Single anchor node super-resolution positioning method and device, storage medium and terminal

Abstract

The invention discloses a single-anchor-node super-resolution positioning method and device, a storage medium and a terminal. The single-anchor-node super-resolution positioning method comprises the following steps: establishing a frequency control array-multiple-input-multiple-output radar system signal model based on disturbance frequency; analyzing the influence of the disturbance frequency on the positioning performance and obtaining a design criterion of a disturbance frequency sequence; and designing an optimization problem, and providing a super-resolution algorithm to realize signal multipath parameter estimation and user positioning. According to the method, frequency disturbance is carried out on signals between transmitting antennas of a frequency control array-multiple input multiple output system, and coupling between a transmitting angle and a signal propagation distance is relieved, so that estimation of a multi-path super-resolution distance and the transmitting angle in a positioning system based on a single anchor node becomes possible; the fuzzy multipath resolution can be realized based on the disturbance frequency design criterion provided by the invention, and the super-resolution parameter estimation algorithm provided by the invention can realize the super-resolution estimation of the multipath parameters and the accurate positioning of the user.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of frequency design and positioning algorithm of single anchor node super-resolution positioning system, which belongs to array signal processing technical field. BACKGROUND

[0002] Because traditional wireless positioning mode based on multiple anchor nodes consumes a lot of communication resources, wireless positioning mode based on single anchor node has become a hot research direction in recent years. In order to eliminate the synchronization error between base station and user, the parameters of multipath can be estimated and the geometric relationship between multipath is used to realize the user positioning without synchronization error. In actual scene, due to the limitation of bandwidth, there is often distance ambiguity between multipath, which leads to that multipath signal cannot be effectively separated, and the accuracy of parameter estimation cannot be guaranteed.

[0003] Considering the single anchor node user positioning problem based on multipath, the following difficulties are mainly faced:

[0004] 1. When there is distance ambiguity between multipath, it is difficult to realize accurate parameter estimation of path;

[0005] 2. In the single anchor node positioning system, the traditional frequency control array-multiple input multiple output system cannot realize super-resolution estimation of the two respectively due to the coupling of transmission angle and distance;

[0006] 3. After introducing frequency disturbance, because different pulses have different frequency sequences, the traditional parameter estimation method is no longer applicable, and a new algorithm needs to be designed to solve the multipath parameters; SUMMARY

[0007] The present application provides a single anchor node super-resolution positioning method, device, storage medium and terminal to overcome the deficiencies in the prior art. A super-resolution single anchor node positioning system based on frequency control array-multiple input multiple output system with frequency disturbance is proposed, which can eliminate the coupling between transmission angle and signal propagation distance in frequency control array-multiple input multiple output, realize super-resolution parameter estimation of multipath when there is distance ambiguity between direct path and non-direct path, solve the problem that the existing method cannot accurately estimate the multipath parameters under distance ambiguity, and design a solving algorithm suitable for the system to realize the estimation of multipath parameters.

[0008] Technical scheme: To achieve the above purpose, the technical scheme adopted by the present application is:

[0009] The present application first provides a single anchor node super-resolution positioning method, comprising the following steps:

[0010] A frequency control array-multiple input multiple output radar system signal model based on disturbance frequency is established:

[0011]

[0012] where Y n,p,q represents the output signal of the signal received by the qth antenna after matching filtering of the signal of the nth pulse at the pth frequency, Y n,p,q is a signal tensor of the receiving end , the element of the coordinate [n, p, q], N represents the number of pulses, P represents the number of transmitting antennas, and Q represents the number of receiving antennas; a0 represents the amplitude of the received signal, r0 represents the distance between the user and the base station, θ A,0 represents the angle between the direct path between the base station and the user and the normal of the user array, θ B,0 represents the angle between the direct path between the base station and the user and the normal of the base station array, f c represents the carrier frequency, Δf represents the frequency increment; c represents the speed of light; d represents the distance between adjacent antennas of the transceiving array; U n,p represents the element of the nth row and the pth column of the perturbation frequency sequence U;

[0013] Based on the established signal model of the frequency control array-multiple input multiple output radar system based on the perturbation frequency, the received signal tensor is subjected to super-resolution parameter estimation to obtain the distance, speed and angle of arrival of the user.

[0014] The application also provides a single-anchor node super-resolution positioning device, which comprises a processor and a memory; the memory stores programs or instructions, which are loaded and executed by the processor to realize the steps of the single-anchor node super-resolution positioning provided above.

[0015] The application also provides a computer readable storage medium, which stores programs or instructions, and the programs or instructions are executed by a processor to realize the steps of the single-anchor node super-resolution positioning provided above.

[0016] The application also provides a signal receiving terminal, which adopts the single-anchor node super-resolution positioning provided above to position the user.

[0017] The signal model of the frequency control array-multiple input multiple output radar system based on the perturbation frequency is established, so that super-resolution estimation of the transmission angle and the propagation distance in the single-anchor node positioning system is possible;

[0018] The influence of the perturbation frequency on the positioning performance is analyzed, and the design criteria of the perturbation frequency sequence are obtained.

[0019] An optimization problem is designed, and a super-resolution algorithm is proposed to realize parameter estimation of the signal ambiguity radius and positioning of the user.

[0020] The signal model between the user and the base station of the frequency control array-multiple input multiple output radar system based on the perturbation frequency is established, and the signal tensor of the receiving end The element with coordinates [n, p, q] is defined as Y n,p,q , represents a complex tensor with dimensions N, P, Q, Y n,p,q represents the output signal of the signal received by the qth antenna after matched filtering the signal of the nth pulse at the pth frequency, which is defined as:

[0021]

[0022] N represents the number of pulses, P represents the number of transmitting antennas, and Q represents the number of receiving antennas; r0 represents the distance between the user and the base station, θ A,0 represents the angle between the direct path between the base station and the user and the normal of the user array, θ B,0 represents the angle between the direct path between the base station and the user and the normal of the base station array, f c represents the carrier frequency, and Δf represents the frequency increment, U n,p represents the element of the perturbation frequency sequence U at the nth row and the pth column, which represents the transmitting frequency index of the pth antenna in the nth pulse; d represents the distance between adjacent antennas of the transceiver array, and c represents the speed of light. The phase difference between is:

[0023]

[0024] In the traditional frequency control array-multiple input multiple output radar model, U n,p = p, which makes the phase difference equivalent to:

[0025]

[0026] This will result in a strong coupling between θ A,0 and r0, which cannot achieve super-resolution estimation of both. Therefore, by designing the perturbation frequency sequence U, the strong coupling between θ A,0 and r0 can be removed, making super-resolution estimation of both possible.

[0027] The influence of the perturbation frequency on the positioning performance is analyzed and the design criteria of the perturbation frequency sequence are obtained. The influence of the proposed perturbation frequency sequence on the positioning performance is analyzed based on the Cramer-Rao bound, and the design criteria of the improved perturbation frequency sequence are obtained.

[0028] The parameter s0 required for direct path positioning is:

[0029] s0 = [r0 θ A,0 θ B,0 ]

[0030] The Fisher information matrix for the required parameters is represented as The element in the i-th row and j-th column is defined as:

[0031]

[0032] where F(s 0,i ,s 0,j ) is the element in the i-th row and j-th column of the Fisher information matrix F, s 0,i represents the i-th parameter in s0; represents taking the real part, represents the noise power, represents Y n,p,q , and 0,i is the derivative of s H with respect to s 0,i , (·) -1 represents the conjugate transpose, represents summing q from 0 to Q-1 in the term to be summed;

[0033] The Cramer-Rao lower bound (CRLB) for the parameter estimates in s is denoted as CRLB, where CRLB is defined as which is denoted as:

[0034]

[0035] where [F -1 ] i,i represents the i-th diagonal element of the inverse matrix of the matrix F; by minimizing the Cramer-Rao lower bound for each parameter estimate in s, the design criterion is obtained: in order to improve the accuracy of the parameter estimates in s, the design of the perturbation frequency sequence U should satisfy that f(U) is maximized, where f(U) is defined as:

[0036]

[0037] The design optimization problem is proposed, and a super-resolution algorithm is implemented to estimate the parameters of the signal ambiguity radius and the positioning of the user, including:

[0038] Based on the established model, the super-resolution parameter estimation of the user distance, speed, and angle of arrival is performed. When there is distance ambiguity between the direct path and the non-direct path, the received signal tensor can be represented as:

[0039]

[0040] Based on the received signal tensor Y, the parameters of the direct path and the non-direct path are estimated, and when there is ambiguity between the direct path and the non-direct path, the distance, transmission angle, and angle of arrival of the two paths still need to be estimated with super-resolution. The parameters to be estimated are x = [r0θ A,0 θ B,0 r1θ A,1 θ B,1 ] Twhere r0represents the direct path distance, r1represents the non-direct path distance, θ A,0 represents the angle between the direct path between the base station and the user and the normal of the user array, θ B,0 represents the angle between the direct path between the base station and the user and the normal of the base station array, θ A,1 represents the angle between the non-direct path and the normal of the user array, θ B,1 represents the angle between the non-direct path between the base station and the user and the normal of the base station array, represents the outer product of tensors. The parameter estimation problem can be written as:

[0041]

[0042] where, represents the signal coefficients to be estimated. By analyzing the correlation of each parameter, it can be found that θ B,0 , θ B,1 are independent of other parameters, so they can be solved directly by using multiple signal classification algorithm Other parameters are solved based on the Newton-orthogonal matching pursuit method. The original signal tensor is unfolded along the second dimension to form a two-dimensional matrix which can be represented as:

[0043]

[0044] is defined as:

[0045]

[0046] is defined as:

[0047]

[0048] where x = [r0θ A,0 r1θ A,1 ] T represents the parameter vector to be estimated. The objective function in the original optimization problem can be represented as:

[0049]

[0050] The parameter coarse estimation is first obtained by the orthogonal matching pursuit method and the estimation of the signal coefficient is obtained by least squares as:

[0051]

[0052] The coarse estimation is further corrected by the Newton method, the first derivative matrix and the second derivative matrix is defined as:

[0053]

[0054] The final parameter estimation of x can be obtained by Newton method iteration, and each iteration process is represented as:

[0055]

[0056] Wherein represents the parameter estimation result of the input after iterative update. The parameter estimation obtained by iterative optimization can realize the estimation of r0 and θ A,0 , and the position of the user can be uniquely determined by the two parameters.

[0057] The application also provides a signal receiving terminal which adopts the super-resolution single-anchor node positioning system and the estimation method to position the user.

[0058] The frequency design, positioning algorithm and terminal of the single-anchor node super-resolution positioning system provided by the application have the following advantages compared with the prior art.

[0059] 1. The frequency disturbance is introduced between the signal transmitting antennas of the frequency control array-multiple input multiple output system, so that the super-resolution estimation of the transmitting angle and the propagation distance in the single-anchor node positioning system becomes possible.

[0060] 2. The influence of the disturbance frequency on the positioning performance is analyzed, and the design criterion of the disturbance frequency sequence is obtained, so that the problem that the traditional frequency control array-multiple input multiple output system cannot realize the parameter estimation of the transmitting angle and the distance due to the coupling of the two in the single-anchor node positioning system is solved.

[0061] 3. The algorithm is suitable for the multipath parameter estimation after the introduction of the frequency disturbance, and can realize the super-resolution performance and the accurate positioning of the user. BRIEF DESCRIPTION OF DRAWINGS

[0062] Figure 1 The schematic diagram of the super-resolution single-anchor node positioning system provided by the application is shown.

[0063] Figure 2 The flowchart of the super-resolution single-anchor node positioning system and the estimation method provided by the application is shown.

[0064] Figure 3 The schematic diagram of the error positioning probability of the system under the ideal frequency sequence based on the design criterion of the frequency sequence is shown.

[0065] Figure 4The error positioning probability diagram under the non-ideal frequency sequence is shown in the figure. DETAILED DESCRIPTION

[0066] The application will be further clarified by the following examples and drawings. It should be understood that these examples are only used to explain the application and not intended to limit the scope of the application. After reading the application, those skilled in the art can make various modifications to the application, which are within the scope of the appended claims.

[0067] A single anchor node super-resolution positioning method, as shown in the figure, comprises the following steps: Figure 1

[0068] Step 1: Establish a signal model between the user and the base station based on the frequency control array-multiple input multiple output radar system based on the perturbation frequency, and receive the end signal tensor The element in the coordinate [n, p, q] is defined as Y n,p,q , represents a complex tensor with three-dimensional dimensions N, P, and Q, Y n,p,q represents the output signal obtained after the signal received by the qth antenna is matched filtered by the transmission frequency (f c +u n,p Δf) of the pth antenna in the nth pulse, which is defined as:

[0069]

[0070] Where N represents the number of pulses, P represents the number of transmitting antennas, and Q represents the number of receiving antennas; r0 represents the distance between the user and the base station, θ A,0 represents the angle between the direct path between the base station and the user and the normal direction of the user array, θ B,0 represents the angle between the direct path between the base station and the user and the normal direction of the base station array, f c represents the carrier frequency, Δf represents the frequency increment, U n,p represents the element of the nth row and pth column of the perturbation frequency sequence U, which represents the transmission frequency index of the pth antenna in the nth pulse; d represents the distance between adjacent antennas of the transceiver array, and c represents the speed of light.

[0071] The phase difference between the output signal obtained after the signal received by the q1th antenna is matched filtered by the transmission frequency of the p1th antenna in the n1th pulse and the output signal obtained after the signal received by the q2th antenna is matched filtered by the transmission frequency of the p2th antenna in the n2th pulse is:

[0072] ​

[0073] where, and denote the elements of Y with coordinates [n1, p1, q1] and [n2, p2, q2] in Y, respectively; Δφ = φ2- φ1denotes the phase difference between and denotes the element of the perturbation frequency sequence U in the nth1row and the p1thcolumn, denotes the element of the perturbation frequency sequence U in the nth2row and the p2thcolumn.

[0074] In the traditional frequency control array - multiple input multiple output radar model, U n,p = p, which makes the phase difference equivalent to:

[0075]

[0076] This will result in a strong coupling between θ A,0 and r0, which cannot achieve the super-resolution estimation of the two. Therefore, by designing the perturbation frequency sequence U, the strong coupling between θ A,0 and r0can be removed, making it possible to achieve super-resolution estimation of the two.

[0077] Step 2, analyze the influence of the disturbance frequency on the positioning performance and get the design criteria of the disturbance frequency sequence, based on the Cramer-Rao bound analysis of the influence of the proposed disturbance frequency sequence on the positioning performance, and get the design criteria of the improved disturbance frequency sequence.

[0078] The parameter s0required for direct path positioning is:

[0079] s0= [r0θ A,0 θ B,0 ]

[0080] The Fisher information matrix for the required parameters is denoted as The element in the ith row and jth column of F is defined as:

[0081]

[0082] where, F(s 0,i ,s 0,j ) is the element in the ith row and jth column of the Fisher information matrix F, s 0,i denotes the ith parameter in s0; denotes taking the real part, denotes the noise power, denotes Y n,p,q , and 0,i is the partial derivative of s H , (·) ​denotes the summation over q in the summation term;

[0083] The Cramer-Rao lower bound (CRLB) for the parameter estimates in s is denoted as CRLB(s), where s 0,i The Cramer-Rao lower bound (CRLB) for the parameter estimates in s is denoted as CRLB(s), where s which is denoted as:

[0084]

[0085] where [F -1 ] i,i denotes the i-th diagonal element of the inverse matrix of F;

[0086] By minimizing the Cramer-Rao lower bound (CRLB) for the parameter estimates in s, the design criterion is obtained as: to improve the accuracy of the parameter estimates in s, the design of the perturbation frequency sequence U should satisfy that f(U) is maximized, where f(U) is defined as:

[0087]

[0088] Step 3, design optimization problem, propose a super-resolution algorithm to realize parameter estimation of signal ambiguity range and positioning of users, when there is distance ambiguity between the direct path and the non-direct path, the received signal tensor Y can be expressed as:

[0089]

[0090] where r0 denotes the direct path distance, r1 denotes the non-direct path distance, θ A,0 denotes the angle between the direct path between the base station and the user and the normal direction of the user array, θ B,0 denotes the angle between the direct path between the base station and the user and the normal direction of the base station array, θ A,1 denotes the angle between the non-direct path and the normal direction of the user array, θ B,1 denotes the angle between the non-direct path between the base station and the user and the normal direction of the base station array, denotes the outer product of the tensor;

[0091] Based on the received signal tensor Y, the parameters of the direct path and the non-direct path are estimated, when there is ambiguity between the direct path and the non-direct path, it is still necessary to realize super-resolution estimation of the distance, transmission angle, arrival angle and other parameters of the two paths, and the parameters to be estimated are x = [r0 θ A,0 θ B,0 r1 θ A,1 θ B,1 ] T where r0 denotes the direct path distance, r1 denotes the non-direct path distance, θ A,0 denotes the angle between the direct path between the base station and the user and the normal direction of the user array, θ B,0denotes the angle between the direct path and the array normal of the base station, θ A,1 denotes the angle between the non-direct path and the array normal of the user, θ B,1 denotes the angle between the non-direct path and the array normal of the base station. The parameter estimation problem can be written as:

[0092]

[0093] where, denotes the signal coefficients to be estimated. By analyzing the correlation of each parameter, it can be known that θ B,0 , θ B,1 are independent of other parameters, so they can be solved directly by using multiple signal classification algorithm Other parameters are solved based on the improvement of Newton-orthogonal matching pursuit method. The original signal tensor is expanded along the second dimension to form a two-dimensional matrix which can be expressed as:

[0094]

[0095] is defined as:

[0096]

[0097] is defined as:

[0098]

[0099] where x = [r0 θ A,0 r1 θ A,1 ] T denotes the parameter vector to be estimated. The objective function in the original optimization problem can be expressed as:

[0100]

[0101] The parameter coarse estimation is first obtained by the orthogonal matching pursuit method and the estimation of the signal coefficient is obtained by least squares as:

[0102]

[0103] The coarse estimation is further corrected by Newton method, the first derivative matrix and the second derivative matrix are defined as:

[0104]

[0105] The final parameter estimation of x can be obtained by Newton method iteration, and each iteration process is represented as:

[0106]

[0107] wherein, represents the parameter estimation result after iterative updating of the input The parameter estimation obtained by iterative optimization can realize the estimation of r0 and θ A,0 , and the position of the user can be uniquely determined by the two parameters.

[0108] The following gives a verification example of the application, which is applied to a frequency perturbation super-resolution single-anchor node positioning system, and verifies that in the system designed in the application, based on the frequency design criteria and algorithm, the user can be positioned even in the case of distance ambiguity of direct path and non-direct path.

[0109] Table 1 simulation parameters

[0110] Parameter Value Number of transmit antennas P 6 Number of receive antennas Q 8 Number of pulses N 5 Frequency increment Δf 1 MHz

[0111] The simulation parameters are shown in Table 1, and the positioning error is shown in Figure 3 , Figure 4 , wherein the positioning error of Figure 3 is obtained when the frequency sequence design satisfies a larger f(U), Figure 4 and the positioning error of Figure 4 is obtained when the frequency sequence design satisfies a smaller f(U). The blue triangle in the figure represents the position of the base station, the orange circle represents the position of the scattering point forming the non-direct path, and each point on the picture represents the probability that the positioning error is greater than 3m when the user appears at this position. It can be seen that the probability of positioning error greater than 3m at most positions tends to 0. In contrast, the probability of positioning deviation in Figure 3 is higher than the positioning error of Figure 4 . This proves the effectiveness of the designed frequency sequence design criteria, and solves the problem that the traditional frequency control array-multiple input multiple output system cannot realize user positioning in the single-anchor node positioning system due to the coupling of the transmission angle and the distance.

[0112] In addition, taking the point of (-30.5m, 10.2m) as an example, when the user is located at the point, the probability of the positioning of the user having an error greater than 3m tends to 0. The direct diameter distance formed by the user being at the position is 40m, the non-direct diameter distance is 57.8m, and the distance difference between the two diameters is 17.8m, which is less than the distance resolution 25m at this time, which confirms that the accurate positioning of the user can still be realized when there is distance ambiguity between the two diameters, and indicates that the system and algorithm have the super-resolution ability to multipath and high-precision positioning performance, and formally have the ability of super-resolution estimation of the transmission angle and propagation distance in the single-anchor node positioning system.

[0113] The application takes single-anchor node user positioning as the background, verifies that the proposed single-anchor node super-resolution positioning system has the ability to realize user positioning in the case of distance ambiguity between the direct diameter and the non-direct diameter, solves the problem of the coupling of the transmission angle and the distance in the single-anchor node positioning system of the traditional frequency control array-multiple-input multiple-output system, and proves that the frequency design criteria and algorithm based on the proposed system can reduce the probability of positioning deviation and improve the positioning accuracy.

[0114] The above only describes the preferred embodiments of the application, and it should be noted that for ordinary skilled persons in the art, several improvements and refinements can be made without departing from the principles of the application, and these improvements and refinements should also be considered as the protection scope of the application.

Claims

1. A single anchor node super-resolution positioning method, characterized in that: The following steps are involved: Establish a frequency-controlled array-multi-input multi-output radar system signal model based on disturbance frequency: Among them, Y n,p,q Y represents the output signal obtained by matching the signal received by the qth antenna to the signal of the pth frequency in the nth pulse. n,p,q is the receiving end signal tensor The coordinates are [n, p, q], where N represents the number of pulses, P represents the number of transmitting antennas, and Q represents the number of receiving antennas; a0 represents the amplitude of the received signal, r0 represents the distance between the user and the base station, and θ A,0 represents the angle between the direct path between the base station and the user and the normal direction of the user array, θ B,0 represents the angle between the direct path between the base station and the user and the normal direction of the base station array, f c represents the carrier frequency, Δf represents the frequency increment; c represents the speed of light; d represents the distance between adjacent antennas in the transceiver array; U n,p Represents the element in the nth row and pth column of the perturbation frequency sequence U; Based on the established perturbation frequency-based frequency-controlled array-multi-input multi-output radar system signal model, super-resolution parameter estimation of the received signal tensor is performed to obtain the user distance, velocity and arrival angle.

2. The single anchor node super-resolution positioning method according to claim 1, characterized in that: The perturbation frequency sequence U is obtained by maximizing f(U), where f(U) is defined as:

3. The single anchor node super-resolution positioning method according to claim 2, characterized in that: The disturbance frequency sequence U is designed based on the influence criterion of the disturbance frequency sequence on the positioning performance proposed by Cramer-Rao bound analysis, including: The parameter s0 required for direct path positioning is: s0=[r0θ A,0 i B,0 ] The Fisher information matrix for the desired parameters is expressed as Its i-th row, j-th column element is defined as: Among them, F(s 0,i ,s 0,j ) is the element in row i and column j of the Fisher information matrix F, s 0,i represents the i-th parameter in s0; represents the real part, represents the noise power, Represents Y n,p,q to s 0,i Find the partial derivative, (·) H represents the conjugate transpose, Indicates that the summation of q in the summation term is from 0 to Q-1; The Cramer-Rao bound for the parameter estimates in s is denoted as CRLB, where 0,i The Cramer-Rao bound estimate is defined as It is represented as: Among them, [F -1 ] i,i , represents the i-th diagonal element of the inverse matrix F; By minimizing the Cramer-Rao bounds on the estimated parameters in s0, the design criterion is: the design of the perturbation frequency sequence U satisfies the maximization of f(U).

4. The single anchor node super-resolution positioning method according to any one of claims 1 to 3, characterized in that: Based on the established perturbation frequency-based frequency-controlled array-multi-input multi-output radar system signal model, super-resolution parameter estimation is performed on the received signal tensor to obtain the user range and arrival angle, including: The received signal tensor Y and the parameters to be estimated s of the direct path and the indirect path are: Y=α0a A (i A,0 ,r0)×3a B (i B,0 )+α1a A (i A,1 ,r1)×3a B (i B,1 ) s=[r0θ A,0 i B,0 r1θ A,1 i B,1 ] T Among them, ×3 represents the tensor outer product in the third dimension, r0 represents the direct path distance, r1 represents the indirect path distance, θ A,0 represents the angle between the direct path between the base station and the user and the normal direction of the user array, θ B,0 represents the angle between the direct path between the base station and the user and the normal direction of the base station array, θ A,1 represents the angle between the non-direct path and the normal of the user array, θ B,1 Represents the angle between the non-direct path between the base station and the user and the normal direction of the base station array; and represent the transmitting array manifold and the receiving array manifold respectively; a A The element in row n and column p in (θ, r) is defined as: a B The qth element in (θ) is defined as: Where θ represents the angle between the signal direction and the normal direction of the array, and r represents the signal transmission distance; The parameter estimation problem is written as: in, represents the signal coefficient to be estimated; represents the square of the Frobenius norm of the matrix; Use the multi-signal classification algorithm to solve θ B,0 ,θ B,1 Estimated value of right r0,θ A,0 , r1,θ A,1 The estimation of is solved based on the improved Newton-orthogonal matching pursuit method; the original signal tensor After expanding along the second dimension, a two-dimensional matrix is ​​formed Expressed as: Defined as: Defined as: Where x = [r0θ A,0 r1θ A,1 ] T represents the parameter vectors to be estimated in the direct and indirect paths at this time, x0, x1, x2, x3 represent the 1st, 2nd, 3rd, and 4th elements in x respectively; the objective function in the original optimization problem is expressed as: Firstly, a rough estimate of the parameters is obtained by the orthogonal matching pursuit method And the signal coefficient is estimated by least squares for: The rough estimate is further corrected by Newton's method, and the first-order derivative matrix and the second-order derivative matrix is defined as: The final parameter estimate of x is obtained by iterating through Newton's method; each iteration process is expressed as: in, Indicates the input The parameter estimation results after iterative update are achieved by iteratively optimizing the parameter estimation to achieve r0,θ A,0 ,r1,θ A,1 Estimates.

5. A single anchor node super-resolution positioning device, characterized in that: It includes a processor and a memory; the memory stores a program or instruction, and the program or instruction is loaded and executed by the processor to implement the steps of the single anchor node super-resolution positioning method according to any one of claims 1 to 4.

6. A computer-readable storage medium, characterized in that The readable storage medium stores a program or instruction, and when the program or instruction is executed by the processor, the steps of the single anchor node super-resolution positioning method according to any one of claims 1 to 4 are implemented.

7. A signal receiving terminal, characterized in that: The user is positioned using the single anchor node super-resolution positioning method described in any one of claims 1 to 4.

Images