Intelligent reflecting surface assisted positioning method in multipath environment

Abstract

The invention discloses a positioning method assisted by an intelligent reflecting surface in a multipath environment, which is suitable for a condition that a radiation source signal has a narrowband characteristic for a global distributed array formed by all base stations, only angle information of the signal needs to be utilized in processing, and receiving synchronization does not need to be carried out on each station; comprising the steps of establishing a signal receiving model of the intelligent reflecting surface; integrating the received signals at the intelligent reflecting surfaces, and constructing a model of global received signals corresponding to the screened frequency points; converting the globally received signal model by separating a radiation source position parameter and a channel fading parameter of a global steering matrix included in the globally received signal model; carrying out sparse representation on the converted global receiving signal model; and performing sparse recovery on the model of the global receiving signal subjected to sparse representation to obtain a sparse recovery result of the to-be-recovered signal, and obtaining a position coordinate positioning result of the radiation source target from the sparse recovery result.

Description

Technical Field

[0001] The present invention relates to the field of passive positioning, and in particular to a multi-radiation source direct positioning method assisted by an intelligent reflecting surface in a multipath environment. Background Art

[0002] Passive positioning technology does not require the use of its own signal transmission. Instead, it estimates the target's position parameters by receiving radio signals radiated or scattered by the target. Passive positioning technology has the advantages of being difficult to detect, having a long detection range, and strong survivability. Depending on the positioning processing method, target positioning methods can be roughly divided into two categories: two-step positioning methods and direct positioning (DPD) methods. Traditional passive positioning technologies are mostly based on a two-step estimation system. However, traditional two-step positioning algorithms have data association issues, especially in multipath environments. How to accurately associate signal measurement parameters with the direct and indirect paths of the target is a highly complex and difficult problem to achieve. The goal of DPD is to estimate the position of the radiation source by directly processing the received raw data. It does not require measurement parameter estimation and data association. It can effectively utilize the correlation between the data received by each observation station, effectively solving the application problems of traditional two-step positioning algorithms in multipath scenarios.

[0003] Due to the extremely difficult data association of traditional two-step positioning algorithms in multipath environments, it is difficult to achieve high-precision estimation of the radiation source position; most existing algorithms process time domain signals under the global narrowband direct positioning model, which makes the delay parameters containing position information blurred with channel fading, and cannot fully utilize the target position information in the received signal, resulting in poor positioning performance. Summary of the Invention

[0004] The purpose of the present invention is to provide a positioning method assisted by an intelligent reflector in a multipath environment to solve the problem of locating a radiation source in a multipath environment.

[0005] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0006] A positioning method assisted by an intelligent reflector in a multipath environment, comprising:

[0007] Establishing a model of the received signal of the intelligent reflective surface; by integrating the received signals at each intelligent reflective surface, constructing a model of the global received signal corresponding to each selected frequency point;

[0008] The model of the global received signal is transformed by separating the radiation source position parameters of the global steering matrix and the channel fading parameters contained in the model of the global received signal;

[0009] sparsely representing the model of the transformed global received signal;

[0010] The sparsely represented global received signal model is sparsely restored to obtain a sparse recovery result of the signal to be restored, and the position coordinate positioning result of the radiation source target is obtained therefrom.

[0011] Furthermore, the model of the global received signal at the hth frequency point is as follows:

[0012]

[0013] Where, is the global receiving signal, is the global amplitude and phase factor matrix, Φ h is the global steering matrix, is the global noise, expressed as follows:

[0014]

[0015] Φ h =[(A h,1 β1) T ,(A h,2 β2) T ,…,(A h,L β L ) T ] T

[0016]

[0017] Where l = 1, 2, ..., L, h = 1, 2, ..., H, g = 1, 2, ..., G k ; L represents the number of smart reflective surfaces, H represents the number of frequency points, G k represents the number of multipaths, and the superscript T represents transposition;

[0018]

[0019] C l =[c l,1 ,c l,2 ,…,c l,P ]

[0020] A h,l =[A h,l (p1),A h,l (p2),…,A h,l (p K )]

[0021] β l =blkdiag(β l,1 ,β l,2 ,…,β l,K )

[0022]

[0023] represents the noise in the frequency domain of the lth smart reflector at the hth frequency point, β l,k,g represents the attenuation coefficient of the gth path of the radiation signal generated by the kth radiation source target reaching the lth smart reflector, a(θ l,k,g ) represents the guidance vector generated by the radiation signal generated by the kth radiation source target reaching the lth smart reflective surface via the gth path, represents the Fourier coefficient of the hth frequency point of the received signal of the kth radiation source target, e is a natural constant, j is an imaginary unit; f h Indicates the frequency of the hth frequency point, c l,p is the amplitude and phase factor matrix of each reflective unit of the lth smart reflective surface in the pth measurement period, and P represents the number of measurement periods.

[0024] Furthermore, the model of the global received signal is transformed by separating the radiation source position parameters of the global steering matrix and the channel fading parameters contained in the model of the global received signal, including:

[0025] The global steering matrix Φ h The radiation source position parameter A in h,l and the channel fading parameter β l Separation, the model can be converted to:

[0026]

[0027] The transformed global steering matrix Ψ h for:

[0028]

[0029] Among them, the symbol Indicates "defined as"; W indicates unknown channel fading, represents the steering matrix of the kth radiation source, Represents the channel fading vector from the kth radiation source to each path to the smart reflection surface.

[0030] Furthermore, a sparse representation is performed on the model of the converted global received signal, including:

[0031] make Then the global received signal model is reformulated as Extending it to the block sparse framework, the sparse signal model is:

[0032]

[0033] Divide the observation area into grids, and set the number of grids to G; set p g =[x g ,y g ] is the position coordinate of the g-th grid; the superscript ~ on the parameter is the sparse representation form of the parameter, then represents the steering matrix corresponding to the g-th grid and is only related to the grid position; is an overcomplete array manifold, i.e. a dictionary matrix, The signal to be restored.

[0034] Furthermore, sparse recovery is performed on the sparsely represented global received signal model to obtain a sparse recovery result of the signal to be recovered, including:

[0035] S4.1, Input: Overcomplete dictionary matrix Global receiving signal at H frequency points The preset sparsity K or residual threshold r;

[0036] S4.2, Initialization: Initial value of residual Index set initial value The initial value of iteration index t is set to 1;

[0037] S4.3, execute S4.1 to S4.8 cyclically:

[0038] S4.4, find the residual R at the t-1th iteration t-1 and the overcomplete dictionary matrix Submatrix of Inner product, find the inner product's two norm, and the same submatrix corresponding to each frequency point Sum the two norms and find the subscript λ corresponding to the maximum value of the submatrix t ,Right now Among them, sum represents summation, <·> represents matrix inner product, argmax represents maximum value function; N represents the complete dictionary matrix in the current round of iteration Number of neutron matrices; overcomplete dictionary matrix Corresponding to G grid points, the jth grid corresponds to The submatrix in

[0039] S4.5, update the index set Λ of the tth iteration t =Λ t-1 ∪{λ t}, record the λ in the overcomplete dictionary matrix found in the tth iteration t The corresponding submatrix Add it to the reconstruction block atom set Φt middle;

[0040] S4.6, calculate the least squares solution for the tth iteration in Indicates the signal to be restored, that is 2 represents the L2 norm;

[0041] S4.7, Update the residual at the tth iteration Update the number of iterations t = t + 1;

[0042] S4.8, determine whether the iteration index satisfies t>K or the residual threshold r≥||R t || F , if satisfied, stop the iteration; if not satisfied, execute step 5; where ||·|| F represents the F-norm;

[0043] S4.9, output That is, the sparse recovery result of the signal to be recovered.

[0044] Furthermore, the position coordinate positioning result of the radiation source target is obtained, including:

[0045] Sparse recovery results The row coordinates of the non-zero rows in correspond to the K radiation source targets and the corresponding over-complete dictionary matrix The columns in the overcomplete array are The position coordinates and order of each grid contained therein are known. According to the corresponding relationship, the grids corresponding to the K radiation source targets can be determined, and their position coordinates are used as the position coordinate positioning results of the radiation source targets.

[0046] A terminal device comprises a processor, a memory and a computer program stored in the memory; when the processor executes the computer program, a positioning method assisted by an intelligent reflective surface in the multipath environment is implemented.

[0047] A computer-readable storage medium stores a computer program; when the computer program is executed by a processor, the positioning method assisted by an intelligent reflector in a multipath environment is implemented.

[0048] Compared with the prior art, the present invention has the following technical features:

[0049] To address the problems of high application complexity and difficulty in implementation of two-step positioning algorithms in mixed environments of line-of-sight and non-line-of-sight conditions under global narrowband conditions, and the inability to utilize the position information contained in the delay parameters in the time domain processing of the signal, the present invention directly estimates the position of the radiation source based on frequency domain processing of the signal and the BSOMP concept. Even assuming that the two-step positioning is based on successful data association, the present invention still has better positioning accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is the relative position of the smart reflective surface in one embodiment of the present invention;

[0051] Figure 2 A normalized positioning spectrum of multiple radiation sources in one embodiment of the present invention;

[0052] Figure 3 A scatter diagram showing the positioning of multiple radiation sources in one embodiment of the present invention;

[0053] Figure 4 This is a graph showing how the positioning accuracy of multiple radiation sources varies with the signal-to-noise ratio in one embodiment of the present invention;

[0054] Figure 5 Schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0055] The present invention provides a positioning method assisted by intelligent reflectors in a multipath environment. The method is applicable to conditions where the radiation source signal has narrowband characteristics for a globally distributed array composed of all base stations. In processing, only the angle information of the signal is used, and there is no need to synchronize the reception of each station. The specific steps of the present invention are as follows:

[0056] S1, establishing a model of the received signal of the smart reflective surface; by integrating the received signals at each smart reflective surface, constructing a model of the global received signal corresponding to each selected frequency point.

[0057] There are L smart reflective surfaces in the environment. Each smart reflective surface has M phase-adjustable reflective units, which are uniformly linearly distributed with a spacing of half the wavelength of the incident electromagnetic wave. Each smart reflective surface is equipped with a single-receive RF link, and all smart reflective surfaces are connected to the same central controller.

[0058] Among them, the position coordinates of the lth smart reflective surface are precisely known, which is u l =(x l ,y l )(l=1,2,…,L),x l ,y l are the x-axis and y-axis coordinates of the l-th smart reflective surface in the plane coordinate system respectively; the position of the m-th reflective unit on the l-th smart reflective surface (m=1,2,…,M) is recorded as dl,m ; There are K far-field radiation source targets to be located, and the position coordinates of the kth radiation source target are p k =(x k ,y k ) T (k=1,2,…,K), the superscript T indicates transposition; the received signal of the lth smart reflector surface contains not only the direct path signals of the K radiation source targets, but also the non-direct path signals after one reflection from other smart reflectors; let G k (G k ≤L) represents the multipath number of the kth radiation source target reaching the smart reflector. Since the signal bandwidth is narrow and the sampling frequency of the smart reflector is high, the signal remains unchanged during multiple measurements. Then the received signal of the lth smart reflector at time t (0≤t≤T) during the pth (p=1,2,…,P)th measurement period can be expressed as:

[0059]

[0060] Where T represents the length of each measurement period, P represents the number of measurement periods, g = 1 represents the control parameter related to the direct path, is the amplitude and phase factor matrix of each reflective unit of the lth smart reflective surface during the pth measurement period, A m,p and φ m,p represents the amplitude and phase of the mth reflector unit on the lth smart reflector surface during the pth measurement period, e is a natural constant, j is an imaginary unit; s k (t-τ l,k,g ) indicates that the kth radiation source target has a delay of τ l,k,g The complex envelope of the baseband signal at time τ l,k,g represents the propagation delay parameter of the radiation signal generated by the kth radiation source target through the gth path to the lth smart reflector reference point; s k (t) represents the complex envelope of the baseband signal of the kth radiation source; β l,k,g represents the attenuation coefficient of the gth path of the radiation signal generated by the kth radiation source target reaching the lth smart reflector; n(t) is the complex Gaussian noise independent of the radiation source signal and has a mean of zero; a(θ l,k,g ) represents the guidance vector generated by the radiation signal generated by the kth radiation source target reaching the lth smart reflector through the gth path, θ l,k,g is the corresponding arrival angle; the received signals during P measurement periods are stacked to form the received signal matrix as follows:

[0061]

[0062] Among them, C l =[c l,1 ,cl,2 ,...,c l,P ].

[0063] By observing the spectrum, H frequency points with higher signal-to-noise ratio of the received signal are selected, where the hth frequency point is f h Denote, h=1,2,...,H; then each received signal in the received signal matrix is ​​divided into T H Frame, where each frame has J samples; applying fast Fourier transform to the received signal of the i-th frame, the received signal matrix of the h-th frequency point of the l-th smart reflector can be obtained as follows:

[0064]

[0065] in, represents the Fourier coefficient of the hth frequency point of the received signal of the kth radiation source target, Represents the noise in the frequency domain of the lth smart reflector at the hth frequency point.

[0066] Since the arrival angle and delay parameters of the direct path and the delay parameters of the indirect path are related to the location information of the radiation source target, and the arrival angle and delay parameters of the indirect path are also related to the position of the smart reflector on the indirect path; according to the mathematical relationship between the arrival angle and delay of the multipath signal and the location parameters of the smart reflector and the radiation source on the direct path and the indirect path, let the vector of the position coordinates of the kth radiation source target be The above formula can be rewritten as:

[0067]

[0068] Where:

[0069]

[0070] The above formula can be further rewritten as:

[0071]

[0072] Where A h,l is the radiation source position parameter, β l is the channel fading parameter; is the Fourier coefficient parameter, expressed as follows:

[0073] A h,l =[A h,l (p1),A h,l (p2),…,A h,l (p K )]

[0074] β l =blkdiag(β l,1,β l,2 ,…,β l,K )

[0075]

[0076] Where blkdiag(·) represents the block diagonal.

[0077] The receiving signal matrices at each smart reflector are integrated together to construct the global receiving signal model for the hth frequency point as follows:

[0078]

[0079] Where, is the global receiving signal, is the global amplitude and phase factor matrix, Φ h is the global steering matrix, is the global noise, expressed as follows:

[0080]

[0081] Φ h =[(A h,1 β1) T ,(A h,2 β2) T ,…,(A h,L β L ) T ] T

[0082]

[0083] S2, transforming the model of the global received signal by separating the radiation source position parameters of the global steering matrix and the channel fading parameters contained in the model of the global received signal.

[0084] Consider the global steering matrix Φ in the above receiving data model h The radiation source position parameter A in h,l and the channel fading parameter β l Separation, the model can be converted to:

[0085]

[0086] The transformed global steering matrix Ψ h for:

[0087]

[0088] Among them, the symbol Indicates "defined as"; W indicates unknown channel fading, represents the steering matrix of the kth radiation source, represents the channel fading vector from the kth radiation source to each path to the smart reflection surface; specifically, and It can be expressed as:

[0089]

[0090] S3, sparsely represents the model of the transformed global received signal.

[0091] In the above global received signal, And Ψ h =ΩW, let Then the global received signal model is reformulated as After reformulation, the unknown channel fading W is implicit in the signal to be recovered H, while Ω is only related to the position parameter. Extending it to the block sparse framework, the sparse signal model is:

[0092]

[0093] Divide the observation area into grids, and set the number of grids to G; set p g =[x g ,y g ] is the position coordinate of the g-th grid; the superscript ~ on the parameter is the sparse representation form of the parameter, then represents the steering matrix corresponding to the g-th grid and is only related to the grid position; is the overcomplete array flow type, that is, the dictionary matrix of the sparse recovery process, which is only related to the position parameters; is the signal to be recovered, including the radiation source signal parameters and channel fading parameters;

[0094] Assume that the signal to be recovered With block sparse structure:

[0095]

[0096] in, Represents the signal waveform corresponding to the g-th grid, g = 1, 2, ...G.

[0097] S4, sparsely recovering the sparsely represented global received signal model to obtain a sparse recovery result of the signal to be recovered, and obtaining the position coordinate positioning result of the radiation source target from it; the specific algorithm is as follows:

[0098] S4.1, Input: Overcomplete dictionary matrix Global receiving signal at H frequency points The preset sparsity K (or residual threshold r);

[0099] S4.2, Initialization: Initial value of residual Index set initial value The initial value of iteration index t is set to 1;

[0100] S4.3, execute S4.1 to S4.8 cyclically:

[0101] S4.4, find the residual R at the t-1th iteration t-1 and the overcomplete dictionary matrix Submatrix of Inner product, find the inner product's two norm, and the same submatrix corresponding to each frequency point Sum the two norms and find the subscript λ corresponding to the maximum value of the submatrix t ,Right now Among them, sum represents summation, <·> represents matrix inner product, argmax represents maximum value function; N represents the complete dictionary matrix in the current round of iteration Number of neutron matrices; overcomplete dictionary matrix Corresponding to G grid points, the jth grid corresponds to The submatrix in

[0102] S4.5, update the index set Λ of the tth iteration t =Λ t-1 ∪{λ t}, record the λ in the overcomplete dictionary matrix found in the tth iteration t The corresponding submatrix Add it to the reconstruction block atom set Φ t middle;

[0103] S4.6, calculate the least squares solution for the tth iteration in Indicates the signal to be restored, that is ||·||2 represents the L2 norm;

[0104] S4.7, Update the residual at the tth iteration Update the number of iterations t = t + 1;

[0105] S4.8, determine whether the iteration index satisfies t>K (or the residual threshold r≥||R t || F ), if satisfied, stop the iteration; if not satisfied, go to step 5;

[0106] S4.9, output That is, the sparse recovery result of the signal to be recovered.

[0107] Among them, the sparse recovery results The row coordinates of the non-zero rows in correspond to the K radiation source targets and the corresponding over-complete dictionary matrix The columns in the overcomplete array are The position coordinates and order of each grid contained therein are known. According to the corresponding relationship, the grids corresponding to the K radiation source targets can be determined, and their position coordinates are used as the position coordinate positioning results of the radiation source targets.

[0108] Simulation experiment:

[0109] The basic setting of the experiment is as follows: there are 3 smart reflective surfaces distributed in the plane, with positions of (-200,0)m, (0,-100)m, and (200,0)m respectively. Each smart reflective surface has 15 reflective units evenly placed parallel to the x-axis, with a reflective unit spacing of d = 0.5λ, an amplitude response of 1, and a phase response that obeys a uniform distribution of [0,2π]. In addition, the channel fading parameter obeys a normal distribution with a mean of 1 and a standard deviation of 0.1, and the phase factor obeys a uniform distribution of [0,2π] and is normalized. Considering that the signal waveform emitted by the target radiation source obeys a random complex Gaussian distribution, the signal wavelength λ = 0.5. The relative position relationship of the smart reflective surfaces is as follows: Figure 1 The comparison method in the experiment is a two-step positioning algorithm based on arrival angle information, and it is assumed that the angle parameters of each path in the two-step positioning are correctly associated with each path of each target.

[0110] Experiment 1: Assume that two narrowband signals are received from the far field, and the radiation source positions are p1 = [-160, 100] T 、p2=[60,160] T ; Set the signal-to-noise ratio SNR = 5dB, the measurement period P = 15, the number of frequency points K = 64, the number of sampling points J = 200, and the number of grid points to 441, Figure 2 This is the normalized positioning spectrum of the method of the present invention, where the x and y axes represent the coordinate axes in the plane respectively. It can be seen from the figure that the method of the present invention forms a higher spectrum peak at the target radiation source, indicating that direct positioning using the present invention is feasible.

[0111] Experiment 2: The radiation source position is the same as Experiment 1, and the signal-to-noise ratio (SNR) is set to 5dB, the measurement period (P) is set to 15, the number of frequency points (K) is set to 64, and the number of sampling points (J) is set to 200. The multiple positioning results are plotted in the same scatter plot, as shown in the following example: Figure 2 As shown in the figure, it can be seen that the method of the present invention is more centralized than the two-step positioning result and is closer to the actual radiation source position.

[0112] Experiment 3: Considering that the signal-to-noise ratio varies from -10 dB to 10 dB with an interval of 2 dB, the number of sampling points is fixed at J = 200, and each point in the simulation is obtained through 200 independent Monte Carlo experiments. Figure 4 The figure shows how positioning accuracy changes with the signal-to-noise ratio (SNR). The horizontal axis is the SNR, and the vertical axis is the Root Mean Squared Error (RMSE). It can be seen that as the SNR increases, the RMSE of the proposed method gradually decreases and is always better than the two-step positioning method, achieving high-precision positioning of the radiation source. The RMSE calculation formula is:

[0113]

[0114] in, represents the estimated value of the nth target source position coordinate, W represents the number of Monte Carlo experiments, and ||·|| represents the 2-norm of the vector.

[0115] 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 positioning method assisted by an intelligent reflector in a multipath environment, characterized in that: include: Establishing a model of the received signal of the intelligent reflective surface; by integrating the received signals at each intelligent reflective surface, constructing a model of the global received signal corresponding to each selected frequency point; The model of the global received signal is transformed by separating the radiation source position parameters of the global steering matrix and the channel fading parameters contained in the model of the global received signal; sparsely representing the model of the transformed global received signal; The sparsely represented global received signal model is sparsely restored to obtain a sparse recovery result of the signal to be restored, and the position coordinate positioning result of the radiation source target is obtained therefrom.

2. The positioning method assisted by intelligent reflective surface in a multipath environment according to claim 1, characterized in that: The model of the global received signal at the hth frequency point is as follows: Where, is the global receiving signal, is the global amplitude and phase factor matrix, Φ h is the global steering matrix, is the global noise, which is expressed as follows: F h =[(A h,1 b1) T ,(A h,2 b2) T ,…,(A h,L b L ) T ] T Where l = 1, 2, ..., L, h = 1, 2, ..., H, g = 1, 2, ..., G k ; L represents the number of smart reflective surfaces, H represents the number of frequency points, G k represents the number of multipaths, and the superscript T represents transposition; C l =[c l,1 ,c l,2 ,...,c l,P ] AND h,l =[A h,l (p1),A h,l (p2),…,A h,l (p K )] b l =blkdiag(β l,1 ,b l,2 ,…,b l,K ) represents the noise in the frequency domain of the lth smart reflector at the hth frequency point, β l,k,g represents the attenuation coefficient of the gth path of the radiation signal generated by the kth radiation source target reaching the lth smart reflector, a(θ l,k,g ) represents the guidance vector generated by the radiation signal generated by the kth radiation source target reaching the lth smart reflective surface via the gth path, represents the Fourier coefficient of the hth frequency point of the received signal of the kth radiation source target, e is a natural constant, j is an imaginary unit; f h Indicates the frequency of the hth frequency point, c l,p is the amplitude and phase factor matrix of each reflective unit of the lth smart reflective surface in the pth measurement period, and P represents the number of measurement periods.

3. The positioning method assisted by intelligent reflective surface in a multipath environment according to claim 1, characterized in that: The global received signal model is transformed by separating the radiation source position parameters of the global steering matrix and the channel fading parameters contained in the global received signal model, including: The global steering matrix Φ h The radiation source position parameter A in h,l and the channel fading parameter β l Separation, the model can be converted to: The transformed global steering matrix Ψ h for: Among them, the symbol Indicates "defined as"; W indicates unknown channel fading, represents the steering matrix of the kth radiation source, Represents the channel fading vector from the kth radiation source to each path to the smart reflection surface.

4. The positioning method assisted by intelligent reflective surface in a multipath environment according to claim 1, characterized in that: The model of the transformed global received signal is sparsely represented, including: make Then the global received signal model is reformulated as Extending it to the block sparse framework, the sparse signal model is: Divide the observation area into grids, and set the number of grids to G; set p g =[x g ,y g ] is the position coordinate of the g-th grid; the superscript ~ on the parameter is the sparse representation form of the parameter, then represents the steering matrix corresponding to the g-th grid and is only related to the grid position; is an overcomplete array manifold, i.e. a dictionary matrix, The signal to be restored.

5. The positioning method assisted by intelligent reflective surface in multipath environment according to claim 1, characterized in that: Perform sparse recovery on the sparsely represented global received signal model to obtain a sparse recovery result of the signal to be recovered, including: S4.1, Input: Overcomplete dictionary matrix Global receiving signal at H frequency points The preset sparsity K or residual threshold r; S4.2, Initialization: Initial value of residual Index set initial value The initial value of iteration index t is set to 1; S4.3, execute S4.1 to S4.8 cyclically: S4.4, find the residual R at the t-1th iteration t-1 and the overcomplete dictionary matrix Submatrix of Inner product, find the inner product's two norm, and the same submatrix corresponding to each frequency point Sum the two norms and find the subscript λ corresponding to the maximum value of the submatrix t ,Right now Among them, sum represents summation, <·> represents matrix inner product, argmax represents maximum value function; N represents the complete dictionary matrix in the current round of iteration Number of neutron matrices; overcomplete dictionary matrix Corresponding to G grid points, the jth grid corresponds to The submatrix in S4.5, update the index set Λ of the tth iteration t =Λ t-1 ∪{λ t }, record the λ in the overcomplete dictionary matrix found in the tth iteration t The corresponding submatrix Add it to the reconstruction block atom set Φ t middle; S4.6, calculate the least squares solution for the tth iteration in Indicates the signal to be restored, that is ||·||2 represents the L2 norm; S4.7, Update the residual at the tth iteration Update the number of iterations t = t + 1; S4.8, determine whether the iteration index satisfies t>K or the residual threshold r≥||R t || F , if satisfied, stop the iteration; if not satisfied, execute step 5; where ||·|| F represents the F-norm; S4.9, output That is, the sparse recovery result of the signal to be recovered.

6. The positioning method assisted by intelligent reflective surface in a multipath environment according to claim 1, characterized in that: The position coordinate positioning results of the radiation source target are obtained, including: Sparse recovery results The row coordinates of the non-zero rows in correspond to the K radiation source targets and the corresponding over-complete dictionary matrix The columns in the overcomplete array are The position coordinates and order of each grid contained therein are known. According to the corresponding relationship, the grids corresponding to the K radiation source targets can be determined, and their position coordinates are used as the position coordinate positioning results of the radiation source targets.

7. 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, it implements the smart reflective surface assisted positioning method in a multipath environment according to any one of claims 1 to 6.

8. A computer-readable storage medium storing a computer program; wherein: When the computer program is executed by a processor, the positioning method assisted by an intelligent reflecting surface in a multipath environment according to any one of claims 1 to 6 is implemented.

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