.42e9Hz, the symbol rate is 20KHz, the observation time of each receiving node is 0.1s, and the sampling rate is 600KHz. The specific simulation parameter settings are shown in Table 1.

[0112] Table 1

[0113]

[0114] The radiation source sensing area is divided into grids, and 40% of the grid points are randomly selected. The remaining grid points are then used for low-rank matrix completion. In the low-rank matrix completion algorithm, the maximum number of iterations K = 50, and the penalty factor ρ = 0.05. In simulation experiments, two positioning methods—GLR-based traversal of all grids and random sampling matrix completion—are compared. The time comparison results are shown in Table 2. It can be seen that the method provided in this embodiment significantly reduces the time required. The positioning accuracy comparison chart is shown below. Figure 3 As shown, from Figure 3 It can be seen that the random sampling matrix completion localization method is not much different from the GLR-based all-grid traversal localization method (theoretically, the all-grid traversal localization method is better than other random sampling matrix completion localization methods).

[0115] Table 2

[0116]

[0117] contrast Figure 4 , Figure 5 It can be seen that the log-likelihood ratio test statistic numerical distribution obtained by the method of this application achieves similar results to the log-likelihood ratio test statistic numerical distribution obtained by the direct location method based on traversing all grids, which proves the reliability of the method.

[0118] Compared with existing technologies, the method provided in this embodiment randomly selects a preset number of grid points according to a uniform distribution. Based on the observed sample data and the selected grid point locations, it calculates the likelihood ratio test statistic after time delay compensation as the matrix element of the grid point location. Using a low-rank matrix completion method, it completes the matrix element completion for the unselected grid points in the entire radiation source sensing area, forming a synchronous likelihood ratio test statistic matrix of the received signal in the sensing area. The position of the peak value in the synchronous likelihood ratio test statistic matrix of the received signal in the sensing area is determined as the location of the radiation source. Compared with the direct positioning method in existing technologies that traverses the entire sensing area to locate the radiation source, the distributed radiation source positioning method based on random sampling in this invention significantly reduces the computational load while ensuring high positioning accuracy. The maximum likelihood ratio test statistic of the received data matrix after time delay compensation provided in this embodiment uses... As elements in the matrix representing the selected grid points, the calculation process is simple and achieves high positioning accuracy. This embodiment proposes a new iterative algorithm to obtain the synchronization likelihood ratio test statistics matrix of the received signal in the entire sensing area. By minimizing the augmented Lagrangian function, the completed synchronization likelihood ratio test statistics matrix of the received signal in the sensing area is obtained. This method does not require sampling the entire sensing area, significantly reducing the required computational load while ensuring positioning performance.

[0119] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0120] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for direct localization of radiation sources based on random sampling, characterized in that, Includes the following steps: S1, utilizing a distributed layout Each receiving node receives the radiation source signal from different directions. ≥3; The received data from each receiving node is sampled to obtain observation sample data at different times; S2. Establish a two-dimensional coordinate system for the radiation source sensing area and perform grid division; randomly select a preset number of grid points according to a uniform distribution, and calculate the likelihood ratio test statistic after time delay compensation based on the observed sample data and the selected grid point locations as the matrix elements of the corresponding grid point locations, including: Based on the positional relationship between the signal receiving node from which each observation sample data comes and the selected grid points, time delay compensation is performed on each observation sample data to generate a time delay compensated received data matrix; The maximum likelihood ratio test statistic is calculated based on the received data matrix after time delay compensation and used as the matrix element for the location of the selected grid point; S3. Based on the low-rank matrix completion method, complete the matrix elements of the unselected grid points in the entire radiation source sensing area to form the synchronous likelihood ratio test statistics matrix of the received signal in the sensing area. The position of the peak value in the synchronous likelihood ratio test statistics matrix of the received signal in the sensing area is determined as the position of the radiation source.

2. The method for directly locating a radiation source according to claim 1, characterized in that, Iterative solution , ,according to , Calculate the maximum likelihood ratio test statistic; where, for Parameters under conditions The estimated value; In the null hypothesis The covariance matrix of the observed sample data; for Parameters under conditions The estimated value; In the alternative hypothesis The covariance matrix of the observed sample data; The iterative solution , It includes the following steps: S1. Initialize the iteration count k=0, and randomly initialize... , generate , ,in, Noise power matrix The estimated matrix, , For the first The noise power of each signal receiving node. H is the channel parameter matrix from the radiation source to each receiving node; In order to be in Assumption or Assume the estimated matrix of H; S2, Updated Estimation , ; ;in, ,right Eigenvalue decomposition yields the eigenvector matrix. and eigenvalue diagonal matrix , For the thresholded eigenvalue matrix, , , It is any orthogonal matrix; S3. Determine whether the iteration has converged according to the following formula: ， If the above formula is true, and In order to be in Assuming the estimated matrix of H is given below, As If the above formula is true, and In order to be in Assuming the estimated matrix of H is given below, As If the above formula is not true, return to step S2 and continue iterating; where, For convergence accuracy.

3. The method for directly locating a radiation source according to claim 2, characterized in that, The formula for calculating the maximum likelihood ratio test statistic of the received data matrix after time delay compensation is: ， in, ; for Parameters under conditions The estimated value; In the null hypothesis The covariance matrix of the observed sample data; for Parameters under conditions The estimated value; In the alternative hypothesis The covariance matrix of the observed sample data; To obtain the matrix The determinant, To obtain the matrix The trace, S is the covariance matrix of the received data matrix after time delay compensation. , This is the received data matrix after time delay compensation. Let t = 1, 2, ..., be the number of samples corresponding to each receiving node in the observed sample data. .

4. The method for directly locating a radiation source according to claim 1, characterized in that, Time delay compensation is performed on the observation sample data of each signal receiving node, including: calculating the number of sampling points that need to be shifted forward or backward in the sampling time series of the observation sample data of each signal receiving node using the following formula: ； In the formula, For the first The data reception delay of each signal receiving node, The data reception delay of the first signal receiving node. Sampling frequency, For the first The number of sampling points that need to be shifted forward or backward in the sampling time series of the observed sample data of each signal receiving node. When the value is >0, shift backward in the time series. One sampling point; When <0, shift forward in the time series. One sampling point; ; To Perform rounding operation.

5. The method for directly locating a radiation source according to claim 1, characterized in that, The synchronization likelihood ratio test statistic matrix of the received signal in the entire sensing area is iteratively calculated to minimize the augmented Lagrangian function, and then completed to form the synchronization likelihood ratio test statistic matrix of the received signal in the sensing area. The iterative process includes: S1. Initialize the maximum likelihood ratio test statistic matrix to be solved. This includes: initializing the selected preset number of grid points with the calculated likelihood ratio test statistic, and randomly initializing the remaining positions to be filled. , , k=0; where Z is the intermediate matrix and T is the augmented Lagrange multiplier matrix; S2, Updated Estimation , ; Where D is a defined operator; P is a defined projection operator; As a penalty factor, This is the set of coordinates of the elements in the matrix corresponding to a preset number of grid points. M is the set of coordinates of the matrix elements corresponding to the remaining grid points in the grid point matrix, excluding the preset number of grid points; M is a matrix initialized with the calculated likelihood ratio test statistic for the preset number of grid points. S3, when or The iteration stops when K is the preset number of iterations. To improve convergence accuracy, To Find the nuclear norm of F.

6. The method for directly locating a radiation source according to claim 5, characterized in that, Operator D is obtained using the following formula: , in, , , Let D be the input matrix of operator D. Let be the output matrix of operator D, and svd be the singular value decomposition function. for The matrix formed by the left singular value vectors, for The singular value matrix, for The matrix formed by the right singular value vectors, For a thresholded singular value matrix, abs( ) is a pair of matrices Find the modulus of the complex number from the elements in the set. To adjust the parameters, H is used for conjugate transpose.

7. The method for directly locating a radiation source according to claim 5, characterized in that, The projection operator P is obtained using the following formula: , Where X is the input matrix of the projection operator P, Let be the set of coordinate points of the matrix region mapped according to the elements in matrix X, where i,j are the coordinates of the elements in the matrix formed according to the projection operator P.

8. The method for directly locating a radiation source according to claim 5, characterized in that, The augmented Lagrange function is expressed by the following formula: ， in, Let T be the penalty factor, and T be the augmented Lagrange multiplier matrix. m is the number of grid rows, and n is the number of grid columns. , Indicates request The nuclear norm number.

9. The method for directly locating a radiation source according to claim 3, characterized in that, exist When estimating H, we assume that the channel is a Ricean channel with parameters following a Ricean distribution, and that the radiation source signal is a narrowband signal.

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