Non-line-of-sight radiation source direct positioning method

Abstract

The invention discloses a non-line-of-sight radiation source direct positioning method, which comprises the following steps of: constructing a signal receiving model for auxiliary positioning of an intelligent reflecting surface aiming at a scene of a plurality of to-be-observed targets, the intelligent reflecting surface and a receiving end; on the basis of the signal receiving model, discrete Fourier transform is utilized, and transform results of different frequency points are subjected to combined representation, so that a matrix related to the phase of the intelligent reflecting surface is determined; grid division is carried out on a plane space, and a sparse dictionary is constructed based on the matrix related to the phase of the intelligent reflecting surface; sparse recovery of the signals is carried out by using a sparse Bayesian learning method; and positioning the to-be-observed target based on the sparse dictionary by using a result after signal sparse recovery. The method provided by the invention has relatively high positioning precision and resolution in a scene with low signal-to-noise ratio and small snapshot.

Description

Technical Field

[0001] The invention relates to the field of array signal processing, and in particular to a method for directly locating a non-line-of-sight radiation source. Background Art

[0002] Current passive positioning technology has many applications in the fields of electronic reconnaissance, search and rescue, and unmanned driving. According to the steps of passive positioning to estimate the position of the radiation source, it can be divided into two categories: two-step positioning and direct positioning (Direct Position Determination, DPD). Traditional two-step positioning requires the estimation of intermediate parameters first, and then parameter association to achieve the estimation of the radiation source position. Compared with two-step positioning, DPD can effectively avoid the data association problem. At the same time, since DPD does not have intermediate processing, it can effectively utilize the correlation between received data. In actual positioning scenarios, the line-of-sight path between the radiation source and the observation station may be blocked. For this scenario, auxiliary positioning is performed by setting a reflector with a known position. However, the existing reflector-assisted direct positioning technology is mostly based on general reflectors, and the information that can be used is very limited. In the research that considers setting the reflector as an intelligent reflective surface (Reconfigurable Intelligence Surface, RIS), most of the targets are estimated for the direction of arrival. Further parameter association is required to achieve positioning. Summary of the invention

[0003] The purpose of the present invention is to provide a non-line-of-sight radiation source direct positioning method to improve the target positioning accuracy in low signal-to-noise ratio scenarios.

[0004] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0005] A non-line-of-sight radiation source direct positioning method, comprising:

[0006] For scenarios with multiple targets to be observed, smart reflective surfaces, and receiving ends, a signal receiving model for smart reflective surface-assisted positioning is constructed;

[0007] Based on the signal receiving model, discrete Fourier transform is used to combine the transform results of different frequency points to determine a matrix related to the phase of the smart reflector;

[0008] Meshing the plane space, and constructing a sparse dictionary based on the matrix related to the phase of the smart reflection surface;

[0009] Use sparse Bayesian learning method to perform sparse recovery of signals;

[0010] The result after signal sparse recovery is used to locate the target based on the sparse dictionary.

[0011] Furthermore, the construction of a signal receiving model for intelligent reflective surface assisted positioning includes:

[0012] Assume that there are K targets to be observed, and their positions are p k (k=1,…K); the number of intelligent reflective surfaces RIS used for auxiliary positioning is L, and their positions are u l (l=1,…L), each intelligent reflector is equipped with a uniform linear array of N elements, the element spacing d=λ / 2, λ represents the wavelength, and each positioning RIS has M measurement time slots; assuming that the signal transmission time of the kth target to be observed is t 0,k ; The receiving end is a single antenna, and the position is u0;

[0013] The reflected signal on the path from the kth target to be observed to the lth RIS and then to the lth RIS at the receiving end is expressed as:

[0014]

[0015] where ρ l,k represents the complex propagation coefficient of the signal of the kth target to be observed in the lth path; represents the measurement matrix corresponding to the lth RIS, where The superscript T indicates transposition, e is a natural constant, j is an imaginary unit, and the same below; and denote the amplitude and phase of the lth RIS at the mth measurement time slot and the nth array element respectively; n = 1, 2, ..., N; m = 1, 2, ..., M; e is a natural constant, j is an imaginary unit; a(α l ) represents the response of the lth RIS reflected signal reaching the receiving end, where the angle α of RIS reaching the receiving end l Known; a(θ l,k ) represents the guidance vector corresponding to the kth target to be observed to the lth RIS, θ l,k represents the arrival angle of the path, which is related to the position of the kth target; s k (t-τ l,k -t 0,k ) represents the signal complex envelope of the kth target to be observed, t is the time parameter, τ l,k represents the delay of the signal from the kth target to the receiving end after passing through the lth RIS; n l (t) represents the complex Gaussian noise corresponding to the lth RIS which is independent of the target signal to be observed;

[0016] The reflected signals of each RIS received by the receiving end are represented by the following signal receiving model:

[0017]

[0018] Where n(t) represents the noise set.

[0019] Furthermore, based on the signal receiving model, discrete Fourier transform is used and the transform results of different frequency points are combined to represent so as to determine a matrix related to the phase of the smart reflector surface; including:

[0020] For the signal at t = fT s Sampling is performed at the time (f=1,2,…,F) and discrete Fourier transform is performed to obtain:

[0021]

[0022] in and They represent the DFT coefficients of the signal and complex Gaussian noise of the target to be observed, f represents the frequency, T s is the sampling period, F is the total number of frequency points;

[0023] Some of the parameters are combined as follows:

[0024]

[0025] Among them, the matrix C related to the phase of the smart reflector is [C1, C2, ..., C L ], C l =B l diag{a(α l )}; A = blkdiag{A1,A2,…,A L}, where blkdiag(·) represents a block diagonal matrix, and the array manifold corresponding to the l-th RIS is A l =[a(θ l,1 ),a(θ l,2 ),…,a(θ l,K )]; Φ=blkdiag{β1,β2,…,β L}, β l =diag[ρ l,1 ,ρ l,2 ,…,ρ l,K ]; T f =blkdiag{τ f,1 ,τ f,2 ,…,τ f,K} represents the delay matrix related to the frequency point, where τ f,k =[τ f,1,k ,τ f,2,k ,…,τ f,L,k ] T , Indicates the fth frequency point and the delay τ l,k The relevant terms, k = 1, 2, ..., K; and the signal of each radiation source can be expressed as

[0026] Furthermore, the gridding of the plane space and the construction of a sparse dictionary based on the matrix related to the phase of the smart reflective surface include:

[0027] Divide G grids in the plane space, then the gth (g = 1, 2, ..., G) grid position is represented by p g Representation; for the l-th RIS, the corresponding array manifold can be sparsely represented as:

[0028]

[0029] where a l (p g ) represents the response vector formed by the g-th grid relative to the l-th RIS;

[0030] The complex propagation coefficient corresponding to the lth RIS and the path delay generated by each frequency point f on different RIS paths are sparsely expressed as:

[0031] V l =diag(ρ l,1 ,…,ρ l,G )

[0032]

[0033] Among them, ρ l，G It represents the complex propagation coefficient of the signal relative to the lth path when the target to be observed exists in the Gth grid; τ l，G represents the delay from the Gth grid to the receiving end after passing through the lth RIS, t 0，G represents the signal emission time when the target to be observed exists in the Gth grid. For the convenience of subsequent representation, let v l =[ρ l,1 ,…,ρ l,G ] T ;

[0034] Considering that the matrix C related to the phase of the smart reflector is known, for the fth frequency point, considering multiple frequency domain snapshots, the sparse representation of the signal is:

[0035]

[0036] in y f(i) represents the signal to be recovered, εf represents the noise, and i represents the i-th frequency domain snapshot corresponding to the f-th frequency point; to further simplify the expression, let the sparse dictionary Each column of the sparse dictionary represents the position of a grid g in the plane space.

[0037] Furthermore, the method of using sparse Bayesian learning to perform sparse recovery of signals includes:

[0038] Assuming the noise ε f Follows complex normal distribution Where α0 represents the error precision, I represents the unit matrix, and the error precision α0 obeys the gamma distribution p(α0|c,d)=Γ(α0|c,d); Γ(c) represents the gamma function, c and d are the gamma distribution parameters;

[0039] For the signal to be restored y f (i) Constructing sparse hierarchical priors:

[0040] In the first level prior y f Obeys a complex Gaussian distribution with zero mean Where Λ=diag(α), α=[α1,...,α G ] T , where α g Represents the signal power parameter at the gth position; in the second layer of priors, the power parameter α is assumed to have a gamma prior distribution The gamma distribution parameters 1 and ρ involved are also fixed values;

[0041] According to the Bayesian principle, the signal to be restored y can be deduced f The posterior distribution of (i) is:

[0042]

[0043] The posterior mean and variance are:

[0044]

[0045] Σ f =(α0Ψ f H Ψ f +Λ -1 ) -1

[0046] In the above formula, the parameter superscript H represents the conjugate transpose;

[0047] After determining the posterior mean and variance, we can further obtain the hyperparameter update expressions contained in the posterior mean and variance; in the case of multiple snapshots, α0, α g、v l The update expression is as follows:

[0048]

[0049] Among them U f (i) = diag(μ f (i)), ⊙ represents the Hadamard product, I represents the total number of frequency domain snapshots, tr(·) represents the trace of the matrix, μ f,g (i) represents μ f The g-th element of (i), Σ f,gg Represents Σ f The g-th row and g-th column element of express The matrix consists of the elements in the (l-1)*N+1th to l*Nth rows.

[0050] Furthermore, the method of using the result after the signal sparse recovery to locate the target to be observed based on the sparse dictionary includes:

[0051] Set the iterative convergence condition and use the iterative expression to calculate α0, α g 、v l Update until convergence; after convergence, determine the posterior mean μ f The position row index value corresponding to the K maximum values ​​in the sparse dictionary and the position of the grid in the plane space corresponding to the column with the same row index value in the sparse dictionary are the target estimation results.

[0052] A receiving end, after receiving a signal of a target to be observed, adopts the non-line-of-sight radiation source direct positioning method to locate the target to be observed.

[0053] A terminal device comprises a processor, a memory and a computer program stored in the memory; the characteristic is that when the processor executes the computer program, the non-line-of-sight radiation source direct positioning method is implemented.

[0054] A computer-readable storage medium having a computer program stored therein; wherein when the computer program is executed by a processor, the non-line-of-sight radiation source direct positioning method is implemented.

[0055] Compared with the prior art, the present invention has the following technical features:

[0056] When the line-of-sight path is blocked during positioning, the present invention can achieve high-precision estimation of the target position of the radiation source; by equipping an intelligent reflective surface with a known position and combining a sparse Bayesian learning method to perform sparse recovery of the signal, the target position of the radiation source can be determined. The present invention has high positioning accuracy and resolution in low signal-to-noise ratio and short snapshot scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 This is a schematic diagram of the RIS-assisted positioning scenario;

[0058] Figure 2 The uniform grid positioning result in the embodiment of the present invention;

[0059] Figure 3 is the non-uniform grid positioning result in an embodiment of the present invention;

[0060] Figure 4 This is a relationship diagram between positioning estimation accuracy and signal-to-noise ratio in an embodiment of the present invention. DETAILED DESCRIPTION

[0061] In actual non-line-of-sight positioning scenarios, due to the presence of obstacles such as tall buildings, trees or mountains, the target to be located is located in the observation blind spot, making it difficult to estimate the target position. Therefore, it is considered to set up intelligent reflective surfaces with known positions and quantities for assistance. However, in multi-target scenarios with low signal-to-noise ratio, when the distance between the observed targets is relatively close, the positioning performance of the traditional subspace method is severely reduced, and sometimes even fails. In order to achieve accurate positioning of targets in such scenarios, the present invention combines the sparse Bayesian Learning (SBL) theory to provide a non-line-of-sight radiation source direct positioning method; the method is applied to a receiving end, which can be, for example, a reconnaissance platform; the method includes the following steps:

[0062] Step 1: For a scenario of multiple targets to be observed, smart reflective surfaces, and receiving ends, a signal receiving model for smart reflective surface assisted positioning is constructed.

[0063] Assume that there are K targets to be observed, and their positions are p k (k=1,…K); the number of intelligent reflective surfaces RIS used for auxiliary positioning is L, and their positions are u l (l=1,…L), each intelligent reflector is equipped with a uniform linear array of N elements, the element spacing d=λ / 2, and each positioning RIS has M measurement time slots; assuming that the signal transmission time of the kth target to be observed is t 0,k ; The receiving end is a single antenna, and the position is u0; the RIS is a planar array or a linear array, and a uniform linear array is used in this scheme.

[0064] According to the model assumption, the reflected signal on the path from the kth target to be observed to the lth RIS and then to the lth RIS at the receiving end is expressed as:

[0065]

[0066] where ρ l,k represents the complex propagation coefficient of the signal of the kth target to be observed in the lth path; represents the measurement matrix corresponding to the lth RIS, where The superscript T indicates transposition, e is a natural constant, j is an imaginary unit, and the same below; and denote the amplitude and phase of the lth RIS at the mth measurement time slot and the nth array element respectively; n = 1, 2, ..., N; m = 1, 2, ..., M; e is a natural constant, j is an imaginary unit; a(α l ) represents the response of the lth RIS reflected signal reaching the receiving end, where the angle α of RIS reaching the receiving end l Known; a(θ l,k ) represents the guidance vector corresponding to the kth target to be observed to the lth RIS, θ l,k represents the arrival angle of the path, which is related to the position of the kth target; s k (t-τ l,k -t 0,k ) represents the signal complex envelope of the kth target to be observed, t is the time parameter, τ l,k represents the delay of the signal from the kth target to the receiving end after passing through the lth RIS; n l (t) represents complex Gaussian noise independent of the target signal to be observed.

[0067] The reflected signals of each RIS received by the receiving end can be represented by the following signal receiving model:

[0068]

[0069] Step 2: Based on the signal receiving model, discrete Fourier transform is used to combine the transform results of different frequency points to determine a matrix related to the phase of the smart reflective surface.

[0070] For data at t = fT s (f=1,2,…,F) is sampled; at the same time, in order to separate the parameters, discrete Fourier transform is performed to obtain:

[0071]

[0072] in and They represent the DFT coefficients of the signal and complex Gaussian noise of the target to be observed, f represents the frequency, T s is the sampling period, and F is the total number of frequency points.

[0073] In order to simplify the model, some of the parameters can be merged and the above expression can be rewritten into matrix form as follows:

[0074]

[0075] Where C=[C1,C2,…,C L ], C l =B l diag{a(α l )}; A = blkdiag{A1,A2,…,A L}, where blkdiag(·) represents a block diagonal matrix, and the array manifold corresponding to the l-th RIS is A l =[a(θ l,1 ),a(θ l,2 ),…,a(θ l,K )]; Φ=blkdiag{β1,β2,…,β L}, β l =diag[ρ l,1 ,ρ l,2 ,…,ρ l,K ]; T f =blkdiag{τ f,1 ,τ f,2 ,…,τ f,K} represents the delay matrix related to the frequency point, where τ f,k =[τ f,1,k ,τ f,2,k ,…,τ f,L,k ] T , Indicates the fth frequency point and the delay τ l,k The relevant terms, k = 1, 2, ..., K; and the signal of each radiation source can be expressed as

[0076] It is worth noting that θ l,k is a parameter related to the position of the kth target to be observed, so the position p of the target can be used k Represents θ l,k , the guidance vector of the target relative to the lth RIS is a l (θ l,k (p k )), in the following text, a l (p k ) abbreviation.

[0077] Step 3, gridding the plane space, and constructing a sparse dictionary based on the matrix related to the phase of the smart reflection surface.

[0078] Divide G (G>>K) grids in the plane space, then the gth (g=1,2,…,G) grid position is represented by p g Representation; Therefore, for the l-th RIS, the corresponding array manifold can be sparsely represented as:

[0079]

[0080] where a l (p g ) represents the response vector formed by the g-th grid relative to the l-th RIS.

[0081] The complex propagation coefficient corresponding to the lth RIS and the path delay generated by each frequency point f on different RIS paths are sparsely expressed as:

[0082] V l =diag(ρ l,1 ,…,ρ l,G )

[0083]

[0084] Among them, ρ l，G It represents the complex propagation coefficient of the signal relative to the lth path when the target to be observed exists in the Gth grid; τ l，G represents the delay from the Gth grid to the receiving end after passing through the lth RIS, t 0，G represents the signal emission time when the target to be observed exists in the Gth grid. For the convenience of subsequent representation, let v l =[ρ l,1 ,...,ρ l,G ] T .

[0085] At the same time, considering that the matrix C related to the RIS phase is known, for the fth frequency point, considering multiple frequency domain snapshots, the sparse representation of the signal is:

[0086]

[0087] in y f (i) represents the signal to be recovered, εf represents the noise, and i represents the i-th frequency domain snapshot corresponding to the f-th frequency point; to further simplify the expression, the sparse dictionary can be made Each column of the sparse dictionary represents the position of a grid g in the plane space.

[0088] Step 4: Use sparse Bayesian learning method to perform sparse recovery of signals.

[0089] Assuming the noise ε f Follows complex normal distribution Where α0 represents the error precision, I represents the unit matrix, and the error precision α0 obeys the gamma distribution p(α0|c,d)=Γ(α0|c,d); Γ(c) represents the gamma function, c and d are the gamma distribution parameters.

[0090] For the signal to be restored y f (i) Constructing sparse hierarchical priors:

[0091] In the first level prior y f Obeys a complex Gaussian distribution with zero mean Where Λ=diag(α), α=[α1,...,α G ] T , where α g Represents the signal power parameter at the gth position; in the second layer of priors, the power parameter α is assumed to have a gamma prior distribution The gamma distribution parameters 1 and ρ involved are also fixed values. Like c and d, they need to be set according to actual conditions, but they should satisfy: c, d→0.

[0092] According to the Bayesian principle, the signal to be restored y can be deduced f The posterior distribution of (i) is:

[0093]

[0094] The posterior mean and variance are:

[0095]

[0096] Σ f =(α0Ψ f H Ψ f +Λ -1 ) -1

[0097] In the above formula, the superscript H represents the conjugate transpose, the same below;

[0098] After determining the posterior mean and variance, we can further obtain the hyperparameter update expressions contained in the posterior mean and variance; in the case of multiple snapshots, α0, α g 、v l The update expression is as follows:

[0099]

[0100] Among them U f (i) = diag(μ f (i)), ⊙ represents the Hadamard product, I represents the total number of frequency domain snapshots, tr(·) represents the trace of the matrix, μ f,g (i) represents μ f The g-th element of (i), Σ f,gg Represents Σ f The g-th row and g-th column element of express The matrix consists of the elements in the (l-1)*N+1th to l*Nth rows.

[0101] Step 5: Using the result of signal sparse recovery, locate the target to be observed based on the sparse dictionary.

[0102] Set the iterative convergence condition and update the relevant parameters through iterative expressions until convergence; after convergence, determine the posterior mean μ f The position row index value corresponding to the K maximum values ​​in the sparse dictionary, and the position of the grid in the plane space corresponding to the column with the same row index value in the sparse dictionary is the target estimation result

[0103] That is, each iteration obtains a posterior mean μ f (i) This value is compared with the value obtained in the previous iteration until the difference between the two is less than the preset value or the maximum number of iterations is reached, that is, convergence; since there are G grids, the number of rows of the posterior mean is G, which corresponds to the G columns of the sparse dictionary one by one, and each column of the sparse dictionary represents the position of a grid in the plane space. Since G is much larger than the number of targets to be observed K, the final recovery result is that the maximum values ​​appear at K positions, and the values ​​of the remaining GK positions are all close to 0. Then the positions corresponding to the K maximum values ​​are the estimated positions of the targets to be measured.

[0104] The invention relates to an iterative setting with two iterative convergence conditions, namely, an error tolerance δ and a maximum number of iterations i max . If only the error tolerance value is set as the iteration termination condition, then in the actual iteration, if the tolerance value is set unreasonably, it may be difficult to reach the error tolerance, resulting in too long iteration time or no iteration termination; if only the maximum number of iterations is set as the iteration termination condition, there may be a situation where the posterior mean error between the two iterations reaches a small value and then increases, resulting in overfitting. It can be seen that whether it is the error tolerance or the maximum number of iterations, it is very important to select appropriate parameter settings. This simulation sets the number of iterations to 5000 and the error tolerance to 5×10 -4 .

[0105] Example:

[0106] In one embodiment of the present invention, the basic settings are as follows: the smart reflective surface adopts a uniform linear array composed of 5 antenna array elements, the array element spacing is half the wavelength of the incident signal, the measurement time slot of the smart reflective surface is 25 times, the number of frequency points of Fourier transform is 32, and the number of frequency bands corresponding to each frequency point is 20; the positions of the targets to be observed are (0, 200) m and (15, 215) m respectively; the positions of the smart reflective surface are (-50, 0) m, (100, 0) m, (100, 100) m respectively, and the receiving station position is (200, 200) m.

[0107] Experiment 1: Uniform grid setting, the number of spatial network grids is 26×26, the search range is -5~20m in the x-coordinate direction, 195~220m in the y-coordinate direction, the interval is 1m, and the signal-to-noise ratio is 10dB. Figure 2 This is the spatial spectrum diagram of the method of the present invention under uniform grid division. It can be seen from the figure that the spectrum peak appears at the actual position of the target position, which proves the effectiveness and accuracy of the method.

[0108] Experiment 2: Non-uniform grid setting. Based on Experiment 1, non-uniform grids are further set. The large grid is set as in Experiment 1, with a grid number of 26×26, a search range of -5 to 20m in the x-coordinate direction, and a search range of 195 to 220m in the y-coordinate direction, with an interval of 1m. Then, with the uniform grid positioning result as a reference, a smaller uniform grid is divided near the estimated result. The number of grids in each small area is 21×21, and the x and y coordinate ranges of the small grid area are set at -2 to 2m around the uniform grid positioning result, that is, the small grid interval is 0.2m. Figure 3 This is the spatial spectrum of the method of the present invention under non-uniform grid division. It can be seen from the figure that a spectrum peak appears near the true value of the target position. Compared with a uniform grid with a larger spacing, its positioning result is more precise. At the same time, it can also prove the effectiveness and accuracy of the method.

[0109] Experiment 3: To further illustrate the effectiveness of the method of the present invention under low signal-to-noise ratio, a direct positioning method based on the rank-reduced (RARE) principle is selected for comparison. The SBL method divides the spatial grid in the same way as in Experiment 2, and the RARE method simultaneously searches for spectrum peaks within this range. The Monte Carlo experiment is performed 400 times, and the signal-to-noise ratio ranges from -5dB to 15dB. The rest of the settings are consistent with the basic experimental settings. Figure 4 The results of the root mean square error (RMSE) of the two methods show that the SBL method has higher positioning accuracy when the signal-to-noise ratio is low and the distance between the target positions is small. However, under high signal-to-noise ratio, the estimation accuracy of the SBL method is lower than that of the RARE method. This is because the SBL method updates the fading coefficient during the iteration process. If the update of the fading coefficient cannot be completely accurate, it will affect the estimation of the radiation source position, while the RARE method will not be affected by this.

[0110] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A method for directly locating a non-line-of-sight radiation source, characterized in that: include: For scenarios with multiple targets to be observed, smart reflective surfaces, and receiving ends, a signal receiving model for smart reflective surface-assisted positioning is constructed; Based on the signal receiving model, discrete Fourier transform is used to combine the transform results of different frequency points to determine a matrix related to the phase of the smart reflector; Meshing the plane space, and constructing a sparse dictionary based on the matrix related to the phase of the smart reflection surface; Use sparse Bayesian learning method to perform sparse recovery of signals; The result after signal sparse recovery is used to locate the target based on the sparse dictionary.

2. The non-line-of-sight radiation source direct positioning method according to claim 1, characterized in that: The construction of a signal receiving model for intelligent reflective surface assisted positioning includes: Assume that there are K targets to be observed, and their positions are p k (k=1,…K); the number of intelligent reflective surfaces RIS used for auxiliary positioning is L, and their positions are u l (l=1,…L), each intelligent reflector is equipped with a uniform linear array of N elements, the element spacing d=λ / 2, λ represents the wavelength, and each positioning RIS has M measurement time slots; assuming that the signal transmission time of the kth target to be observed is t 0,k ; The receiving end is a single antenna, and the position is u0; The reflected signal on the path from the kth target to be observed to the lth RIS and then to the lth RIS at the receiving end is expressed as: where ρ l,k represents the complex propagation coefficient of the signal of the kth target to be observed in the lth path; represents the measurement matrix corresponding to the lth RIS, where The superscript T indicates transposition, e is a natural constant, j is an imaginary unit, and the same below; and denote the amplitude and phase of the lth RIS at the mth measurement time slot and the nth array element respectively; n = 1, 2, ..., N; m = 1, 2, ..., M; e is a natural constant, j is an imaginary unit; a(α l ) represents the response of the lth RIS reflected signal reaching the receiving end, where the angle α of RIS reaching the receiving end l Known; a(θ l,k ) represents the guidance vector corresponding to the kth target to be observed to the lth RIS, θ l,k represents the arrival angle of the path, which is related to the position of the kth target; s k (t-τ l,k -t 0,k ) represents the signal complex envelope of the kth target to be observed, t is the time parameter, τ l,k represents the delay of the signal from the kth target to the receiving end after passing through the lth RIS; n l (t) represents the complex Gaussian noise corresponding to the lth RIS which is independent of the target signal to be observed; The reflected signals of each RIS received by the receiving end are represented by the following signal receiving model: Where n(t) represents the noise set.

3. The non-line-of-sight radiation source direct positioning method according to claim 1, characterized in that: Based on the signal receiving model, discrete Fourier transform is used and the transformation results of different frequency points are combined to represent to determine the matrix related to the phase of the smart reflection surface; including: For the signal at t = fT s Sampling is performed at the time (f=1,2,…,F) and discrete Fourier transform is performed to obtain: in and They represent the DFT coefficients of the signal and complex Gaussian noise of the target to be observed, f represents the frequency, T s is the sampling period, F is the total number of frequency points; Some of the parameters are combined as follows: in ， The matrix C related to the phase of the smart reflector is [C1, C2, … ,C L ], C l =B l diag{a(α l )}; A = blkdiag{A1,A2,…,A L }, where blkdiag(·) represents a block diagonal matrix, and the array manifold corresponding to the l-th RIS is A l =[a(θ l,1 ),a(θ l,2 ), … ,a(θ l,K )];Φ=blkdiag{β1,β2, … ,β L }, β l =diag[ρ l,1 ,ρ l,2 ,…,ρ l,K ]; T f =blkdiag{τ f,1 ,τ f,2 ,…,τ f,K } represents the delay matrix related to the frequency point, where τ f,k =[τ f,1,k ,τ f,2,k , … ,τ f,L,k ] T , Indicates the fth frequency point and the delay τ l,k The relevant terms, k = 1, 2, ..., K; and the signal of each radiation source can be expressed as 4. The method for directly locating a non-line-of-sight radiation source according to claim 1, characterized in that: The gridding of the plane space and constructing a sparse dictionary based on the matrix related to the phase of the smart reflection surface include: Divide G grids in the plane space, then the gth (g = 1, 2, ..., G) grid position is represented by p g Representation; for the l-th RIS, the corresponding array manifold can be sparsely represented as: where a l (p g ) represents the response vector formed by the g-th grid relative to the l-th RIS; The complex propagation coefficient corresponding to the lth RIS and the path delay generated by each frequency point f on different RIS paths are sparsely expressed as: V l =diag(ρ l,1 ,...,r l,G ) Among them, ρ l，G It represents the complex propagation coefficient of the signal relative to the lth path when the target to be observed exists in the Gth grid; τ l，G represents the delay from the Gth grid to the receiving end after passing through the lth RIS, t 0，G represents the signal emission time when the target to be observed exists in the Gth grid. For the convenience of subsequent representation, let v l =[ρ l,1 ,...,ρ l,G ] T ; Considering that the matrix C related to the phase of the smart reflector is known, for the fth frequency point, considering multiple frequency domain snapshots, the sparse representation of the signal is: in y f (i) represents the signal to be restored, ε f represents noise, i represents the i-th frequency domain snapshot corresponding to the f-th frequency point; to further simplify the expression, let the sparse dictionary Each column of the sparse dictionary represents the position of a grid g in the plane space.

5. The method for directly locating a non-line-of-sight radiation source according to claim 1, characterized in that: The method of using sparse Bayesian learning to perform sparse recovery of signals includes: Assuming the noise ε f Follows complex normal distribution Where α0 represents the error precision, I represents the unit matrix, and the error precision α0 follows the gamma distribution p(α 0| c,d)=Γ(α 0| c,d); where Γ(c) represents the gamma function, c and d are the gamma distribution parameters; For the signal to be restored y f (i) Constructing sparse hierarchical priors: In the first level prior y f Obeys a complex Gaussian distribution with zero mean Where Λ=diag(α), α=[α1, ... ,α G ] T ， where α g Represents the signal power parameter at the gth position; in the second layer of priors, the power parameter α is assumed to have a gamma prior distribution The gamma distribution parameters 1 and ρ involved are also fixed values; According to the Bayesian principle, the signal to be restored y can be deduced f The posterior distribution of (i) is: The posterior mean and variance are: S f =(α0Ψ f H P f +L -1 ) -1 In the above formula, the parameter superscript H represents the conjugate transpose; After determining the posterior mean and variance, we can further obtain the hyperparameter update expressions contained in the posterior mean and variance; in the case of multiple snapshots, α0, α g 、v l The update expression is as follows: Among them U f (i) = diag(μ f (i)), ⊙ represents the Hadamard product, I represents the total number of frequency domain snapshots, tr(·) represents the trace of the matrix, μ f,g (i) represents μ f The g-th element of (i), Σ f,gg Represents Σ f The g-th row and g-th column element of express The matrix consists of the elements in the (l-1)*N+1th to l*Nth rows.

6. The non-line-of-sight radiation source direct positioning method according to claim 1, characterized in that: The method of using the result of signal sparse recovery to locate the target to be observed based on the sparse dictionary includes: Set the iterative convergence condition and use the iterative expression to calculate α0, α g 、v l Update until convergence; after convergence, determine the posterior mean μ f The position row index value corresponding to the K maximum values ​​in the sparse dictionary and the position of the grid in the plane space corresponding to the column with the same row index value in the sparse dictionary are the target estimation results.

7. A receiving end, after receiving a signal of a target to be observed, the receiving end uses the non-line-of-sight radiation source direct positioning method according to any one of claims 1 to 6 to locate the target to be observed.

8. A terminal device comprising a processor, a memory and a computer program stored in the memory; characterized in that: When the processor executes the computer program, the method for directly locating a non-line-of-sight radiation source according to any one of claims 1 to 6 is implemented.

9. A computer-readable storage medium, wherein a computer program is stored in the medium; characterized in that: When the computer program is executed by a processor, the method for directly locating a non-line-of-sight radiation source according to any one of claims 1 to 6 is implemented.

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