Positioning method based on single anchor node positioning system and terminal

Abstract

The invention relates to a positioning method based on a single anchor node positioning system and a terminal, and the method comprises the following steps: S1, introducing an intelligent reflection surface into the single anchor node positioning system, forming a high-power indirect path, and building a signal model of the single anchor node positioning system based on the intelligent reflection surface; s2, establishing an optimization problem based on the model, and estimating parameters of the distance, the speed and the angle of arrival of the user; and S3, realizing positioning of the user based on parameter estimation of the user. Compared with the prior art, the method has the advantages that the high-power indirect path is realized by introducing the intelligent reflecting surface, the positioning deviation caused by the synchronization error of the user side and the base station side is removed, and the multi-path parameter estimation and the user positioning are realized by designing a low-complexity algorithm.

Description

Technical Field

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

[0002] The positioning of users in communication systems has important application value in many fields such as intelligent transportation and the Internet of Things. Due to the performance degradation and high latency problems of satellite positioning in complex and obstructed scenes, user positioning methods based on wireless positioning have great application potential. Traditional wireless positioning methods rely on the signal arrival time difference between multiple anchor nodes to locate users, but the communication between multiple anchor nodes will consume a lot of communication resources. Measurements based on a single anchor node often locate users based on signal propagation time and arrival angle estimation, but the signal propagation time will be affected by the synchronization error between the anchor node and the user. Although two-way ranging can eliminate synchronization errors, it requires high-precision clocks and frequent communications, which imposes a great burden on the user end. Assisting user positioning through non-direct path signal parameter estimation is regarded as another way to eliminate the influence of synchronization errors. By using the geometric relationship between the direct path and the non-direct path, the influence of synchronization errors can be removed based on the parameter estimation of the direct path and the non-direct path.

[0003] Considering the single anchor node user positioning problem based on direct and indirect paths, the main difficulties are as follows:

[0004] 1) The signal reaching the base station through the indirect path is often of low power, making it difficult to achieve accurate indirect path parameter estimation;

[0005] 2) Since multipath has a lot of parameter information and the models of direct path and indirect path are different, the parameter estimation of multipath is often very complex. Summary of the invention

[0006] The purpose of the present invention is to provide a positioning method and a terminal based on a single anchor node positioning system in order to overcome the defects of the above-mentioned prior art.

[0007] The purpose of the present invention can be achieved by 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, introducing an intelligent reflective surface into a single anchor node positioning system to form a non-direct path with high power, and establishing a signal model of the single anchor node positioning system based on the intelligent reflective surface;

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

[0011] Step S3: Positioning the user 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 and multiple output single anchor node positioning system;

[0013] After the intelligent reflective surface is introduced into the single anchor node positioning system, the receiving end signal tensor Y∈￡ N×P×Q It can be expressed as:

[0014] Y=Y LOS +Y NLOS

[0015] where Y LOS ∈￡ N×P×Q is the output tensor obtained after signal processing at the base station receiving end. The element with coordinates [n, p, q] of the output signal tensor represents the output signal obtained after the signal received at the qth antenna is matched and filtered for the signal of the pth frequency in the nth pulse; N×P×Q represents a complex tensor with three-dimensional dimensions N, P, and Q, respectively; N represents the number of pulses, P represents the number of transmitting antennas, and Q represents the number of receiving antennas;

[0016] Y NLOS ∈￡ N×P×Q It is the output tensor obtained by the base station receiving end after processing the signal propagated through the non-direct path formed by the smart reflector.

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

[0018]

[0019] in 0 represents the distance between the user and the base station with synchronization error, 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 It represents the angle between the direct path between the base station and the user and the normal direction of the base station array. represents the coefficient of the output signal after echo processing; o represents the outer product of the tensor; w∈￡ N×P×Q represents additive white Gaussian noise, a A (θ,r)∈￡ N×P represents the steering vector related to the user's direct path distance and launch angle, a B (θ)∈￡ Q×1 Represents the steering vector associated with the angle of arrival of the user signal at the base station.

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

[0021]

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

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

[0024]

[0025] in represents the distance between the user and the base station through the non-direct path containing synchronization error formed by the smart reflector, θ A,1 represents the angle between the non-direct path and the user array normal, θ R,A Satisfy sinθ R,AOA = sinθ R,A +sinθ R,AOD , where θ R,AOA With θ R,AOD They represent the arrival angle and departure angle of the non-direct path at the smart reflector and the normal direction of the smart reflector array, θ B,1 represents the angle between the non-direct path and the normal direction of the base station array, represents the coefficient of the output non-direct path signal after echo processing; o represents the outer product of the tensor, indicating that diag(·) takes the diagonal elements of the matrix; ψ∈￡ N×M It represents the phase encoding matrix corresponding to the M units of the pulse smart reflection surface in N pulses, w∈￡ N×P×Q represents additive white Gaussian noise, a A (θ,r)∈￡ N×P represents the steering vector related to the user's direct path distance and launch angle, a B (θ)∈￡ Q×1represents the steering vector associated with the arrival angle of the user signal at the base station, a R (θ)∈￡ M×1 Represents the steering vector related to the arrival angle of the user signal on the smart reflector.

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

[0027]

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

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

[0030] The parameters to be estimated are in represents the direct path distance including synchronization error, represents the non-direct path distance containing synchronization error, 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 user array normal, θ R,A 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 a priori, θ B,1 is regarded as a known quantity; the parameter estimation problem is expressed as follows:

[0031]

[0032] in

[0033] Represents the signal coefficient to be estimated. By analyzing the correlation of various parameters, we know that θ B,0 Independent of other parameters, θ is directly solved by using the multi-signal classification algorithm B,0 , and other parameters are solved based on the improved Newton-orthogonal matching pursuit method.

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

[0035] First, a rough estimate of the parameters is obtained by using the orthogonal matching pursuit method And the signal coefficient is estimated by least squares

[0036] Then, when the rough estimate is further corrected by Newton's method, the first-order derivative matrix Sum and second-order derivative matrix is defined as:

[0037]

[0038] Analyzing the elements in the second-order derivative matrix, the second-order derivative matrix is ​​further written as:

[0039]

[0040] express The upper left corner 2×2 matrix, express The 3×3 matrix in the lower right corner is based on the second-order derivative structure. When iterating through Newton's method, each update step is expressed as:

[0041]

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

[0043]

[0044] Defined as:

[0045]

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

[0047]

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

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

[0050] where r 0 represents the direct path distance without synchronization error, r 1 represents the non-direct path distance without synchronization error, Δt represents the synchronization error, c represents the speed of light, 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, θ A,1 represents the angle between the non-direct path and the user array normal, θ B,1 represents the angle between the non-direct path and the normal direction of the base station array, θ R,A represents the angle between the non-direct path at the smart reflector and the normal of the smart reflector array, θ R,AOA With θ R,AOD They represent the arrival angle and departure angle of the non-direct path at the smart reflector and the normal direction of the smart reflector array. By solving this equation, we can get the angle of arrival and the angle of departure of the non-direct path at the smart reflector and the normal direction of the smart reflector array. 0 With θ A,0 The user's location can be uniquely determined through these two parameters.

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

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

[0053] 1) The present invention greatly increases the signal power reaching the base station through the indirect path by introducing the intelligent reflection surface, making it possible to estimate the indirect path signal parameters with high precision;

[0054] 2) The present invention simplifies the iterative process and reduces the complexity of multipath parameter estimation based on the second-order derivative characteristics of the signal matrix in the established model. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0057] Figure 3 The figure 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 position, BS represents base station, and RIS represents intelligent reflective surface.

[0058] Figure 4 The simulation diagram of the positioning performance of the proposed system and method under different signal-to-noise ratios and numbers of smart reflective surface array elements, where RMSE of estimated location of agent represents the root mean square error of user positioning, and SNR represents the signal-to-noise ratio. DETAILED DESCRIPTION

[0059] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0060] The present invention forms a non-direct path with high power by introducing an intelligent reflective surface, and realizes decoupling of synchronization error by combining the parameter estimation of the direct path and the non-direct path; improves the Newton method-orthogonal matching pursuit algorithm according to the properties of the second-order derivative matrix, so that it has a faster iteration speed when estimating parameters in the system; removes synchronization errors based on the parameter estimation of the direct path and the non-direct path to realize user positioning. Compared with the traditional single anchor node positioning system, the present invention realizes a non-direct path with high power by introducing an intelligent reflective surface, removes the positioning deviation caused by the synchronization error between the user end and the base station end, and designs a low-complexity algorithm to realize parameter estimation of multipath and user positioning.

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

[0062] Step S1, introduce intelligent reflector into the frequency controlled array-multi-input multi-output single anchor node positioning system to form a non-direct path with high power, and the receiving end signal tensor Y∈￡ N×P×Q It can be expressed as:

[0063] Y=Y LOS +Y NLOS .

[0064] Among them, Y LOS ∈￡ N×P×Q is the output tensor obtained after signal processing at the base station receiving end. The element with coordinates [n, p, q] of the output signal tensor represents the output signal obtained after the signal received at the qth antenna is matched and filtered for the signal of the pth frequency in the nth pulse; N×P×Q represents a complex tensor with three-dimensional dimensions N, P, and Q respectively; N represents the number of pulses, P represents the number of transmitting antennas, and Q represents the number of receiving antennas; Y LOS It is expressed as:

[0065]

[0066] in represents the distance between the user and the base station with synchronization error, 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 It represents the angle between the direct path between the base station and the user and the normal direction of the base station array. represents the coefficient of the output signal after echo processing; o represents the outer product of the tensor; w∈￡ N×P×Q represents additive white Gaussian noise, a A (θ,r)∈￡ N×P represents the steering matrix related to the user's direct path distance and launch angle, a B (θ)∈￡ Q×1 represents the steering vector associated with the arrival angle of the user signal at the base station, where the elements are as follows:

[0067]

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

[0069]

[0070] Among them, Y NLOS ∈￡ N×P×Q It is the output tensor obtained by the base station receiving end after processing the signal propagated through the non-direct path formed by the smart reflector. represents the distance between the user and the base station through the non-direct path containing synchronization error formed by the smart reflector, θ A,1 represents the angle between the non-direct path and the user array normal, θ R,A Satisfy sinθ R,AOA = sinθ R,A +sinθ R,AOD , where θ R,AOA With θ R,AOD They represent the arrival angle and departure angle of the non-direct path at the smart reflector and the normal direction of the smart reflector array, θ B,1 represents the angle between the non-direct path and the normal direction of the base station array, represents the coefficient of the output non-direct path signal after echo processing; o represents the outer product of the tensor, indicating that diag(·) takes the diagonal elements of the matrix; ψ∈￡ N×M It represents the phase encoding matrix corresponding to the M units of the pulse smart reflection surface in N pulses, w∈￡ N×P×Q represents additive white Gaussian noise, a A (θ,r)∈￡ N×P represents the steering matrix related to the user's direct path distance and launch angle, a B (θ)∈￡ Q×1 represents the steering vector associated with the arrival angle of the user signal at the base station, a R (θ)∈￡ M×1 Represents the steering vector related to the arrival angle of the user signal on the smart reflector, where the elements are as follows:

[0071]

[0072]

[0073] Step S2, based on the established model, designing an optimization problem, and improving the Newton method-orthogonal matching pursuit algorithm according to the properties of the second-order derivative matrix, so that it has a faster iteration speed when estimating parameters in the system, including:

[0074] The parameters to be estimated are in represents the direct path distance including synchronization error, represents the non-direct path distance containing synchronization error, 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 user array normal, θ R,A 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 a priori, θ B,1 is considered as a known quantity. The parameter estimation problem can be written as:

[0075]

[0076] in

[0077]

[0078] Represents the signal coefficient to be estimated. By analyzing the correlation of various parameters, we can know that θ B,0 is independent of other parameters, so θ can be directly solved by using the multi-signal classification algorithm B,0 The other parameters are solved based on the improved Newton-orthogonal matching pursuit method. First, the rough estimate of the parameters is obtained by the orthogonal matching pursuit method. And the signal coefficient is estimated by least squares Then, when the rough estimate is further corrected by Newton's method, the first-order derivative matrix Sum and second-order derivative matrix is defined as:

[0079]

[0080] Analyzing the elements in the second-order derivative matrix, the second-order derivative matrix is ​​further written as:

[0081]

[0082] express The upper left corner 2×2 matrix, express The 3×3 matrix in the lower right corner is based on the second-order derivative structure. When iterating through Newton's method, each update step is expressed as:

[0083]

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

[0085] ...

[0087] S 0 (x,α), S 1 (x,α) is defined as:

[0088]

[0089] Compared with the original iterative method, the proposed simplified algorithm only needs to calculate the elements of two sub-matrices in the second-order derivative matrix, and the computational complexity is lower than that of the original Newton-orthogonal matching pursuit iterative method.

[0090] Step S3, constructing an equation group through geometric relationships and estimated parameters, and obtaining a user location estimation without synchronization error by solving the equation group, the equation group is expressed as:

[0091]

[0092] θ R,AOA =π-(θ A,0 -θ A,1 )-(θ B,0 -θ B,1 )-θ R,AOD ,

[0093] sinθ R,AOA = sinθ R,A +sinθ R,AOD .

[0094] where r 0 represents the direct path distance without synchronization error, r 1 represents the non-direct path distance without synchronization error, Δt represents the synchronization error, and c represents the speed of light. By solving this equation, we can get the value of r 0 With θ A,0 The user's location can be uniquely determined through these two parameters.

[0095] A verification example of the present invention is given below, which is applied to a single anchor node positioning system based on an intelligent reflective surface to verify that the present invention can achieve parameter estimation of direct paths and indirect paths and positioning of users when there is a synchronization error between the base station and the user.

[0096] Table 1

[0097]

[0098]

[0099] The simulation parameters are shown in Table 1. The single anchor node positioning system based on the intelligent reflective surface is as follows: Figure 1 The positioning results are shown in Figure 3 As shown in the figure, Estimation represents the user positioning result under multiple Monte Carlo simulations, Ground-truth represents the real position of the user, BS represents the base station, and RIS represents the intelligent reflector. The relationship between the root mean square error of user positioning and the number of array elements and signal-to-noise ratio of different intelligent reflectors Figure 4 As shown. Figure 3 From the simulation results shown in the figure, we can see that the multiple positioning results are all near the user, which proves that when there is a synchronization error, the proposed positioning system and algorithm can still achieve accurate positioning of the target. Figure 4 As shown in the figure, when there are more smart reflective surface elements, the positioning error of the user is significantly reduced, among which the smart reflective surface of one element can be regarded as a general scatterer. The performance improvement brought by the multi-element smart reflective surface reflects the necessity and advantage of using smart reflective surfaces.

[0100] The present invention takes single anchor node user positioning as the background and verifies that the proposed single anchor node positioning system based on intelligent reflective surface has the ability to realize user positioning when there is synchronization error between the base station and the user. By introducing intelligent reflective surface to provide high-power non-direct path, the proposed system can realize accurate parameter estimation of non-direct path, and then realize accurate positioning of users based on geometric relationship.

[0101] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present invention, and these modifications or replacements should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A positioning method based on a single anchor node positioning system, characterized in that: The method comprises the following steps: Step S1, introducing an intelligent reflection surface into a single anchor node positioning system to form a non-direct path with high power, and establishing a signal model of the single anchor node positioning system based on the intelligent reflection surface; Step S2, establishing an optimization problem based on the model and estimating the parameters of user distance, speed, and angle of arrival; Step S3: Positioning the user based on the user's parameter estimation.

2. According to claim 1, a positioning method based on a single anchor node positioning system is characterized in that: The single anchor node positioning system in step S1 is a frequency controlled array-multiple input and multiple output single anchor node positioning system; After the intelligent reflective surface is introduced into the single anchor node positioning system, the receiving end signal tensor Y∈￡ N×P×Q It can be expressed as: Y=Y LOS +Y NLOS where Y LOS ∈￡ N×P×Q is the output tensor obtained after signal processing at the base station receiving end. The element with coordinates [n, p, q] of the output signal tensor represents the output signal obtained after the signal received at the qth antenna is matched and filtered for the signal of the pth frequency in the nth pulse; N×P×Q represents a complex tensor with three-dimensional dimensions N, P, and Q, respectively; N represents the number of pulses, P represents the number of transmitting antennas, and Q represents the number of receiving antennas; Y NLOS ∈￡ N×P×Q It is the output tensor obtained by the base station receiving end after processing the signal propagated through the non-direct path formed by the smart reflector.

3. According to claim 2, a positioning method based on a single anchor node positioning system is characterized in that: The Y LOS Specifically expressed as: in represents the distance between the user and the base station with synchronization error, 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 It represents the angle between the direct path between the base station and the user and the normal direction of the base station array. represents the coefficient of the output signal after echo processing; o represents the outer product of the tensor; w∈￡ N×P×Q represents additive white Gaussian noise, a A (θ,r)∈￡ N×P represents the steering vector related to the user's direct path distance and launch angle, a B (θ)∈￡ Q×1 Represents the steering vector associated with the angle of arrival of the user signal at the base station.

4. According to claim 3, a positioning method based on a single anchor node positioning system is characterized in that: The steering vector a A (θ, r) and a B The elements in (θ) are as follows: Where r, v, θ represent the target’s distance, velocity, and angle with the array normal, respectively. A,n,p (θ, r) represent the steering vector a A The element in the nth row and pth column of (θ,r), a B,q (θ) represents a B The qth element in (θ); the frequency of the signal transmitted by the pth activated antenna in the nth pulse is f c +U n,p Δf, f c represents the carrier frequency, Δf represents the frequency increment, U n,p represents the number of frequency increments; d represents the distance between adjacent antennas in the transceiver array; c represents the speed of light; P represents the number of transmitting antennas; and Q represents the number of receiving antennas.

5. According to claim 2, a positioning method based on a single anchor node positioning system is characterized in that: The Y NLOS Specifically expressed as: in represents the distance between the user and the base station through the non-direct path containing synchronization error formed by the smart reflector, θ A,1 represents the angle between the non-direct path and the user array normal, θ R,A Satisfy sinθ R,AOA = sinθ R,A +sinθ R,AOD , where θ R,AOA With θ R,AOD They represent the arrival angle and departure angle of the non-direct path at the smart reflector and the normal direction of the smart reflector array, θ B,1 represents the angle between the non-direct path and the normal direction of the base station array, represents the coefficient of the output non-direct path signal after echo processing; o represents the outer product of the tensor, indicating that diag(·) takes the diagonal elements of the matrix; ψ∈￡ N×M It represents the phase encoding matrix corresponding to the M units of the pulse smart reflection surface in N pulses, w∈￡ N×P×Q represents additive white Gaussian noise, a A (θ,r)∈￡ N×P represents the steering vector related to the user's direct path distance and launch angle, a B (θ)∈￡ Q×1 represents the steering vector associated with the arrival angle of the user signal at the base station, a R (θ)∈￡ M×1 Represents the steering vector related to the arrival angle of the user signal on the smart reflector.

6. A positioning method based on a single anchor node positioning system according to claim 5, characterized in that: The steering vector a A (θ,r),a B (θ) and a R The elements in (θ) are as follows: Where r, v, θ represent the target’s distance, velocity, and angle with the array normal, respectively. A,n,p (θ, r) represent the steering vector a A The element in the nth row and pth column of (θ,r) is a B,q (θ) represents a B The qth element in (θ), a R,m (θ) represents a R The mth element in (θ); the frequency of the signal transmitted by the pth activated antenna in the nth pulse is f c +U n,p Δf, f c represents the carrier frequency, Δf represents the frequency increment, U n,p represents the number of frequency increments; d represents the distance between adjacent antennas in the transceiver array; c represents the speed of light; and M represents the number of array elements of the smart reflective surface.

7. A positioning method based on a single anchor node positioning system according to claim 2, characterized in that: In step S2, based on the established model, an optimization problem is designed, and the Newton method-orthogonal matching pursuit algorithm is improved according to the properties of the second-order derivative matrix, as follows: The parameters to be estimated are in represents the direct path distance including synchronization error, represents the non-direct path distance containing synchronization error, 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 user array normal, θ R,A 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 a priori, θ B,1 is regarded as a known quantity; the parameter estimation problem is expressed as follows: in Represents the signal coefficient to be estimated. By analyzing the correlation of various parameters, we know that θ B,0 Independent of other parameters, θ is directly solved by using the multi-signal classification algorithm B,0 , and other parameters are solved based on the improved Newton-orthogonal matching pursuit method.

8. The positioning method based on a single anchor node positioning system according to claim 7, characterized in that: The Newton-orthogonal matching pursuit method is as follows: First, a rough estimate of the parameters is obtained by using the orthogonal matching pursuit method And the signal coefficient is estimated by least squares Then, when the rough estimate is further corrected by Newton's method, the first-order derivative matrix Sum and second-order derivative matrix is defined as: Analyzing the elements in the second-order derivative matrix, the second-order derivative matrix is ​​further written as: express The upper left corner 2×2 matrix, express The 3×3 matrix in the lower right corner is based on the second-order derivative structure. When iterating through Newton's method, each update step is expressed as: in Indicates the input The parameter estimation results after iterative update are: Defined as: ... S0(x,α), S1(x,α) are defined as:

9. The positioning method based on a single anchor node positioning system according to claim 3, characterized in that: In step S3, a set of equations is constructed by using geometric relationships and estimated parameters, and a user positioning estimate without synchronization error is obtained by solving the set of equations. The set of equations is expressed as: 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 indirect path distance without synchronization error, Δt represents the synchronization error, c represents the speed of light, 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 user array normal, θ B,1 represents the angle between the non-direct path and the normal direction of the base station array, θ R,A represents the angle between the non-direct path at the smart reflector and the normal of the smart reflector array, θ R,AOA With θ R,AOD They represent the arrival angle and departure angle of the non-direct path between the smart reflector and the normal of the smart reflector array. By solving this equation, we can get the relationship between r0 and θ A,0 The user's location can be uniquely determined through these two parameters.

10. A terminal, characterized in that: The terminal uses the positioning method based on the single anchor node positioning system described in any one of claims 1-9 to locate the user.

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