A non-line-of-sight radiation source direct positioning method

Abstract

The application discloses a non-line-of-sight radiation source direct positioning method, comprising the following steps: constructing a signal receiving model of intelligent reflecting surface assisted positioning for a scene of multiple to-be-observed targets, intelligent reflecting surfaces and a receiving end; based on the signal receiving model, using a discrete Fourier transform and combining and representing transform results of different frequency points to determine a matrix related to the phase of the intelligent reflecting surface; performing grid division on a plane space and constructing a sparse dictionary based on the matrix related to the phase of the intelligent reflecting surface; using a sparse Bayesian learning method to perform sparse recovery of signals; and using the result of the sparse recovery of the signals to perform positioning of the to-be-observed targets based on the sparse dictionary. The application has high positioning precision and resolution in a low signal-to-noise ratio and small snapshot scene.

Description

Technical Field

[0001] The present 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 numerous applications in electronic reconnaissance, search and rescue, and unmanned driving. Passive positioning can be divided into two categories based on the steps involved in estimating the emitter's position: two-step positioning and direct position determination (DPD). Traditional two-step positioning requires the estimation of intermediate parameters followed by parameter correlation to achieve emitter position estimation. Compared to two-step positioning, DPD effectively avoids the data correlation problem. Furthermore, because DPD eliminates the need for intermediate processing, it effectively leverages the correlation between received data. In real-world positioning scenarios, the line-of-sight path between the emitter and the observation station may be obstructed. To address this, reflectors with known locations can be deployed to assist positioning. However, existing reflector-assisted direct positioning technologies are mostly based on general reflectors, utilizing very limited information. Research that considers reflectors as reconfigurable intelligence surfaces (RIS) primarily estimates the target's direction of arrival, requiring further parameter correlation to achieve positioning. Summary of the Invention

[0003] The present invention aims 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 receivers, a signal reception model for smart reflective surface-assisted positioning is constructed.

[0007] Based on the signal receiving model, discrete Fourier transform is used and the transform results of different frequency points are combined to represent 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 reflector;

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

[0010] The target to be observed is located based on the sparse dictionary using the result of signal sparse recovery.

[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, with an element spacing of d=λ / 2, where λ represents the wavelength. Each positioning RIS has M measurement time slots. Assume that the signal transmission time of the kth target to be observed is t 0,k ; The receiving end is a single antenna, 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 l-th 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 the RIS reaching the receiving end l Given; a(θ l,k ) represents the guidance vector from the kth target 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 complex envelope of the signal 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 the 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 time delay τ l,k The relevant terms are k=1, 2, ..., K; and the signals 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 g-th (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 follows:

[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 It represents the delay from the Gth grid to the receiving end through the lth RIS, t 0，G It 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; in order 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 sparse recovery of signals using the sparse Bayesian learning method includes:

[0038] Assuming the noise ε f Obey the 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 parameters of the gamma distribution;

[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 prior, 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 recovered 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 superscript H represents the conjugate transpose;

[0047] After determining the posterior mean and variance, we can further obtain the hyperparameter update expression 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 gth element of (i), Σ f,gg Represents Σ f The element in the gth row and gth column 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 of signal sparse recovery to locate the target 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 row index values ​​corresponding to the K maximum values ​​in the sparse dictionary and the grid positions in the plane space corresponding to the columns with the same row index values ​​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 includes a processor, a memory, and a computer program stored in the memory; characterized in 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] This invention enables high-precision estimation of the radiation source's target location when the line-of-sight path is obstructed during positioning. By deploying intelligent reflective surfaces with known positions and combining them with sparse Bayesian learning methods to perform sparse signal recovery, the radiation source's target location can be determined. This invention achieves high positioning accuracy and resolution in low signal-to-noise ratio (SNR) 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 This is the uniform grid positioning result in the embodiment of the present invention;

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

[0060] Figure 4 Graph showing the relationship 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 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 seriously reduced, and sometimes even fails. In order to achieve accurate positioning of targets in such scenarios, the present invention combines sparse Bayesian Learning (SBL) theory to provide a non-line-of-sight radiation source direct positioning method; the method is applied to the receiving end, which can be, for example, a reconnaissance platform; the method includes the following steps:

[0062] Step 1: For a scenario with 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, with an element spacing of 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 l-th 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 the RIS reaching the receiving end l Given; a(θ l,k ) represents the guidance vector from the kth target 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 complex envelope of the signal 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 reception model:

[0068]

[0069] Step 2: Based on the signal receiving model, discrete Fourier transform is used and the transform results of different frequency points are combined to represent the matrix related to the phase of the smart reflector.

[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 time delay τ l,k The relevant terms are k=1, 2, ..., K; and the signals of each radiation source can be expressed as

[0076] It is worth noting that θ l,k It 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: grid the plane space and construct a sparse dictionary based on the matrix related to the phase of the smart reflective surface.

[0078] Divide the plane space into G (G>>K) grids, then the g-th (g=1,2,…,G) grid position is represented by p g 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 follows:

[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 It represents the delay from the Gth grid to the receiving end through the lth RIS, t 0，G It 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; in order 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 Obey the 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 prior, 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 the actual situation, but they should satisfy: c, d→0.

[0092] According to the Bayesian principle, the signal to be recovered 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 expression 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 gth element of (i), Σ f,gg Represents Σ f The element in the gth row and gth column 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 based on the sparse dictionary.

[0102] Set the iterative convergence condition and update the relevant parameters through the iterative expression until convergence; after convergence, determine the posterior mean μ f The row index values ​​corresponding to the K maximum values ​​in the sparse dictionary and the grid positions in the plane space corresponding to the columns with the same row index values ​​are the target estimation results.

[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, which means convergence. Since there are G grids, the number of rows of the posterior mean is G, which corresponds one-to-one to the G columns of the sparse dictionary, 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 the iterative setting of two iterative convergence conditions, namely the error tolerance δ and the 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 error of the posterior mean before and after the iteration reaches a small value and then increases, resulting in overfitting. It can be seen from this that it is very important to select appropriate parameter settings for both the error tolerance and the maximum number of iterations. 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 configuration is as follows: the smart reflector uses a uniform linear array consisting of five antenna elements, the element spacing is half the wavelength of the incident signal, the measurement time slot of the smart reflector is 25 times, the number of Fourier transform frequency points 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 reflector are (-50, 0) m, (100, 0) m, and (100, 100) m respectively, and the receiving station is located at (200, 200) m.

[0107] Experiment 1: Uniform grid setting, the number of spatial grids is 26×26, the search range is -5 to 20 meters in the x-coordinate direction and 195 to 220 meters in the y-coordinate direction, the interval is 1 meter, 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, a non-uniform grid was further set. The large grid was set as in Experiment 1, with a grid cell count of 26×26. The search range was -5 to 20 meters in the x-coordinate direction and 195 to 220 meters in the y-coordinate direction, with a 1-meter interval. Then, using the uniform grid positioning results as a reference, smaller uniform grids were created around the estimated results. Each small grid area had a grid cell count of 21×21. The x and y coordinate ranges of the small grid areas were set to -2 to 2 meters around the uniform grid positioning results, with a grid interval of 0.2 meters. Figure 3 This is the spatial spectrum of the method in the present invention under non-uniform grid division. As can be seen from the figure, the spectrum peak appears near the true value of the target position. Compared with the uniform grid with larger spacing, the positioning result is more precise. It also proves the effectiveness and accuracy of the method.

[0109] Experiment 3: To further demonstrate the effectiveness of our method under low signal-to-noise ratio (SNR) conditions, we compared it with a direct localization method based on the rank-reduced (RARE) principle. The SBL method used the same spatial grid as Experiment 2, while the RARE method also performed a spectral peak search within this range. 400 Monte Carlo experiments were performed, with the SNR varying from -5dB to 15dB. All other settings remained the same as the basic experimental setup. Figure 4 The following are the root mean squared error (RMSE) results for the two methods. It can be seen that the SBL method has higher positioning accuracy when the signal-to-noise ratio is low and the distance between target locations is small. However, at high signal-to-noise ratios, the SBL method has lower estimation accuracy than the RARE method. This is because the SBL method updates the fading coefficient during the iteration process. If the fading coefficient update is not completely accurate, it will affect the estimation of the emitter position, while the RARE method is not 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 various embodiments of the present application, and should all be included in the scope of protection 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 receivers, a signal reception model for smart reflective surface-assisted positioning is constructed. Based on the signal receiving model, discrete Fourier transform is used and the transform results of different frequency points are combined to represent 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 reflector; Use sparse Bayesian learning method to perform sparse signal recovery; The target to be observed is located based on the sparse dictionary using the result of signal sparse recovery.

2. The non-line-of-sight radiation source direct positioning method according to claim 1, characterized in that: The construction of the signal receiving model for intelligent reflective surface assisted positioning includes: Assuming existence The target to be observed is located at ; The number of intelligent reflective surfaces RIS used for auxiliary positioning is , whose location is , each smart reflective surface is equipped with Uniform linear array of array elements, array element spacing , Indicates wavelength, each time RIS is positioned measurement time slots; assuming the k The signal transmission time of the target to be observed is ; The receiving end is a single antenna, located at ; For the k The target to be observed l RIS to the receiving end The reflected signal on the RIS path is expressed as: in Indicates the The signal of the target to be observed is in The complex propagation coefficient of each path; Indicates the The measurement matrix corresponding to the RIS is , superscript T represents transpose, e is a natural constant, j is an imaginary unit, the same below; and Respectively represent A RIS in the measurement time slots, Amplitude and phase at each array element; ; e is a natural constant, j is an imaginary unit; Indicates the The response of the RIS reflected signal to the receiver, where the angle of RIS reaching the receiver is known; Indicates the The target to be observed The steering vector corresponding to each RIS, represents the arrival angle of the path, which is the same as the The location of the target is related to Indicates the k The complex envelope of the signal of the target to be observed, t is the time parameter, Indicates the The signal of the target passes through the The delay of each RIS reaching the receiving end; Indicates the Each RIS corresponds to a complex Gaussian noise that 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: in represents the noise set.

3. The method for directly locating a non-line-of-sight radiation source according to claim 2, wherein: 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 a matrix related to the phase of the smart reflector; including: For signal Sampling is performed at the same time, and discrete Fourier transform is performed to obtain: in and Respectively represent the DFT coefficients corresponding to the signal and complex Gaussian noise of the target to be observed, Indicates frequency, is the sampling period, F is the total number of frequency points; Some of the parameters are combined as follows: Among them, the matrix related to the phase of the smart reflector is , ; ,in represents a block diagonal matrix, and the The array manifold corresponding to each RIS is: ; , ; represents the delay matrix related to the frequency point, where , Indicates the Frequency and delay The relevant items, ; The signal of each radiation source is expressed as .

4. The method for directly locating a non-line-of-sight radiation source according to claim 3, wherein: The gridding of the plane space and constructing a sparse dictionary based on the matrix related to the phase of the smart reflective surface include: Divide in plane space grid, then the Grid positions Indicates; for RIS, the corresponding array manifold sparse representation is: in Indicates the The grid is relative to the The response vector formed by the RIS; And the l The complex propagation coefficient corresponding to each RIS and each frequency point f The path delays generated on different RIS paths are sparsely represented as follows: in, Indicates the assumption G When there is an object to be observed in the grid, its signal is relative to the l The complex propagation coefficient of each path; Indicates the G The grid passes through l The delay of a RIS reaching the receiving end, Indicates the assumption G When there is a target to be observed in a grid, the signal emission time is, for the convenience of subsequent representation, let ; Considering the matrix related to the phase of the smart reflector is known, so for the frequency points, considering multiple frequency domain snapshots, the sparse representation of the signal is: in , Indicates the signal to be restored, represents noise, Indicates the The corresponding frequency frequency domain snapshots; to further simplify the expression, let the sparse dictionary ; Each column of the sparse dictionary represents a grid in the plane space g location.

5. The method for directly locating a non-line-of-sight radiation source according to claim 4, characterized in that: The method of using sparse Bayesian learning to perform sparse recovery of signals includes: Assuming noise Obey the complex normal distribution ,in Indicates the error accuracy, represents the unit matrix, and the error accuracy Also obeys the gamma distribution ;in , represents the gamma function, is the gamma distribution parameter; For signals to be restored Construct a sparse hierarchical prior: In the first layer of prior Obeys a complex Gaussian distribution with zero mean ,in , ,in Indicates the The signal power parameters at each position; the power parameters in the second layer prior Make a gamma prior distribution assumption ; The gamma distribution parameters involved are 1, They are also fixed values; The signal to be recovered is derived based on the Bayesian principle The posterior distribution of : The posterior mean and variance are: The parameters in the above formula are superscript H represents the conjugate transpose; After determining the posterior mean and variance, we can further obtain the hyperparameter update expression contained in the posterior mean and variance; in the case of multiple snapshots, 、 、 The update expression is as follows: in , represents the Hadamard product, I represents the total number of frequency domain snapshots, tr (•) means finding the trace of the matrix, express No. g elements, express No. g Rank g Column elements, express No. arrive A matrix consisting of row elements.

6. The method for directly locating a non-line-of-sight radiation source according to claim 5, characterized in that: The method of using the result of signal sparse recovery to locate the target based on the sparse dictionary includes: Set the iterative convergence condition and use the iterative expression to 、 、 Update until convergence; after convergence, determine the posterior mean middle The row index value corresponding to the maximum value, and the position of the grid in the plane space corresponding to the column of the same row index value in the sparse dictionary is the target estimation result.

7. A receiving end, after receiving a signal of a target to be observed, adopting 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 storing a computer program; wherein: When the computer program is executed by a processor, the non-line-of-sight radiation source direct positioning method according to any one of claims 1 to 6 is implemented.

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