RIS-assisted wireless positioning method

Abstract

The invention belongs to the technical field of wireless positioning, and particularly relates to an RIS-assisted wireless positioning method, which comprises the following steps of: establishing a positioning system model; constructing a signal model before incidence of the spherical wave; a position error limit PEB and a direction error limit OEB of the UE are deduced, a Fisher information matrix FIM is constructed, the relation between channel parameters and the position and direction of the UE is established through a transfer matrix, and analytical expressions of the PEB and the OEB are solved; and optimizing RIS phase shift configuration. According to the RIS-assisted wireless positioning method provided by the invention, through multi-dimensional technical innovation, the positioning precision and the system adaptability in a near-field environment are remarkably improved. Firstly, a cascade link model is constructed based on Fresnel area spherical wave propagation characteristics, signal transmission processes from UE to RIS and from RIS to BS are accurately depicted, the problem of channel modeling errors caused by near-field distance and angle parameter coupling is effectively solved, and a positioning model is made to better meet actual scene requirements such as indoor and complex shielding.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless positioning, and in particular relates to a RIS-assisted wireless positioning method. Background Art

[0002] Wireless positioning technology is widely used in the Internet of Things, intelligent transportation, indoor navigation, and other fields. Traditional GPS positioning accuracy is insufficient indoors or in complex obstructed scenarios, making positioning technology based on wireless communication networks an important supplement. With the development of 5G and 6G technologies, the integration of high-precision positioning and communications has become a hot topic. Reconfigurable intelligent surface (RIS)-assisted positioning is key to improving positioning performance due to its low cost, low power consumption, and high flexibility. In near-field positioning scenarios, signal propagation is in the Fresnel region, where spherical wave characteristics are significant. Traditional positioning technologies are mostly based on the far-field plane wave assumption, resulting in large errors in near-field channel modeling and reduced positioning accuracy.

[0003] Existing RIS-assisted positioning technology suffers from numerous shortcomings. First, the coupling relationship between distance and angle in spherical wave propagation is not fully considered in near-field environments, making it difficult to accurately describe signal link characteristics. Second, most studies focus solely on user position estimation, ignoring the importance of device orientation information for multi-antenna systems, making it impossible to achieve joint optimization of positioning and orientation estimation. Third, RIS phase shift configuration is often based on communication performance optimization, without considering positioning error bounds. Furthermore, the optimization algorithm is highly complex and difficult to adapt to real-time scenarios. Fourth, positioning error analysis lacks unified modeling of position error bounds and orientation error bounds, making it impossible to balance the performance of these two according to actual needs. Summary of the Invention

[0004] To address the technical issues existing in the aforementioned existing RIS-assisted positioning technology, the present invention provides a RIS-assisted wireless positioning method. This method accurately models the cascaded link channel under near-field spherical wave propagation, derives position and direction error bounds, and utilizes a particle swarm algorithm to optimize the RIS phase shift configuration to minimize the weighted joint error bound. This method addresses issues such as inaccurate models, one-sided dimensionality, and insufficient optimization in near-field positioning, providing a new path for the integration of high-precision positioning and communications.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is: A RIS-assisted wireless positioning method comprises the following steps: S1, establishing a positioning system model: constructing a positioning system consisting of a multi-antenna base station BS, a multi-antenna user equipment UE and a RIS in a rectangular coordinate system, defining the coordinates of the BS, UE and RIS, wherein the RIS is placed in the yz plane with the x coordinate being 0, determining the position of the antenna and reflective unit of each device, and defining the direction vector and distance parameters; S2. Construct a signal model of the incident spherical wavefront: Based on near-field propagation conditions, establish a signal transmission model from UE to RIS and then to BS in the uplink, derive the channel matrices of the UE-RIS link and the RIS-BS link, and construct the RIS phase shift matrix, taking into account the spherical wave propagation characteristics and signal power and noise models; S3. Perform positioning performance analysis: derive the UE's position error bound (PEB) and orientation error bound (OEB), construct the Fisher information matrix (FIM), establish the relationship between channel parameters and UE position and orientation through the transfer matrix, and solve the analytical expressions for PEB and OEB. S4. Optimize RIS phase shift configuration: Use particle swarm optimization (PSO) algorithm to optimize the RIS phase shift matrix with the goal of minimizing weighted joint PEB and OEB. The weighted joint optimization satisfies Minimum, among which , and is the weighting coefficient.

[0006] The method for defining the coordinates of BS, UE and RIS in S1 is: defining the center position coordinates of BS as , BS The coordinates of the root antenna are , ; The center position coordinates of UE are ,UE No. The position coordinates of the root antenna are ; RIS Reflection units, the center position coordinates are , No. The position coordinates of the unit are , ; From the placement of RIS, we can see that ; At the same time, the rotation angle of the UE antenna is defined as ; Since the main scenario of the study is the near-field environment, the BS, RIS and UE are located in the Fresnel area, that is, the distance is within the interval ,in Indicates that RISRIS and UE are in the Fresnel area, that is, the distance is within the interval ,in represents the pore size of RIS, represents the wavelength of the signal, Indicates the spacing between components.

[0007] The method for defining the direction vector and distance parameters in S1 is: Define the direction vector as: Where, and Indicates the elevation angle and azimuth angle; with the BS as the center of the three-dimensional coordinate system, the coordinates of the UE and RIS centers are expressed as: Where, , 、 and Represents the distance, elevation and azimuth relative to the BS respectively; and its corresponding antenna array or reflector unit , the antenna coordinates of each array are expressed as: The distance between each unit is expressed as: , , , .

[0008] The method for establishing the signal transmission model from UE to RIS and then to BS in the uplink in S2 is: In the uplink, the system operates at wavelength Corresponding carrier frequency The signal bandwidth is , UE transmission OFDM subcarriers, for the subcarriers, Described as: It is The normalized data signal corresponding to the subcarriers satisfies the condition . is the beamforming matrix, satisfying and .

[0009] The method for deriving the channel matrices of the UE-RIS link and the RIS-BS link in S2 and constructing the RIS phase shift matrix is ​​as follows: The BS estimates the UE position and direction by using the distance and angle information in the spherical waveform model; assuming that the LOS path from the UE to the BS is blocked, the BS can only receive the signal through the cascade link UE-RIS-BS; therefore, The received signal associated with each subcarrier is expressed as: Where, is the signal power, is the signal vector transmitted by the system, is the observation noise, and the observation noise is modeled as having a mean of zero and a variance of Independent and identically distributed additive Gaussian white noise; and are the channel matrices of the UE-RIS and RIS-BS links respectively, is the RIS phase shift matrix;

[0010] in: is the gain of a single UE antenna unit, is the gain of a single BS antenna unit.

[0011] The method of considering the propagation characteristics of spherical waves, signal power, and noise model in S2 is as follows: for the phase shift of the reflection unit , that is, assuming that each reflective element can only take a finite discrete phase shift, The number of phase shift control bits for each reflective element of RIS is determined by Uniform quantization is performed within the interval to obtain discrete phase shift values, and we get: In the analysis process, it is assumed that the synchronization process is always performed between the BS and the UE. After synchronization, the time and angle information of the received signal are jointly processed to study the difference between the two. The general model of the received signal with subcarrier correlation can be rewritten to obtain the scalar representation of the received signal: After removing the noise, the useful part of the signal is , represents the gain of the reflected path through RIS, represents the subcarrier considered, and Respectively represent UE Antenna to RIS Unit and RIS Units to BS The delay of the antenna, Indicates the speed of light, UE's The first antenna and the RIS The distance between the reflection units It is given by: Where, , , which contains the angle information of the signal, , ; Similarly, The first RIS reflection unit and the Reach distance between BS antennas in accordance with Make a statement.

[0012] In S3, the position error bound PEB and the direction error bound OEB of the UE are derived, and the Fisher information matrix FIM is constructed as follows: Receive signal As a random vector, its joint probability density function is expressed as: As the channel parameter Conditional receiving signal The likelihood function of is the covariance matrix of the noise; therefore, according to the maximum likelihood estimation principle, The estimate of is expressed as: A two-stage approach is adopted to estimate the UE position and direction. In the first step, the general form of the system channel parameters is determined, which is expressed as: In the formula, including gain, elevation, azimuth and delay channel information. In the second step, through the channel parameters To estimate the UE's location and direction , the estimated values ​​of position and direction are expressed as and : Where, express and The function between express Unbiased estimation of UE position and orientation; minimize the CRLB of UE position and orientation, which are called position error bound PEB and rotation error bound OEB respectively;

[0013] Where, express The covariance of the channel parameters The Fisher information matrix is ​​derived, and based on the Cramer-Rao theorem, the lower bound of the error is expressed as: Where, for The Fisher information matrix of is defined as follows: In a wide-sense stationary process Written as: According to the signal processing and error analysis theory, the Fisher information matrix FIM of the position error lower bound PEB and the rotation angle error lower bound OEB is obtained through the transfer matrix Get, expressed as: In the formula, the transfer matrix As a bridge for building the parameter relationship of the positioning system, its physical significance lies in characterizing the conversion characteristics between different state parameters in the system, which can be specifically expressed as: In S3, the relationship between the channel parameters and the UE position and direction is established through the transfer matrix. The method for solving the analytical expressions of PEB and OEB is: Solving for the elements in the given set and , the following equality exists:

[0014] Depend on Get PEB and OEB, PEB is The first Square root of the trace of the submatrix: OEB is The square root of the trace of the submatrix of rows 4 to 6 and columns 4 to 6: .

[0015] The method for optimizing the RIS phase shift configuration in S4 is: A weighted joint optimization strategy is adopted, that is, PEB and OEB are optimized simultaneously by introducing weighting coefficients to balance the position error and angle error. The selection of weighting coefficients is adjusted according to the system's requirements for positioning accuracy and direction accuracy. The optimization problem is expressed as:

[0016]

[0017]

[0018] Where, For all are all optimization variables.

[0019] The particle swarm PSO algorithm in S4 includes the following steps: S4.1, initializing the particle swarm: randomly generating particles, represents the position of each particle, i.e., a possible phase-shift configuration of RIS; since RIS has reflection units, the dimension of the position vector of each particle is , the phase shift values ​​corresponding to its elements are taken from the phase shift set At the same time, a velocity vector is initialized for each particle. S4.2. Evaluate particle fitness: For each particle, calculate the fitness value of each particle based on the RIS phase shift configuration it represents and the optimization objective function. The smaller the fitness value, the more optimal the RIS phase shift configuration represented by the particle. S4.3. For each particle, update its velocity and position according to the following formula; Velocity update formula: Where, It is a particle In the The velocity vector at the iteration, , is the maximum number of iterations of the algorithm, and is the particle learning factor, and yes A random number between It is a particle The best position found so far, is the optimal position found by the entire particle swarm so far, It is a particle In the The position vector at the iteration, is the inertia weight, which is updated using an adaptive adjustment strategy; Position update formula: During the update process, it is necessary to ensure that the particle position, i.e., the phase shift value of RIS, is within the range of given conditions; S4.4, Update individual optimality and global optimality: For each particle , compare its current fitness value and the individual optimal fitness value, that is, the corresponding The fitness value of the individual is updated if the current value is better. is the current position; compare the individual optimal fitness values ​​of all particles to find the global optimal fitness value and the corresponding global optimal position ; S4.5, determine the stopping condition: set the maximum number of iterations As the stopping condition, when the condition is met, the algorithm stops and the global optimal position is output. The RIS phase configuration corresponding to this position is the optimized result, and its corresponding PEB and OEB values ​​are the optimized performance indicators.

[0020] Compared with the prior art, the present invention has the following beneficial effects: 1. The RIS-assisted wireless positioning method proposed in this paper significantly improves positioning accuracy and system adaptability in near-field environments through multi-dimensional technological innovation. First, a cascaded link model constructed based on the propagation characteristics of spherical waves in the Fresnel region accurately depicts the signal transmission process from the UE to the RIS and from the RIS to the base station. Compared with the traditional far-field plane wave assumption, this effectively solves the channel modeling error caused by the coupling of near-field distance and angle parameters, making the positioning model more suitable for practical scenarios such as indoor environments and complex obstructions.

[0021] 2. This invention achieves simultaneous optimization of the UE's three-dimensional coordinates and antenna orientation by jointly deriving the position error bound (PEB) and orientation error bound (OEB) and constructing a Fisher information matrix. This design, which expands the positioning dimension from single position estimation to joint position and orientation estimation, not only meets the device orientation accuracy requirements of multi-antenna systems but also establishes a correlation between channel parameters and positioning parameters through a transfer matrix, providing a more comprehensive theoretical basis for error analysis and avoiding the lack of orientation accuracy caused by traditional methods that focus solely on position estimation.

[0022] 3. Regarding RIS phase shift optimization, this invention employs a particle swarm optimization (PSO) algorithm for weighted joint optimization of the phase shift matrix. By introducing adjustable weighting coefficients to balance the weights of PEB and OEB, the system can flexibly adjust positioning emphasis based on different scenarios, such as navigation and beamforming. Compared to traditional exhaustive methods or complex convex optimization algorithms, this optimization strategy significantly reduces computational complexity while maintaining optimization accuracy, making it more suitable for real-time positioning scenarios. Furthermore, the discrete phase shift quantization design and the PSO iteration mechanism with adaptive inertia weights further enhance the algorithm's adaptability to RIS hardware constraints and convergence efficiency, achieving the coordinated optimization of positioning performance and engineering feasibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments or the description of the prior art. Obviously, the drawings described below are merely exemplary, and those skilled in the art can, without inventive effort, derive other implementation drawings based on the provided drawings.

[0024] The structures, proportions, sizes, etc. illustrated in this specification are intended solely to complement the contents disclosed herein and to facilitate understanding and reading by persons skilled in the art. They are not intended to limit the conditions under which the present invention may be implemented and therefore have no substantive technical significance. Any structural modifications, changes in proportions, or adjustments in sizes, without affecting the efficacy and objectives of the present invention, shall remain within the scope of the technical contents disclosed herein.

[0025] Figure 1 This is a diagram of the substation indoor near-field positioning scene of the present invention; Figure 2 The geometric diagram of the positioning system of the present invention; Figure 3 This is the flow chart of the PSO algorithm of the present invention; Figure 4 This is a diagram showing the impact of the number of RIS units and phase design strategy on system error in the present invention; Figure 5This is a diagram showing the influence of the number of quantization bits of the RIS phase shift on the position error of the present invention; Figure 6 This is a diagram showing the impact of the RIS position on system performance in the present invention; Figure 7 This is the convergence diagram of the PSO algorithm of the present invention. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only part of the embodiments of this application, not all the embodiments. These descriptions are only to further illustrate the features and advantages of the present invention, rather than to limit the claims of the present invention. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0027] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following embodiments are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0028] 1. System Model 1. Scene and geometric expression like Figure 1 The indoor positioning scenario shown in the substation is densely populated with various power equipment, such as transformers, switchgear, and distribution cabinets. These devices are large, occupying a significant amount of space and featuring metal casings that significantly shield and reflect wireless signals. To locate inspection equipment in this environment, an indoor base station and a RIS device are deployed. The RIS intelligently controls incoming wireless signals, providing additional reflection paths between the inspection equipment and the base station. During actual positioning, the inspection equipment periodically transmits signals carrying its status information and location identifier to its surroundings. The base station receives these signals and calculates the distance and angle between the inspection equipment and the base station, thereby determining the inspection equipment's location. Combined with the reflected signals provided by the RIS, the base station can obtain richer positioning information, further improving positioning accuracy and reliability. In this study, it is assumed that the inspection equipment's line-of-sight path is always obstructed during operation.

[0029] Based on the positioning scenario, a RIS-assisted target position determination positioning system for near-field environments is established in a rectangular coordinate system. The system consists of a multi-antenna BS, a multi-antenna UE, and a RIS. Assuming that the position of the BS is known, the RIS is placed on the yz plane. The base station locates the user by receiving signals from the user. The mobility of the UE is very limited. The system geometry is represented as follows: Figure 2Next, define the center position coordinates of BS as , BS The coordinates of the root antenna are , ; The center position coordinates of UE are The coordinates of the antenna are , ; The center position coordinates of UE are Depend on Reflection units, the center position coordinates are , No. The position coordinates of the unit are , From the placement of RIS, we can see that At the same time, the rotation angle of the UE antenna is defined as Since the main scenario of the study is the near-field environment, the BS, RIS and UE are located in the Fresnel area, that is, the distance is within the interval ,in represents the pore size of RIS, represents the wavelength of the signal, Indicates the spacing between components. (1) In the formula, and Indicates the elevation angle and azimuth angle. Taking BS as the center of the three-dimensional coordinate system, the coordinates of the UE and RIS center can be expressed as: (2) In the formula, , 、 and Represent the distance, elevation and azimuth relative to the BS respectively. Further, for and its corresponding antenna array or reflector unit , the antenna coordinates of each array can be expressed as: (3) Without loss of generality, the distance between each unit can be expressed as: , , , .

[0030] 2. Signal Model of Incident Spherical Wavefront This embodiment establishes a spherical wavefront model suitable for near-field propagation conditions. In the uplink, the system operates at a wavelength of Corresponding carrier frequency The signal bandwidth is , UE transmission OFDM subcarriers, for the subcarriers, Described as: (4) It is The normalized data signal corresponding to the subcarriers satisfies the condition . is the beamforming matrix, satisfying and The BS estimates the UE position and direction by using the distance and angle information in the spherical waveform model. Assuming that the LOS path from the UE to the BS is blocked, the BS can only receive the signal through the cascade link UE-RIS-BS. The received signal associated with each subcarrier can be expressed as: (5) In the formula, is the signal power, is the signal vector transmitted by the system, is the observation noise, and the observation noise is modeled as having zero mean and variance Independent and identically distributed additive Gaussian white noise. and are the channel matrices of the UE-RIS and RIS-BS links respectively, is the RIS phase shift matrix. (6) (7) (8) is the gain of a single UE antenna unit, is the gain of a single BS antenna unit. Here, the phase shift of the reflector unit is Assuming that each reflective element can only take a finite discrete phase shift, The number of phase shift control bits for each reflective element of RIS is determined by By uniformly quantizing the interval to obtain discrete phase shift values, we can obtain: (9) In the analysis, this embodiment assumes that the BS and UE are always synchronized. After synchronization, the study is conducted by jointly processing the time and angle information of the received signal. The general model of the received signal in equation (5) can be rewritten to obtain a scalar representation of the received signal, which is specifically expressed as follows: (10) After removing the noise, the useful part of the signal is . represents the gain of the reflected path through RIS, represents the subcarrier considered, and Respectively represent UE Antenna to RIS Unit and RIS Units to BS The delay of the antenna, Represents the speed of light. Based on formula (4-3), the UE’s The first antenna and the RIS The distance between the reflection units can be It is given by: (11) In the formula, , , which contains the angle information of the signal, , . (12) Similarly, The first RIS reflection unit and the Reach distance between BS antennas According to formula (11), Make a statement.

[0031] It can be seen that, unlike the far-field communication scheme where the signal is assumed to be an incident plane wave, the propagation mode of spherical waves causes the wavefront morphology of the signal to vary significantly at different locations. This variation contains rich spatial information and can provide key clues for precise positioning. Therefore, in near-field communication, the ability to accurately handle the curvature changes of spherical waves will directly affect the accuracy and reliability of ranging and azimuth estimation. It should be noted that the mathematical representation of this embodiment is based on the results of clock synchronization between the base station, RIS, and user equipment.

[0032] 2. Positioning Performance Analysis Taking into account complex factors such as signal propagation characteristics and measurement errors, a reasonable mathematical model is established to derive the CRLB of the UE's position and direction to measure the positioning performance of the system. After the derivation is completed, in order to optimize the positioning accuracy, this embodiment introduces a weighted sum optimization strategy. As a random vector, its joint probability density function can be expressed as: (13) Can be used as channel parameters Conditional receiving signal The likelihood function of is the covariance matrix of the noise. Therefore, according to the maximum likelihood estimation principle, The estimate of can be expressed as: (14) This embodiment adopts a two-stage method to estimate the position and direction of the UE. In the first step, the general form of the system channel parameters is determined, which is specifically expressed as: (15) includes channel information such as gain, elevation angle, azimuth angle and time delay. In the second step, this embodiment uses the channel parameters To estimate the UE's location and direction , where the estimated values ​​of position and direction are expressed as and . (16) Where, express and The function between express Unbiased estimation of all system parameters. Among all system parameters, the estimation focus of this embodiment is on the UE position and rotation angle. Therefore, the goal of this embodiment is to minimize the CRLB of the UE position and orientation, which are called the position error bound (PEB) and the rotation error bound (OEB), respectively. (17) (18) In the formula, express In order to obtain the analytical expressions of PEB and OEB, this embodiment first uses the channel parameters The Fisher information matrix is ​​derived. Based on the Cramer-Rao theorem, the lower bound of the error is expressed as: (19) In formula, for The Fisher information matrix of is defined as follows: (20) Furthermore, in a wide-sense stationary process It can be written as: (21) According to the theory of signal processing and error analysis, the Fisher information matrix FIM of the position error lower bound PEB and the rotation angle error lower bound OEB can be obtained by the transfer matrix Get, expressed as: (22) In the formula, the transfer matrix As a bridge for building the parameter relationship of the positioning system, its physical significance lies in characterizing the conversion characteristics between different state parameters in the system, which can be specifically expressed as: (23) For the matrix Solving for the elements in the given set and , the following equality exists: (twenty four) (25) (26) (27) By PEB and OEB can be obtained. PEB is The first Square root of the trace of the submatrix: (28) OEB is The square root of the trace of the submatrix of rows 4 to 6 and columns 4 to 6: (29) 3. Near-field RIS phase shift optimization In near-field environments, optimizing the RIS in conjunction with a spherical waveform can improve signal transmission performance and thus enhance communications. Unlike plane wave propagation in the far field, near-field signals typically propagate as spherical waves, with the wavefront exhibiting an outward-expanding spherical shape. The RIS must adjust its phase based on the curvature of the wavefront to compensate for the curvature of the wavefront in near-field propagation. Optimizing the RIS phase ensures that the signal is more concentrated away from the RIS, thereby improving signal quality and reducing multipath interference. Furthermore, the RIS can more flexibly handle complex propagation conditions in the near-field environment, enhancing signal strength and transmission stability, enabling efficient near-field communications and precise beam steering.

[0033] The performance of user location specifically includes two parts: PEB and OEB. PEB and OEB evaluate the system error from two different dimensions, position and angle, respectively, so their optimization objectives are often independent of each other. However, during the actual inspection work performed indoors in the substation, this embodiment needs to optimize the estimation accuracy of both position and angle at the same time, thereby improving the overall performance of the system. This embodiment considers adopting a weighted joint optimization strategy, that is, optimizing PEB and OEB at the same time by introducing a weighting coefficient to balance the position error and angle error. The choice of weighting coefficient is adjusted according to the system's requirements for positioning accuracy and direction accuracy. The optimization problem can be expressed as:

[0034]

[0035] In formula (30), For all are all optimization variables. Since the objective function in the optimization problem (30) is non-convex, this embodiment considers applying the particle swarm optimization (PSO) algorithm to solve it. PSO is a random optimization method that attempts to imitate the social behavior of animal species with collective cooperation capabilities. It is a simple method with low computational complexity, but it shows high efficiency in non-convex optimization and has been widely used to solve problems in the telecommunications field.

[96] The PSO algorithm mainly involves the following terms: particle, group, speed, position, and A particle is a possible solution to the optimization problem and represents a position in the search space. A group represents all possible solutions in the current iteration. A velocity is the speed at which a particle changes its position in the search space, which depends on and . Define collective cognition, Defines its own cognition. These parameters are obtained by calculating the position of each particle through the fitness function. In addition, each particle has its own value, all particles have the same For each iteration, the velocity and position of each particle are updated based on the strategy proposed in

[97] . Figure 3 As shown in the figure, it is a flowchart of applying the PSO algorithm to phase optimization. Next, the specific steps of solving the optimization problem (30) based on PSO will be introduced in detail: 1) Initialize the particle swarm: randomly generate particles, represents the position of each particle, i.e., a possible phase shift configuration of RIS. reflection units, the dimension of the position vector of each particle is , the phase shift values ​​corresponding to its elements are taken from the phase shift set . At the same time, a velocity vector is initialized for each particle.

[0036] 2) Evaluate particle fitness: For each particle, the fitness value of each particle is calculated based on the RIS phase shift configuration it represents and the optimization objective function (30). The smaller the fitness value, the more optimal the RIS phase shift configuration represented by the particle.

[0037] 3) For each particle, update its velocity and position according to the following formula.

[0038] Velocity update formula: In formula (31), It is a particle In the The velocity vector at the iteration, , is the maximum number of iterations of the algorithm, and is the particle learning factor, and yes A random number between It is a particle The best position found so far, is the optimal position found by the entire particle swarm so far, It is a particle In the The position vector at the iteration, is the inertia weight, which is updated using the adaptive adjustment strategy in formula (4-32). (32) Position update formula: (33) During the updating process, it is necessary to ensure that the particle position, i.e., the phase shift value of RIS, is within the range of given conditions. 4) Update individual optimality and global optimality: For each particle , compare its current fitness value and the individual optimal fitness value (corresponding to Fitness value), if the current value is better, update the individual optimal position is the current position. Compare the individual optimal fitness values ​​of all particles to find the global optimal fitness value and the corresponding global optimal position 5) Determine the stopping condition: set the maximum number of iterations As the stopping condition. When the condition is met, the algorithm stops and the global optimal position is output The RIS phase configuration corresponding to this position is the optimized result, and its corresponding PEB and OEB values ​​are the optimized performance indicators.

[0039] 4. Simulation Analysis Based on the MIMO system under consideration, in this section, Matlab is used to conduct an in-depth performance analysis and verification of the proposed RIS-assisted user positioning system in a near-field environment, thereby providing a corresponding reference for the design of this mode in actual smart substations. Unless otherwise specified, the default values ​​of simulation parameters and data are set as follows: The number of antennas of the base station is , the number of antennas of the inspection equipment is , the base station location coordinates are , the user's location coordinates are , RIS location area is , the carrier frequency is , the system bandwidth is , the subcarrier spacing is , the speed of light is , the wavelength is , the antenna spacing is , the gain of the antenna is , the noise value noise power spectrum density is For the weight coefficient and PEB and OEB reflect the system positioning performance from different dimensions. When deriving the lower limit of the system's positioning accuracy, both are calculated based on the Cramer-Rao lower bound and are equally important in comprehensively evaluating the system's positioning capability. In actual application, the weights of the two have different emphases. For the substation inspection process, this embodiment pays more attention to the specific location of the inspection equipment, which can better determine the point where the problem occurs. Therefore, in the experiment, .

[0040] , the rotation angle of the UE antenna , using a single subcarrier, that is , the number of phase shift control bits As mentioned above, the optimized CRLB phase design strategy is obtained by numerically minimizing PEB and OEB. Since the CRLB optimization problem is non-convex, the algorithm can converge to a local minimum when the initial point is far from the true solution. For PEB and OEB in the figure, it can be seen that the proposed phase shift optimization performance is better than random phase shift. In addition, under the condition of optimized phase shift, the error gradually decreases with the increase of the number of RIS reflection units, while when When Figure 4 The position and direction errors are depicted for different numbers of RIS units and different phase shift design strategies, including phase shift design strategies from 0 to There are two methods: generating random phase shift and optimizing phase shift by using PSO algorithm. The center coordinate of RIS is set as , the rotation angle of the UE antenna , using a single subcarrier, that is , the number of phase shift control bits As mentioned above, the optimized CRLB phase design strategy is obtained by numerically minimizing PEB and OEB. Since the CRLB optimization problem is non-convex, the algorithm can converge to a local minimum when the initial point is far from the true solution. For PEB and OEB in the figure, it can be seen that the proposed phase shift optimization performance is better than random phase shift. In addition, under the condition of optimized phase shift, the error gradually decreases with the increase of the number of RIS reflection units, while when Therefore, the number of reflectors on the RIS side can be relaxed while achieving good positioning performance.

[0041] Figure 5 Depicts the number of control bits for different phase shifts The influence of positioning error on the next level, the PSO algorithm strategy is used to optimize the RIS phase shift during simulation, and the user's transmission power , the number of phase shift control bits , the number of RIS units is set to The remaining parameters are the same as in Experiment 1. The curves in the figure show that increasing transmit power and enhancing signal strength help improve the quality of the RIS reflected signal, thereby reducing positioning error. Furthermore, the curves for different numbers of phase shift control bits in the figure exhibit different effects. A higher number of phase shift control bits can further optimize the RIS reflected signal and effectively reduce error at the same transmit power. At high transmit power, the system error can be significantly reduced. Therefore, in applications requiring high-precision positioning, appropriately increasing transmit power and combining it with an optimized RIS phase shift control strategy can effectively improve positioning accuracy.

[0042] The simulation parameters are set as follows: the positions of BS and UE are fixed. , , UE rotation angle , when RIS moves along the y-axis, Figure 6 The effect of RIS placement on user orientation and position error is shown. RIS is placed in the yz plane and only needs to be considered. , when RIS moves along the z-axis, , the number of phase shift control bits , the number of subcarriers , number of RIS units From 6(a), we can see that RIS is located at When , the PEB value is the smallest and the system positioning performance is good. In the synchronous communication scenario, the system obtains an additional dimension of positioning information through delay estimation, which effectively enhances the completeness of the position solution. This signal strength and time domain information complement each other to improve the overall positioning accuracy of the system. As can be seen from 6(b), the RIS moves along the z axis and moves to When the RIS is located at the base station (BS), PEB and OEB are minimized, achieving optimal system performance. In a three-dimensional deployment, when the RIS is dynamically configured along the z-axis, an ideal geometric triangle is formed between the base station, user terminal, and RIS. Because the system uses uplink signals for positioning, when the RIS is close to the BS, the optimized geometry and reduced path loss combine to further improve positioning performance. Analysis shows that an effective and near-optimal RIS is more effective when close to the BS, as the signal is weaker near the terminal.

[0043] Simulation experiments were conducted using 8×8 and 12×12 RIS reflect arrays to verify the effectiveness of the proposed PSO phase shift optimization scheme. Figure 7 The simulation results show that as the number of iterations increases, the error bound gradually approaches a stable state, without significant fluctuations. This demonstrates that the PSO algorithm can effectively optimize the RIS phase shift configuration and stably achieve the optimal positioning and direction error bounds. Furthermore, a 12×12 RIS array provides lower positioning error than an 8×8 RIS array because a larger RIS array provides the system with more reflective elements, enabling more refined signal conditioning and helping the system better cope with complex multipath propagation and signal obstruction.

[0044] This embodiment, designed for indoor substation environments, breaks through far-field limitations and introduces a near-field spherical wave model to investigate reliable positioning technology based on RIS in near-field communication scenarios. Using the user position error bound (PEB) and the angle error bound (OEB) as performance evaluation metrics, the analysis focuses on the impact of phase shift optimization strategies and RIS placement on system performance. Simulation results show that, given a fixed number of RIS reflectors, the PSO optimization strategy employed in this embodiment achieves better system performance than random phase shifting. Furthermore, changes in RIS location mean a change in the number of line-of-sight paths; increasing signal transmission paths can improve system performance. Furthermore, increasing the number of RIS reflectors and transmit power both improves system performance, but the performance gains diminish after reaching a certain level.

[0045] The above only describes in detail the preferred embodiments of the present invention, but the present invention is not limited to the above embodiments. Various changes can be made within the knowledge of ordinary technicians in this field without departing from the purpose of the present invention, and various changes should be included in the scope of protection of the present invention.

Claims

1. A RIS-assisted wireless positioning method, characterized in that: The following steps are involved: S1. Establish a positioning system model: Construct a positioning system consisting of a multi-antenna base station (BS), a multi-antenna user equipment (UE), and a RIS in a rectangular coordinate system. Define the coordinates of the BS, UE, and RIS, where the RIS is placed in the yz plane with the x coordinate set to 0. Determine the positions of the antennas and reflective elements of each device, and define the direction vector and distance parameters. S2. Construct a signal model of the incident spherical wavefront: Based on near-field propagation conditions, establish a signal transmission model from UE to RIS and then to BS in the uplink, derive the channel matrices of the UE-RIS link and the RIS-BS link, and construct the RIS phase shift matrix, taking into account the spherical wave propagation characteristics and signal power and noise models; S3. Perform positioning performance analysis: derive the UE's position error bound (PEB) and orientation error bound (OEB), construct the Fisher information matrix (FIM), establish the relationship between channel parameters and UE position and orientation through the transfer matrix, and solve the analytical expressions for PEB and OEB. S4. Optimize RIS phase shift configuration: Use particle swarm optimization (PSO) algorithm to optimize the RIS phase shift matrix with the goal of minimizing weighted joint PEB and OEB. The weighted joint optimization satisfies Minimum, among which , and is the weighting coefficient.

2. A RIS-assisted wireless positioning method according to claim 1, characterized in that: The method for defining the coordinates of BS, UE and RIS in S1 is: defining the center position coordinates of BS as , BS The coordinates of the root antenna are , ; The center position coordinates of UE are ,UEth The position coordinates of the root antenna are ; RIS Reflection units, the center position coordinates are , No. The position coordinates of the unit are , ; From the placement of RIS, we can see that ; At the same time, the rotation angle of the UE antenna is defined as ; Since the main scenario of the study is the near-field environment, the BS, RIS and UE are located in the Fresnel area, that is, the distance is within the interval ,in represents the pore size of RIS, represents the wavelength of the signal, Indicates the spacing between components.

3. A RIS-assisted wireless positioning method according to claim 1, characterized in that: The method for defining the direction vector and distance parameters in S1 is: Define the direction vector as: Where, and Indicates the elevation angle and azimuth angle; with the BS as the center of the three-dimensional coordinate system, the coordinates of the UE and RIS centers are expressed as: Where, , 、 and Represents the distance, elevation and azimuth relative to the BS respectively; and its corresponding antenna array or reflector unit , the antenna coordinates of each array are expressed as: The distance between each unit is expressed as: , , , .

4. The RIS-assisted wireless positioning method according to claim 1, wherein: The method for establishing the signal transmission model from UE to RIS and then to BS in the uplink in S2 is: In the uplink, the system operates at wavelength Corresponding carrier frequency The signal bandwidth is , UE transmission OFDM subcarriers, for the subcarriers, Described as: It is The normalized data signal corresponding to the subcarriers satisfies the condition . is the beamforming matrix, satisfying and .

5. The RIS-assisted wireless positioning method according to claim 1, wherein: The method for deriving the channel matrices of the UE-RIS link and the RIS-BS link in S2 and constructing the RIS phase shift matrix is ​​as follows: The BS estimates the UE position and direction by using the distance and angle information in the spherical waveform model; assuming that the LOS path from the UE to the BS is blocked, the BS can only receive the signal through the cascade link UE-RIS-BS; therefore, The received signal associated with each subcarrier is expressed as: Where, is the signal power, is the signal vector transmitted by the system, is the observation noise, and the observation noise is modeled as having zero mean and variance Independent and identically distributed additive Gaussian white noise; and are the channel matrices of the UE-RIS and RIS-BS links respectively, is the RIS phase shift matrix; in: is the gain of a single UE antenna unit, is the gain of a single BS antenna unit.

6. A RIS-assisted wireless positioning method according to claim 1, characterized in that: The method of considering the propagation characteristics of spherical waves, signal power, and noise model in S2 is as follows: for the phase shift of the reflection unit , that is, assuming that each reflective element can only take a finite discrete phase shift, The number of phase shift control bits for each reflective element of RIS is determined by Uniform quantization is performed within the interval to obtain discrete phase shift values, and we get: In the analysis process, it is assumed that the synchronization process is always performed between the BS and the UE. After synchronization, the time and angle information of the received signal are jointly processed to study the difference between the two. The general model of the received signal with subcarrier correlation can be rewritten to obtain the scalar representation of the received signal: After removing the noise, the useful part of the signal is , represents the gain of the reflected path through RIS, represents the subcarrier considered, and Respectively represent UE Antenna to RIS Unit and RIS Units to BS The delay of the antenna, Indicates the speed of light, UE's The first antenna and the RIS The distance between the reflection units It is given by: Where, , , which contains the angle information of the signal, , ; Similarly, The first RIS reflection unit and the Reach distance between BS antennas in accordance with Make a statement.

7. The RIS-assisted wireless positioning method according to claim 1, wherein: In S3, the position error bound PEB and the direction error bound OEB of the UE are derived, and the Fisher information matrix FIM is constructed as follows: Receive signal As a random vector, its joint probability density function is expressed as: As the channel parameter Conditional receiving signal The likelihood function of is the covariance matrix of the noise; therefore, according to the maximum likelihood estimation principle, The estimate of is expressed as: A two-stage approach is adopted to estimate the UE position and direction. In the first step, the general form of the system channel parameters is determined, which is expressed as: In the formula, including gain, elevation, azimuth and delay channel information. In the second step, through the channel parameters To estimate the UE's location and direction , the estimated values ​​of position and direction are expressed as and : Where, express and The function between express Unbiased estimation of UE position and direction; minimize the CRLB of UE position and direction, which are called position error bound PEB and rotation error bound OEB respectively. Where, express The covariance of the channel parameters The Fisher information matrix is ​​derived, and based on the Cramer-Rao theorem, the lower bound of the error is expressed as: Where, for The Fisher information matrix of is defined as follows: In a wide-sense stationary process Written as: According to the signal processing and error analysis theory, the Fisher information matrix FIM of the position error lower bound PEB and the rotation angle error lower bound OEB is obtained through the transfer matrix Get, expressed as: In the formula, the transfer matrix As a bridge for building the parameter relationship of the positioning system, its physical significance lies in characterizing the conversion characteristics between different state parameters in the system, which can be specifically expressed as: 。 8. The RIS-assisted wireless positioning method according to claim 1, wherein: In S3, the relationship between the channel parameters and the UE position and direction is established through the transfer matrix. The method for solving the analytical expressions of PEB and OEB is: Pair Matrix Solving for the elements in the given set and , the following equality exists: Depend on Get PEB and OEB, PEB is The first Square root of the trace of the submatrix: OEB is The square root of the trace of the submatrix of rows 4 to 6 and columns 4 to 6: 。 9. The RIS-assisted wireless positioning method according to claim 1, wherein: The method for optimizing the RIS phase shift configuration in S4 is: A weighted joint optimization strategy is adopted, that is, PEB and OEB are optimized simultaneously by introducing weighting coefficients to balance the position error and angle error. The selection of weighting coefficients is adjusted according to the system's requirements for positioning accuracy and direction accuracy. The optimization problem is expressed as: Where, For all are all optimization variables.

10. The RIS-assisted wireless positioning method according to claim 1, characterized in that: The particle swarm optimization (PSO) algorithm in S4 includes the following steps: S4.

1. Initialize particle swarm: randomly generate particles, represents the position of each particle, i.e., a possible phase-shift configuration of RIS; since RIS has reflection units, the dimension of the position vector of each particle is , the phase shift values ​​corresponding to its elements are taken from the phase shift set ; At the same time, initialize a velocity vector for each particle; S4.

2. Evaluate particle fitness: For each particle, calculate the fitness value of each particle based on the RIS phase shift configuration it represents and the optimization objective function. The smaller the fitness value, the more optimal the RIS phase shift configuration represented by the particle. S4.

3. For each particle, update its velocity and position according to the following formula; Velocity update formula: Where, It is a particle In the The velocity vector at the iteration, , is the maximum number of iterations of the algorithm, and is the particle learning factor, and yes A random number between It is a particle The best position found so far is the optimal position found by the entire particle swarm so far, It is a particle In the The position vector at the iteration, is the inertia weight, which is updated using an adaptive adjustment strategy; Position update formula: During the updating process, it is necessary to ensure that the particle position, i.e., the phase shift value of RIS, is within the value range of the given conditions; S4.

4. Update individual optimality and global optimality: For each particle , compare its current fitness value and the individual optimal fitness value, that is, the corresponding The fitness value of the individual is updated if the current value is better. is the current position; compare the individual optimal fitness values ​​of all particles to find the global optimal fitness value and the corresponding global optimal position ; S4.

5. Determine the stopping condition: set the maximum number of iterations As the stopping condition, when the condition is met, the algorithm stops and the global optimal position is output. The RIS phase configuration corresponding to this position is the optimized result, and its corresponding PEB and OEB values ​​are the optimized performance indicators.

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