A positioning method and terminal based on single anchor node positioning system

Abstract

This invention relates to a positioning method and terminal based on a single-anchor node positioning system. The method includes the following steps: Step S1, introducing a smart reflector into the single-anchor node positioning system to form a high-power non-direct path, and establishing a signal model of the single-anchor node positioning system based on the smart reflector; Step S2, establishing an optimization problem based on the model, and estimating the parameters of user distance, speed, and angle of arrival; Step S3, achieving user positioning based on the user's parameter estimation. Compared with the prior art, this invention achieves a high-power non-direct path by introducing a smart reflector, eliminates the positioning deviation caused by synchronization errors between the user end and the base station, and designs a low-complexity algorithm to achieve parameter estimation of the multipath and user positioning.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, and in particular to a positioning method and terminal based on a single anchor node positioning system. Background Technology

[0002] User positioning in communication systems has significant application value in various fields such as intelligent transportation and the Internet of Things. Due to the performance degradation and high latency issues of satellite positioning in complex and obstructed environments, wireless positioning-based user positioning methods have enormous application potential. Traditional wireless positioning methods rely on the time difference of arrival (TTA) between multiple anchor nodes to locate users, but communication between these anchor nodes consumes substantial communication resources. Measurements based on a single anchor node often locate users based on signal propagation time and angle of arrival (Angle of Arrival) estimation, but the signal propagation time is affected by synchronization errors between the anchor node and the user. While two-way ranging can eliminate synchronization errors, it requires a high-precision clock and frequent communication, placing a significant burden on the user end. Using non-direct path signal parameter estimation to assist user positioning is considered another way to eliminate the impact of synchronization errors. By utilizing the geometric relationship between direct and non-direct paths, the influence of synchronization errors can be removed based on the parameter estimation of the direct and non-direct paths.

[0003] Taking into account both direct and indirect routes for single-anchor node user location, the main challenges are as follows:

[0004] 1) Signals reaching the base station via indirect paths often have low power, making it difficult to accurately estimate the parameters of indirect paths;

[0005] 2) Due to the large amount of parameter information in multipaths and the different models for direct and indirect paths, parameter estimation for multipaths often has high complexity. Summary of the Invention

[0006] The purpose of this invention is to overcome the defects of the prior art and provide a positioning method and terminal based on a single anchor node positioning system.

[0007] The objective of this invention can be achieved through the following technical solutions:

[0008] According to one aspect of the present invention, a positioning method based on a single anchor node positioning system is provided, the method comprising the following steps:

[0009] Step S1: Introduce a smart reflector into the single anchor node positioning system to form a non-direct path with high power, and establish a signal model of the single anchor node positioning system based on the smart reflector.

[0010] Step S2: Establish an optimization problem based on the model, and estimate the parameters of user distance, speed, and angle of arrival;

[0011] Step S3: The user is located based on the user's parameter estimation.

[0012] As a preferred technical solution, the single anchor node positioning system in step S1 is a frequency-controlled array-multiple-input multiple-output single anchor node positioning system;

[0013] After introducing a smart reflective surface into the single-anchor node positioning system, the receiver signal tensor It can be represented as:

[0014] Y = Y LOS +Y NLOS

[0015] in The output tensor obtained by the base station receiver after signal processing, the elements of the output signal tensor with coordinates [n, p, q] represent the output signal obtained after the signal received by the q-th antenna is matched and filtered by the signal of the p-th frequency in the n-th pulse; Let N be a complex tensor with three dimensions N, P, and Q; N represents the number of pulses, P represents the number of transmit antennas, and Q represents the number of receive antennas.

[0016] This is the output tensor obtained by the base station receiver after processing the signal propagating through the non-direct path formed by the intelligent reflector.

[0017] As a preferred technical solution, the Y LOS Specifically, it is expressed as follows:

[0018]

[0019] in θ represents the distance between the user and the base station, including synchronization errors. A,0 θ represents the angle between the direct path between the base station and the user and the normal of the user array. B,0 This represents the angle between the direct path between the base station and the user and the normal of the base station array. The coefficients represent the output signal after echo processing; Represents the outer product of tensors; This represents additive white Gaussian noise. This represents the steering vector related to the user's direct path distance and launch angle. This represents the steering vector associated with the user signal's angle of arrival at the base station.

[0020] As a preferred technical solution, the guiding vector a A (θ,r) and a B The elements in (θ) are as follows:

[0021]

[0022] Where r, v, and θ represent the target's distance, velocity, and angle with the array normal, respectively, and a A,n,p (θ, r) represent the guiding vector a, respectively. A The element in the nth row and pth column of (θ,r), a B,q (θ) represents a B The q-th element in (θ); the frequency of the p-th activated antenna transmission signal in the n-th pulse is f. c +U n,p Δf, f c U represents the carrier frequency, Δf represents the frequency increment, and U n,p The frequency increment is represented by d, the distance between adjacent antennas in the transceiver array is represented by c, the speed of light is represented by P, the number of transmitting antennas is represented by Q, and the number of receiving antennas is represented by Q.

[0023] As a preferred technical solution, the Y NLOS Specifically, it is expressed as follows:

[0024]

[0025] in θ represents the distance between the user and the base station via a smart reflector, which includes synchronization errors and is not a direct path. A,1 θ represents the angle between the non-direct path and the normal of the user array. R,A Satisfy sinθ R,AOA =sinθ R,A +sinθ R,AOD , where θ R,AOA With θ R,AOD θ represents the arrival angle and departure angle of the non-direct path between the smart reflector and the normal of the smart reflector array, respectively. B,1 This indicates the angle between the non-direct path and the normal of the base station array. The coefficients represent the output non-direct path signal after echo processing; This represents the outer product of tensors, and it means that diag(·) takes the diagonal elements of the matrix. This represents the phase encoding matrix corresponding to the M units of the pulse intelligent reflector in N pulses. This represents additive white Gaussian noise. This represents the steering vector related to the user's direct path distance and launch angle. This represents the steering vector related to the user signal's angle of arrival at the base station. This represents the steering vector associated with the angle of arrival of the user signal at the smart reflector.

[0026] As a preferred technical solution, the guiding vector a A (θ,r), a B(θ) and a R The elements in (θ) are as follows:

[0027]

[0028] Where r, v, and θ represent the target's distance, velocity, and angle with the array normal, respectively, and a A,n,p (θ, r) represent the guiding vector a, respectively. A The element in the nth row and pth column of (θ,r), a B,q (θ) represents a B The q-th element in (θ), a R,m (θ) represents a R The m-th element in (θ); the frequency of the p-th activated antenna transmission signal in the n-th pulse is f. c +U n,p Δf, f c U represents the carrier frequency, Δf represents the frequency increment, and U n,p d represents the number of frequency increments; c represents the distance between adjacent antennas of the transceiver array; M represents the speed of light; and M represents the number of elements of the smart reflector.

[0029] As a preferred technical solution, in step S2, based on the established model, an optimization problem is designed, and the Newton-orthogonal matching pursuit algorithm is improved according to the property of the second derivative matrix, as follows:

[0030] The parameters to be estimated are in This represents the direct path distance, including synchronization errors. θ represents the non-direct path distance containing synchronization errors. A,0 θ represents the angle between the direct path between the base station and the user and the normal of the user array. B,0 θ represents the angle between the direct path between the base station and the user and the normal of the base station array. A,1 θ represents the angle between the non-direct path and the normal of the user array. R,A This represents the angle between the non-direct path at the smart reflector and the normal of the smart reflector array. Since the position of the smart reflector is prior, θ... B,1 The parameters are considered as known quantities; the parameter estimation problem is expressed as follows:

[0031]

[0032] in

[0033] Let θ represent the signal coefficients to be estimated. By analyzing the correlation of each parameter, we can obtain θ. B,0 Independent of other parameters, θ is solved directly using a multi-signal classification algorithm.B,0 Other parameters are solved by improving the Newton-orthogonal matching pursuit method.

[0034] As a preferred technical solution, the Newton-orthogonal matching pursuit method is as follows:

[0035] First, a rough estimate of the parameters is obtained using the orthogonal matching pursuit method. The signal coefficients are estimated using least squares.

[0036] Then, when further refining the coarse estimate using Newton's method, the first derivative matrix... Sum and second derivative matrix Defined as:

[0037]

[0038] Analyzing the elements of the second derivative matrix, the second derivative matrix is ​​further written as follows:

[0039]

[0040] express The top left corner 2×2 matrix, express The 3×3 matrix in the lower right corner, based on the second derivative structure, is updated at each step using Newton's method during iteration as follows:

[0041]

[0042] in Indicates the input The parameter estimation results after iterative updates. Defined as:

[0043]

[0044] Defined as:

[0045]

[0046] As a preferred technical solution, in step S3, a system of equations is constructed using geometric relationships and estimated parameters. The user positioning estimate without synchronization errors is obtained by solving the system of equations. This system of equations is expressed as follows:

[0047]

[0048] θ R,AOA =π-(θ) A,0 -θ A,1 )-(θB,0 -θ B,1 )-θ R,AOD ,

[0049] sinθ R,AOA =sinθ R,A +sinθ R,AOD .

[0050] Where r0 represents the direct path distance without synchronization error, r1 represents the non-direct path distance without synchronization error, Δt represents the synchronization error, c represents the speed of light, and θ... A,0 θ represents the angle between the direct path between the base station and the user and the normal of the user array. B,0 θ represents the angle between the direct path between the base station and the user and the normal of the base station array. A,1 θ represents the angle between the non-direct path and the normal of the user array. B,1 θ represents the angle between the non-direct path and the normal of the base station array. R,A θ represents the angle between the non-direct path at the smart reflector and the normal of the smart reflector array. R,AOA With θ R,AOD Let r0 and θ represent the arrival angle and departure angle of the non-direct path between the smart reflector and the normal of the smart reflector array, respectively. By solving this equation, the angles r0 and θ can be obtained. A,0 The user's location can be uniquely determined using these two parameters.

[0051] According to another aspect of the present invention, a terminal is provided that uses the positioning method based on the single anchor node positioning system described above to locate a user.

[0052] Compared with the prior art, the present invention has the following advantages:

[0053] 1) By introducing a smart reflective surface, this invention greatly increases the signal power reaching the base station through non-direct paths, making it possible to estimate the signal parameters of non-direct paths with high accuracy.

[0054] 2) Based on the second derivative features of the signal matrix in the established model, this invention simplifies the iteration process and reduces the complexity of multipath parameter estimation. Attached Figure Description

[0055] Figure 1 This is a schematic diagram of the single-anchor node positioning system based on an intelligent reflective surface according to the present invention, where Reflectingintelligent surface represents the intelligent reflective surface, Agent represents the user, and Base station represents the base station.

[0056] Figure 2 This is a flowchart of the positioning method based on the single anchor node positioning system of the present invention.

[0057] Figure 3 This is a schematic diagram of user positioning under multiple Monte Carlo simulations, where Estimation represents the user positioning result under multiple Monte Carlo simulations, Ground-truth represents the user's actual location, BS represents the base station, and RIS represents the intelligent reflector.

[0058] Figure 4 The simulation results show the positioning performance of the proposed system and method under different signal-to-noise ratios and the number of intelligent reflective array elements. Here, RMSE of estimated location of agent represents the root mean square error of positioning the user, and SNR represents the signal-to-noise ratio. Detailed Implementation

[0059] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0060] This invention introduces a smart reflector to create a high-power non-direct path, and decouples synchronization errors by combining parameter estimation of the direct and non-direct paths. It improves the Newton-orthogonal matching pursuit algorithm based on the property of the second derivative matrix, resulting in faster iteration speeds for parameter estimation in this system. By eliminating synchronization errors through parameter estimation of both direct and non-direct paths, it achieves user positioning. Compared to traditional single-anchor node positioning systems, this invention introduces a smart reflector to create a high-power non-direct path, eliminates positioning deviations caused by synchronization errors between the user and base station, and designs a low-complexity algorithm for parameter estimation of the multipath and user positioning.

[0061] like Figure 1 and 2 As shown, the present invention employs a user positioning method based on a single anchor node positioning system with an intelligent reflective surface, comprising the following steps:

[0062] Step S1: In the frequency-controlled array-multiple-input multiple-output single-anchor node positioning system, a smart reflector is introduced to form a high-power non-direct path, and the receiver signal tensor... It can be represented as:

[0063] Y = Y LOS +Y NLOS .

[0064] in, The output tensor obtained by the base station receiver after signal processing, the elements of the output signal tensor with coordinates [n, p, q] represent the output signal obtained after the signal received by the q-th antenna is matched and filtered by the signal of the p-th frequency in the n-th pulse; Y represents a complex tensor with three dimensions N, P, and Q; N represents the number of pulses, P represents the number of transmit antennas, and Q represents the number of receive antennas; LOS Represented as:

[0065]

[0066] in θ represents the distance between the user and the base station, including synchronization errors. A,0 θ represents the angle between the direct path between the base station and the user and the normal of the user array. B,0 This represents the angle between the direct path between the base station and the user and the normal of the base station array. The coefficients represent the output signal after echo processing; Represents the outer product of tensors; This represents additive white Gaussian noise. This represents the steering matrix related to the user's direct path distance and launch angle. This represents the steering vector associated with the user signal's angle of arrival at the base station, where the elements are as follows:

[0067]

[0068] Where r, v, and θ represent the target's distance, velocity, and angle with the array normal, respectively, and a A,n,p (θ, r) represent the guiding vector a, respectively. A The element in the nth row and pth column of (θ,r), a B,q (θ) represents a B The q-th element in (θ); the frequency of the p-th activated antenna transmission signal in the n-th pulse is f. c +U n,p Δf, f c U represents the carrier frequency, Δf represents the frequency increment, and U n,p represents the number of frequency increments; d represents the spacing between adjacent antennas of the transceiver array, and c represents the speed of light. The signal model for reaching the base station via a non-direct path is as follows;

[0069]

[0070] in, This is the output tensor obtained by the base station receiver after processing the signal propagating through the non-direct path formed by the intelligent reflector. θ represents the distance between the user and the base station via a smart reflector, which includes synchronization errors and is not a direct path.A,1 θ represents the angle between the non-direct path and the normal of the user array. R,A Satisfy sinθ R,AOA =sinθ R,A +sinθ R,AOD , where θ R,AOA With θ R,AOD θ represents the arrival angle and departure angle of the non-direct path between the smart reflector and the normal of the smart reflector array, respectively. B,1 This indicates the angle between the non-direct path and the normal of the base station array. The coefficients represent the output non-direct path signal after echo processing; This represents the outer product of tensors, and it means that diag(·) takes the diagonal elements of the matrix. This represents the phase encoding matrix corresponding to the M units of the pulse intelligent reflector in N pulses. This represents additive white Gaussian noise. This represents the steering matrix related to the user's direct path distance and launch angle. This represents the steering vector related to the user signal's angle of arrival at the base station. This represents the steering vector associated with the angle of arrival of the user signal at the smart reflector, where the elements are as follows:

[0071]

[0072]

[0073] Step S2: Based on the established model, design an optimization problem and improve the Newton-orthogonal matching pursuit algorithm according to the property of the second derivative matrix, so that it has a faster iteration speed in parameter estimation in this system, including:

[0074] The parameters to be estimated are in This represents the direct path distance, including synchronization errors. θ represents the non-direct path distance containing synchronization errors. A,0 θ represents the angle between the direct path between the base station and the user and the normal of the user array. B,0 θ represents the angle between the direct path between the base station and the user and the normal of the base station array. A,1 θ represents the angle between the non-direct path and the normal of the user array. R,A This represents the angle between the non-direct path at the smart reflector and the normal of the smart reflector array. Since the position of the smart reflector is prior, θ... B,1 It is considered a known quantity. This parameter estimation problem can be written as:

[0075]

[0076] in

[0077]

[0078] This represents the signal coefficients to be estimated. By analyzing the correlation of each parameter, we can determine θ. B,0 Independent of other parameters, θ can be directly solved using a multi-signal classification algorithm. B,0 Other parameters are solved using an improved version of the Newton-orthogonal matching pursuit method. First, a coarse estimate of the parameters is obtained using the orthogonal matching pursuit method. The signal coefficients are estimated using least squares. Then, when further refining the coarse estimate using Newton's method, the first derivative matrix... Sum and second derivative matrix Defined as:

[0079]

[0080] Analyzing the elements of the second derivative matrix, the second derivative matrix is ​​further written as follows:

[0081]

[0082] express The top left corner 2×2 matrix, express The 3×3 matrix in the lower right corner, based on the second derivative structure, is updated at each step using Newton's method during iteration as follows:

[0083]

[0084] in Indicates the input The parameter estimation results after iterative updates. Defined as:

[0085]

[0086] Defined as:

[0087]

[0088] Compared with the original iterative method, the proposed simplified algorithm only needs to calculate the elements of two submatrices in the second derivative matrix, and the computational complexity is lower than that of the original Newton-orthogonal matching pursuit iterative method.

[0089] Step S3: Construct a system of equations using geometric relationships and estimated parameters. Solve the system of equations to obtain the user positioning estimate without synchronization error. The system of equations is expressed as:

[0090]

[0091] θ R,AOA =π-(θ) A,0 -θ A,1 )-(θ B,0 -θ B,1 )-θ R,AOD ,

[0092] sinθ R,AOA =sinθ R,A +sinθ R,AOD .

[0093] Where r0 represents the direct path distance without synchronization error, r1 represents the non-direct path distance without synchronization error, Δt represents the synchronization error, and c represents the speed of light. Solving this equation yields the relationship between r0 and θ. A,0 The user's location can be uniquely determined using these two parameters.

[0094] The following is a verification example of the present invention, applied to a single-anchor node positioning system based on a smart reflective surface, verifying that the present invention can achieve parameter estimation of direct and indirect paths and positioning of users even when there is a synchronization error between the base station and the user.

[0095] Table 1

[0096]

[0097]

[0098] Simulation parameters are shown in Table 1. The single-anchor node positioning system based on the intelligent reflective surface is as follows: Figure 1 As shown, the positioning results are as follows: Figure 3 As shown, Estimation represents the user localization results under multiple Monte Carlo simulations, Ground-truth represents the user's true location, BS represents the base station, and RIS represents the smart reflector. The relationship between the root mean square error of user localization and the number of elements and signal-to-noise ratio of different smart reflectors is illustrated. Figure 4 As shown. According to... Figure 3 The simulation results show that multiple positioning results indicate the target is near the user, proving that the proposed positioning system and algorithm can still achieve accurate target positioning even in the presence of synchronization errors. Figure 4As shown, with more intelligent reflective surface elements, the positioning error for the user is significantly reduced. The intelligent reflective surface with one element can be regarded as a general scatterer. The performance improvement brought by the multi-element intelligent reflective surface demonstrates the necessity and advantages of using intelligent reflective surfaces.

[0099] This invention, using single-anchor node user positioning as an example, verifies that the proposed single-anchor node positioning system based on intelligent reflective surfaces can achieve user positioning even when synchronization errors exist between the base station and the user. By introducing intelligent reflective surfaces to provide high-power non-direct paths, the proposed system can achieve accurate parameter estimation of non-direct paths, and thus achieve accurate user positioning based on geometric relationships.

[0100] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A positioning method based on a single-anchor node positioning system, characterized in that, The method includes the following steps: Step S1: Introduce a smart reflector into the single anchor node positioning system to form a non-direct path with high power, and establish a signal model of the single anchor node positioning system based on the smart reflector. Step S2: Establish an optimization problem based on the model, and estimate the parameters of user distance, speed, and angle of arrival; Step S3: Locate the user based on the user's parameter estimation; The single anchor node positioning system in step S1 is a frequency-controlled array-multiple-input multiple-output single anchor node positioning system; After introducing a smart reflective surface into the single-anchor node positioning system, the receiver signal tensor It can be represented as: Y / Y LOS +And NLOS in The output tensor obtained by the base station receiver after signal processing, the elements of the output tensor with coordinates [n, p, q] represent the output signal obtained after the signal received by the q-th antenna is matched and filtered by the signal of the p-th frequency in the n-th pulse; Let N be a complex tensor with three dimensions N, P, and Q; N represents the number of pulses, P represents the number of transmit antennas, and Q represents the number of receive antennas. This is the output tensor obtained by the base station receiver after processing the signal propagating through the non-direct path formed by the intelligent reflector. The Y LOS Specifically, it is expressed as follows: in θ represents the distance between the user and the base station, including synchronization errors. A,0 θ represents the angle between the direct path between the base station and the user and the normal of the user array. B,0 This represents the angle between the direct path between the base station and the user and the normal of the base station array. The coefficients represent the output signal after echo processing; Represents the outer product of tensors; This represents additive white Gaussian noise. This represents the steering vector related to the user's direct path distance and launch angle. This represents the steering vector associated with the user signal's angle of arrival at the base station; The guiding vector a A (θ,r) and a B The elements in (θ) are as follows: Where r, v, and θ represent the target's distance, velocity, and angle with the array normal, respectively, and a A,n,p (θ, r) represent the guiding vector a, respectively. A The element in the nth row and pth column of (θ,r), a B,q (θ) represents a B The q-th element in (θ); the frequency of the p-th activated antenna transmission signal in the n-th pulse is f. c +U n,p Δf, f c U represents the carrier frequency, Δf represents the frequency increment, and U n,p d represents the number of frequency increments; c represents the distance between adjacent antennas of the transceiver array; P represents the number of transmitting antennas; and Q represents the number of receiving antennas. The Y NLOS Specifically, it is expressed as follows: in θ represents the distance between the user and the base station via a smart reflector, which includes synchronization errors and is not a direct path. A,1 θ represents the angle between the non-direct path and the normal of the user array. R,A Satisfy sinθ R,AOA =sinθ R,A +sinθ R,AOD , where θ R,AOA With θ R,AOD θ represents the arrival angle and departure angle of the non-direct path between the smart reflector and the normal of the smart reflector array, respectively. B,1 This indicates the angle between the non-direct path and the normal of the base station array. The coefficients represent the output non-direct path signal after echo processing; This represents the outer product of tensors, and it means that diag(·) takes the diagonal elements of the matrix. This represents the phase encoding matrix corresponding to the M units of the pulse intelligent reflector in N pulses. This represents additive white Gaussian noise. This represents the steering vector related to the user's direct path distance and launch angle. This represents the steering vector related to the user signal's angle of arrival at the base station. This represents the steering vector related to the angle of arrival of the user signal at the smart reflector. The guiding vector a A (θ,r), a B (θ) and a R The elements in (θ) are as follows: Where r, v, and θ represent the target's distance, velocity, and angle with the array normal, respectively, and a A,n,p (θ, r) represent the guiding vector a, respectively. A The element in the nth row and pth column of (θ,r), a B,q (θ) represents a B The q-th element in (θ), a R,m (θ) represents a R The m-th element in (θ); the frequency of the p-th activated antenna transmission signal in the n-th pulse is f. c +U n,p Δf, f c U represents the carrier frequency, Δf represents the frequency increment, and U n,p d represents the number of frequency increments; c represents the distance between adjacent antennas of the transceiver array; M represents the speed of light; and M represents the number of elements of the smart reflector. In step S2, based on the established model, an optimization problem is designed, and the Newton-orthogonal matching pursuit algorithm is improved according to the property of the second derivative matrix, as follows: The parameters to be estimated are in This represents the direct path distance, including synchronization errors. θ represents the non-direct path distance containing synchronization errors. A,0 θ represents the angle between the direct path between the base station and the user and the normal of the user array. B,0 θ represents the angle between the direct path between the base station and the user and the normal of the base station array. A,1 θ represents the angle between the non-direct path and the normal of the user array. R,A This represents the angle between the non-direct path at the smart reflector and the normal of the smart reflector array. Since the position of the smart reflector is prior, θ... B,1 The parameters are considered as known quantities; the parameter estimation problem is expressed as follows: in Let θ represent the signal coefficients to be estimated. By analyzing the correlation of each parameter, we can obtain θ. B,0 Independent of other parameters, θ is solved directly using a multi-signal classification algorithm. B,0 Other parameters are solved by improving the Newton-orthogonal matching pursuit method; The Newton-orthogonal matching pursuit method is described in detail below: First, a rough estimate of the parameters is obtained using the orthogonal matching pursuit method. The signal coefficients are estimated using least squares. Then, when further refining the coarse estimate using Newton's method, the first derivative matrix... Sum and second derivative matrix Defined as: Analyzing the elements of the second derivative matrix, the second derivative matrix is ​​further written as follows: express The top left corner 2×2 matrix, express The 3×3 matrix in the lower right corner, based on the second derivative structure, is updated at each step using Newton's method during iteration as follows: in Indicates the input The parameter estimation results after iterative updates. Defined as: Defined as:

2. The positioning method based on a single-anchor node positioning system according to claim 1, characterized in that, In step S3, a system of equations is constructed using geometric relationships and estimated parameters. Solving this system yields a user positioning estimate without synchronization errors. This system of equations is expressed as follows: i R,AOA =π-(θ A,0 -θ A,1 )-(θ B,0 -θ B,1 )-θ R,AOD , sinθ R,AOA =sinθ R,A +sinθ R,AOD . Where r0 represents the direct path distance without synchronization error, r1 represents the non-direct path distance without synchronization error, Δt represents the synchronization error, c represents the speed of light, and θ... A,0 θ represents the angle between the direct path between the base station and the user and the normal of the user array. B,0 θ represents the angle between the direct path between the base station and the user and the normal of the base station array. A,1 θ represents the angle between the non-direct path and the normal of the user array. B,1 θ represents the angle between the non-direct path and the normal of the base station array. R,A θ represents the angle between the non-direct path at the smart reflector and the normal of the smart reflector array. R,AOA With θ R,AOD Let r0 and θ represent the arrival angle and departure angle of the non-direct path between the smart reflector and the normal of the smart reflector array, respectively. By solving this equation, the angles r0 and θ can be obtained. A,0 The user's location can be uniquely determined using these two parameters.

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