A RIS-assisted wireless positioning method

Abstract

The present application belongs to the field of wireless positioning technology, and specifically relates to a RIS-assisted wireless positioning method, comprising the following steps: establishing a positioning system model; constructing a signal model of an incident spherical wave front; performing positioning performance analysis: deducing the position error bound (PEB) and orientation error bound (OEB) of a UE, constructing a Fisher information matrix (FIM), establishing the relationship between channel parameters and UE position and orientation through a transfer matrix, and solving the analytical expression of PEB and OEB; and optimizing the RIS phase shift configuration. The RIS-assisted wireless positioning method proposed in the present application significantly improves the positioning accuracy and system adaptability in a near-field environment through multi-dimensional technical innovation. Firstly, the cascaded link model constructed based on the spherical wave propagation characteristics in the Fresnel region accurately depicts the signal transmission process from the UE to the RIS and from the RIS to the BS, effectively solves the channel modeling error problem caused by the coupling of near-field distance and angle parameters, and makes the positioning model more suitable for the actual scene requirements such as indoor and complex shielding.

Description

Technical Field

[0001] This invention belongs to the field of wireless positioning technology, specifically relating to a RIS-assisted wireless positioning method. Background Technology

[0002] Wireless positioning technology is widely used in fields such as the Internet of Things (IoT), intelligent transportation, and indoor navigation. Traditional GPS lacks sufficient positioning accuracy indoors or in complex, obstructed environments, making wireless communication-based positioning technologies an important supplement. With the development of 5G and 6G technologies, the integration of high-precision positioning and communication has become a hot topic. Among these technologies, reconfigurable smart surface (RIS) assisted positioning, due to its low cost, low power consumption, and high flexibility, has become key to improving positioning performance. In near-field positioning scenarios, signal propagation occurs in the Fresnel region, exhibiting significant spherical wave characteristics. However, traditional positioning technologies are mostly based on the far-field plane wave assumption, leading to large near-field channel modeling errors and decreased positioning accuracy.

[0003] Existing RIS-assisted positioning technology has several shortcomings. First, in near-field environments, it does not fully consider the coupling relationship between distance and angle in spherical wave propagation, making it difficult to accurately describe the signal link characteristics. Second, most studies only focus on user position estimation, ignoring the importance of device orientation information for multi-antenna systems, thus failing to achieve joint optimization of positioning and orientation estimation. Third, RIS phase shift configurations are mostly based on communication performance optimization, without designing for positioning error limits, and the optimization algorithms are highly complex, making them difficult to adapt to real-time scenarios. Fourth, positioning error analysis lacks a unified model for position error limits and orientation error limits, making it impossible to balance the performance of both according to actual needs. Summary of the Invention

[0004] To address the technical problems of existing RIS-assisted positioning technologies, this invention provides a RIS-assisted wireless positioning method. By accurately modeling the cascaded link channel under near-field spherical wave propagation, the position and orientation error limits are derived. The particle swarm optimization algorithm is used to optimize the RIS phase shift configuration, thereby minimizing the weighted joint error limit. This solves the problems of inaccurate models, one-sided dimensions, and insufficient optimization in near-field positioning, providing a new path for the integration of high-precision positioning and communication.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0006] A RIS-assisted wireless positioning method includes 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 BS, UE, and RIS, wherein the RIS is placed in the yz plane and the x-coordinate is 0, determining the positions of the antennas and reflection units of each device, and defining the direction vector and distance parameters.

[0007] S2. Constructing the signal model of the incident spherical wavefront: Based on the near-field propagation conditions, establish the 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, construct the RIS phase shift matrix, and consider the spherical wave propagation characteristics and signal power and noise models.

[0008] S3. Perform positioning performance analysis: Derive the UE's position error limit PEB and orientation error limit OEB, construct the Fisher information matrix FIM, establish the relationship between channel parameters and UE position and orientation through the transition matrix, and solve the analytical expressions of PEB and OEB.

[0009] S4. Optimize RIS phase shift configuration: Using the Particle Swarm Optimization (PSO) algorithm, the phase shift matrix of the RIS is optimized with the goal of minimizing the weighted joint PEB and OEB. The weighted joint optimization satisfies... Minimum, of which , and These are the weighting coefficients.

[0010] The method for defining the coordinates of BS, UE, and RIS in S1 is as follows: the center position coordinates of BS are defined as follows. BS The coordinates of the root antenna are , The center position coordinates of the UE are ,UE No. The position coordinates of the root antenna are ;

[0011] RIS is It consists of several reflective units, with the center position coordinates being... , No. The position coordinates of each unit are , The placement of the RIS indicates that... Meanwhile, the rotation angle of the UE antenna is defined as follows: Since the main research scenario is a near-field environment, BS, RIS, and UE are located in the Fresnel region, meaning the distance is within the range of... ,in This indicates that RISRIS and UE are located in the Fresnel region, meaning the distance between them is within the interval [0, 1]. ,in Indicates the aperture size of the RIS. Indicates the wavelength of the signal. Indicates the spacing between components.

[0012] The method for defining the direction vector and distance parameter in S1 is as follows:

[0013] Define the direction vector as:

[0014] In the formula, and Indicates elevation and azimuth angles; with BS as the center of the three-dimensional coordinate system, the center coordinates of UE and RIS are represented as: In the formula, , , and These represent the distance, elevation angle, and azimuth angle relative to BS, respectively; for and its corresponding antenna array or reflector unit. The antenna coordinates of each array are represented as follows: The distance between each unit is represented as: , , , .

[0015] The method for establishing the signal transmission model from UE to RIS and then to BS in the uplink in S2 is as follows:

[0016] In the uplink, the system operates at wavelength corresponding carrier frequency Above, the signal bandwidth is UE transmission For the first orthogonal frequency division multiplexing (OFDM) subcarrier, Subcarriers, Described as: It is the first The normalized data signals corresponding to each subcarrier satisfy the condition . It is a beamforming matrix that satisfies and .

[0017] The method for deriving the channel matrices of the UE-RIS link and the RIS-BS link and constructing the RIS phase shift matrix in S2 is as follows:

[0018] The BS estimates the UE's position and orientation using distance and angle information from a spherical waveform model; assuming the LOS path from the UE to the BS is blocked, the BS can only receive signals via the cascaded link UE-RIS-BS; therefore, compared to the first... The received signal associated with each subcarrier is represented as follows: In the formula, It is signal power. It is the signal vector transmitted by the system. It is observation noise, which is modeled as having a mean of zero and a variance of... Independent and identically distributed additive white Gaussian noise; and These are the channel matrices for the UE-RIS and RIS-BS links, respectively. This is the RIS phase shift matrix;

[0019] in: For the gain of a single UE antenna element, This represents the gain of a single BS antenna element.

[0020] The method in S2 that considers the propagation characteristics of spherical waves, signal power, and noise models is as follows: for the phase shift of the reflecting unit... That is, assuming that each reflecting element can only take on a finite discrete phase shift. The number of phase shift control bits for each reflective element of the RIS is determined by... Uniform quantization is performed within the interval to obtain discrete phase shift values, resulting in: During the analysis, it is assumed that a synchronization process is always performed between the BS and UE. After synchronization, the time and angle information of the received signal are jointly processed for further study, which will be compared with the first... The general model of the subcarrier-correlated received signal is rewritten to obtain the scalar representation of the received signal: After removing noise, the useful part of the signal is , Indicates the gain via the RIS reflection path. Indicates the subcarriers under consideration. and Representing the UE's first root antenna to RIS Unit and RIS Unit 1 to BS The delay of the root antenna, Representing the speed of light, the UE's first The root antenna and the RIS's first The distance between each reflective unit It is given by the following formula: In the formula, , This includes the angle information of the signal. , ; Similarly, the first The RIS reflection unit and the first Distance between BS antennas in accordance with To express.

[0021] In S3, the position error limit PEB and orientation error limit OEB of the UE are derived, and the Fisher information matrix FIM is constructed as follows:

[0022] Received signal As a random vector, its joint probability density function is expressed as: As a channel parameter Received signal under certain conditions The likelihood function, Let be the covariance matrix of the noise; therefore, according to the principle of maximum likelihood estimation, for The estimate is expressed as: A two-stage method is used to estimate the UE's position and orientation. In the first step, the general form of the system channel parameters is determined, expressed as: The formula includes gain, elevation angle, azimuth angle, and time delay channel information. In the second step, channel parameters are used... To estimate the position of the UE and direction The estimated values ​​of position and direction are expressed as follows: and : In the formula, express and Functions between express Unbiased estimation; minimizing the CRLB of UE position and orientation, which are called the position error limit PEB and rotation angle error limit OEB, respectively;

[0023] In the formula, express The covariance; first from 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: In the formula, for Fisher's information matrix, The definition is as follows: In a generalized stationary process Written as: Based on signal processing and error analysis theory, the Fisher information matrix (FIM) of the lower bound of position error (PEB) and the lower bound of rotation angle error (OEB) is obtained through the transition matrix. The result is represented as: In the formula, the transition matrix As a bridge for constructing the parameter relationships of a positioning system, its physical significance lies in characterizing the transformation characteristics between different state parameters in the system, specifically expressed as: In S3, the relationship between channel parameters and UE position and orientation is established through the transition matrix. The method for solving the analytical expressions of PEB and OEB is as follows: [The text abruptly ends here, likely due to an incomplete sentence or missing information.] Find the elements in a given set. and The following equation relationship exists:

[0024] Depend on We obtain PEB and OEB, where PEB is... The first The square root of the trace of the submatrix: OEB is The square root of the trace of the submatrix in rows 4 to 6 and columns 4 to 6:

[0025] .

[0026] The method for optimizing the RIS phase shift configuration in S4 is as follows:

[0027] A weighted joint optimization strategy is adopted, which simultaneously optimizes PEB and OEB by introducing weighting coefficients to balance position and angle errors. The selection of weighting coefficients is adjusted according to the system's requirements for positioning and orientation accuracy. The optimization problem is expressed as:

[0028]

[0029]

[0030] In the formula, For all All of these are optimization variables.

[0031] The Particle Swarm Optimization (PSO) algorithm in S4 includes the following steps: S4.1, Initialize the particle swarm: randomly generate... One particle, This represents the position of each particle, i.e., one possible phase shift configuration of the RIS; since the RIS has If there are 1000 reflecting units, then the position vector dimension of each particle is 1000. The phase shift values ​​corresponding to its elements are taken from the phase shift set. Simultaneously, 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 is.

[0032] S4.3 For each particle, update its velocity and position according to the following formula;

[0033] Speed ​​update formula: In the formula, It is a particle In the The velocity vector at the next iteration , This represents the maximum number of iterations for the algorithm. and It is a particle learning factor. and yes Random numbers between It is a particle The best location found so far It is the optimal position found so far for the entire particle swarm. It is a particle In the The position vector at the next iteration. It is an inertial weight, which is updated using an adaptive adjustment strategy; Position update formula:

[0034] During the update process, it is necessary to ensure that the particle's 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 with the individual's optimal fitness value, i.e., the corresponding The fitness value is used to update the individual's optimal position if the current value is better. The current position is determined by comparing the individual optimal fitness values ​​of all particles to find the global optimal fitness value and its corresponding global optimal position. S4.5, Determine the stopping condition: Set the maximum number of iterations. As a stopping condition, the algorithm stops when the condition is met and outputs the globally optimal position. The RIS phase configuration corresponding to this position is the optimized result, and its corresponding PEB and OEB values ​​are the optimized performance indicators.

[0035] Compared with the prior art, the beneficial effects of this invention are:

[0036] 1. The RIS-assisted wireless positioning method proposed in this invention significantly improves positioning accuracy and system adaptability in near-field environments through multi-dimensional technological innovation. First, the 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 BS. Compared with the traditional far-field plane wave assumption, it effectively solves the channel modeling error problem caused by the coupling of near-field distance and angle parameters, making the positioning model more suitable for actual scenarios such as indoor environments and complex obstructions.

[0037] 2. This invention achieves simultaneous optimization of the UE's three-dimensional coordinates and antenna orientation by jointly deriving the Position Error Boundary (PEB) and Orientation Error Boundary (OEB) and constructing the Fisher information matrix. This design, which extends the positioning dimension from single position estimation to joint position and orientation estimation, not only meets the orientation accuracy requirements of multi-antenna systems but also establishes a correlation between channel parameters and positioning parameters through the transition matrix, providing a more comprehensive theoretical basis for error analysis and avoiding the loss of orientation accuracy caused by focusing only on position estimation in traditional methods.

[0038] 3. In terms of RIS phase shift optimization, this invention employs a particle swarm optimization (PSO) algorithm to perform 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 its positioning emphasis according to different scenario requirements such as navigation and beamforming. Compared with 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 iterative mechanism with adaptive inertial weights further improve the algorithm's adaptability to RIS hardware constraints and convergence efficiency, achieving synergistic optimization of positioning performance and engineering feasibility. Attached Figure Description

[0039] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0040] The structures, proportions, sizes, etc. illustrated in this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed herein, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0041] Figure 1 This is a scene diagram of the indoor near-field positioning in a substation according to the present invention;

[0042] Figure 2 This is a geometric diagram of the positioning system of the present invention;

[0043] Figure 3 This is a flowchart of the PSO algorithm of the present invention;

[0044] Figure 4 This diagram illustrates the impact of the RIS cell number and phase design strategy on system error in this invention.

[0045] Figure 5 This is a diagram illustrating the effect of the number of RIS phase-shift quantization bits on the position error in this invention.

[0046] Figure 6 This is a diagram illustrating the impact of the RIS location on system performance in this invention.

[0047] Figure 7 This is a convergence graph of the PSO algorithm of this invention. Detailed Implementation

[0048] To make the objectives, 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 some embodiments of this application, and not all embodiments. These descriptions are only for further illustrating the features and advantages of the present invention, and not for limiting the claims of the present invention. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0049] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0050] I. System Model

[0051] 1. Scene and geometric representation

[0052] like Figure 1The illustrated indoor positioning scenario in a substation features a dense distribution of various electrical equipment, such as transformers, switchgear, and distribution cabinets. These bulky devices not only occupy significant space but also possess metal casings, providing strong shielding and reflection of wireless signals. In this environment, to locate the inspection equipment, an indoor base station and a RIS (Radio Reflection Path) device are deployed. The RIS intelligently modulates the incident wireless signal, providing an additional reflection path between the inspection equipment and the base station. During actual positioning, the inspection equipment periodically transmits signals carrying its status information and location identifier. The base station receives these signals, calculates the distance and angle between the inspection equipment and the base station, and thus determines the location of the inspection equipment. Combining the reflected signals provided by the RIS, the base station can obtain richer positioning information, further improving the accuracy and reliability of positioning. In this study, it is assumed that the line-of-sight path of the inspection equipment is always obstructed during operation.

[0053] Based on the positioning scenario, a RIS-assisted target location determination positioning system for near-field environments is established in a Cartesian coordinate system. The system consists of a multi-antenna base station (BS), a multi-antenna user equipment (UE), and an RIS. It is assumed that the position of the BS is known, the RIS is placed in the yz plane, and the base station locates the user by receiving signals. The UE has very limited mobility. The geometric representation of the system is as follows: Figure 2 As shown. Next, the center position coordinates of BS are defined as follows. BS The coordinates of the root antenna are , The center position coordinates of the UE are The coordinates of the antenna are , The center position coordinates of the UE are Depend on It consists of several reflective units, with the center position coordinates being... , No. The position coordinates of each unit are , The placement of the RIS indicates that... The rotation angle of the UE antenna is defined as follows: Since the main research scenario is a near-field environment, BS, RIS, and UE are located in the Fresnel region, meaning the distance is within the range [missing information]. ,in Indicates the aperture size of the RIS. Indicates the wavelength of the signal. Indicates the spacing between components. (1) In the formula, and This represents the elevation and azimuth angles. With BS as the center of the three-dimensional coordinate system, the center coordinates of UE and RIS can be represented as: (2) In the formula, , , and These represent the distance, elevation angle, and azimuth angle relative to BS, respectively. Further, for... and its corresponding antenna array or reflector unit. The antenna coordinates of each array can be represented as: (3) Without loss of generality, the distance between each unit can be expressed as: , , , .

[0054] 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 wavelength... corresponding carrier frequency Above, the signal bandwidth is UE transmission For the first orthogonal frequency division multiplexing (OFDM) subcarrier, Subcarriers, Described as: (4) It is the first The normalized data signals corresponding to each subcarrier satisfy the condition . It is a beamforming matrix that satisfies and The BS estimates the UE's position and orientation by utilizing distance and angle information from a spherical waveform model. Assuming the LOS path from the UE to the BS is blocked, the BS can only receive signals via the cascaded link UE-RIS-BS. Therefore, compared to the... The received signal associated with each subcarrier can be represented as: In formula (5), It is signal power. It is the signal vector transmitted by the system. It is observation noise, which is modeled as having a mean of zero and a variance of . Independent and identically distributed additive white Gaussian noise. and These are the channel matrices for the UE-RIS and RIS-BS links, respectively. This is the RIS phase shift matrix. (6)

[0055] (7) (8) For the gain of a single UE antenna element, This represents the gain of a single BS antenna element. Here, the phase shift for the reflecting element is... Assuming that each reflective element can only achieve a finite number of discrete phase shifts, The number of phase shift control bits for each reflective element of the RIS is determined by... By performing uniform quantization within the interval to obtain discrete phase shift values, we can get: (9) In the analysis process, this embodiment assumes that the BS and UE always perform a synchronization process. After synchronization, the time and angle information of the received signal are jointly processed for research. The general model of the received signal in equation (5) can be rewritten to obtain the scalar representation of the received signal, specifically expressed as follows: (10) So after removing the noise, the useful part of the signal is . Indicates the gain via the RIS reflection path. Indicates the subcarriers under consideration. and Representing the UE's first root antenna to RIS Unit and RIS Unit 1 to BS The delay of the root antenna, Represents the speed of light. Based on equation (4-3), the UE's... The root antenna and the RIS's first The distance between each reflective unit can be It is given by the following formula: In equation (11), , This includes the angle information of the signal. , . (12) Similarly, the first The RIS reflection unit and the first Distance between BS antennas It can be based on the formula (11) To express.

[0056] As can be seen, unlike the assumption of an incident plane wave in far-field communication schemes, the propagation mode of spherical waves results in significant variations in the wavefront shape of the signal at different locations. These variations contain rich spatial information and can provide crucial clues for accurate positioning. Therefore, in near-field communication, the ability to accurately handle the curvature variations of spherical waves directly affects the accuracy and reliability of ranging and azimuth estimation. It should be noted that the mathematical representations in this embodiment consider the clock synchronization of the BS, RIS, and UE.

[0057] II. Positioning Performance Analysis

[0058] 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 orientation to measure the system's positioning performance. After the derivation, a weighted sum optimization strategy is introduced in this embodiment to optimize positioning accuracy. (Received signal) As a random vector, its joint probability density function can be expressed as: (13) Can be used as channel parameters Received signal under certain conditions The likelihood function, Let be the covariance matrix of the noise. Therefore, according to the principle of maximum likelihood estimation, for... The estimate can be expressed as: (14) This embodiment uses a two-stage method to estimate the position and orientation of the UE. In the first step, the general form of the system channel parameters is determined, specifically as follows: Equation (15) includes channel information such as gain, elevation angle, azimuth angle, and time delay. In the second step, this embodiment uses channel parameters... To estimate the position of the UE and direction Here, the estimated values ​​for position and direction are expressed as follows: and . In equation (16), express and Functions between express Unbiased estimation. Among all system parameters, the estimation focus of this embodiment is on the UE's position and rotation angle. Therefore, the goal of this embodiment is to minimize the CRLB of the UE's position and orientation, referred to as the position error bound (PEB) and rotation angle error bound (OEB), respectively. (17)

[0059] In equation (18), express The covariance. To obtain the analytical expressions for PEB and OEB, this embodiment first starts from the channel parameters. The Fisher information matrix is ​​derived. Based on the Cramer-Rao theorem, the lower bound of the error is expressed as: In equation (19), for Fisher's information matrix, The definition is as follows: (20) Furthermore, in the generalized stationary process It can be written as: (21) Based on signal processing and error analysis theory, the Fisher information matrix FIM of the lower bound of position error PEB and the lower bound of rotation angle error OEB can be obtained through the transition matrix. The result is represented as: In equation (22), the transition matrix is... As a bridge for constructing the parameter relationships of a positioning system, its physical significance lies in characterizing the transformation characteristics between different state parameters in the system, which can be specifically expressed as: (23) For the matrix Find the elements in a given set. and The following equation relationship exists: (twenty four) (25) (26) (27) By You can obtain PEB and OEB. PEB is... The first The square root of the trace of the submatrix: (28) OEB is The square root of the trace of the submatrix in rows 4 to 6 and columns 4 to 6: (29)

[0060] III. Near-field RIS phase shift optimization

[0061] In near-field environments, RIS optimization combined with spherical waveforms can improve signal transmission performance and thus enhance communication. Unlike plane wave propagation in the far-field region, near-field signals typically exhibit spherical wave propagation, with the wavefront displaying an outwardly expanding spherical shape during propagation. RIS needs to adjust the phase according to the wavefront curvature to compensate for the wavefront bending effect during near-field propagation. Phase optimization of RIS ensures that the signal is more concentrated away from the RIS, thereby improving signal quality and reducing multipath interference. Simultaneously, RIS can more flexibly handle complex propagation conditions in near-field environments, enhancing signal strength and transmission stability, achieving efficient near-field communication and precise beam control.

[0062] The performance of user location tracking specifically includes two parts: PEB and OEB. PEB and OEB evaluate system errors from two different dimensions: position and angle, respectively, so their optimization objectives are often independent. However, in the actual inspection work performed indoors in substations, this embodiment needs to simultaneously optimize the estimation accuracy of position and angle to improve the overall system performance. This embodiment considers adopting a weighted joint optimization strategy, that is, simultaneously optimizing PEB and OEB by introducing weighting coefficients to balance position and angle errors. The selection of weighting coefficients is adjusted according to the system's requirements for positioning and orientation accuracy. The optimization problem can be expressed as:

[0063]

[0064] In equation (30), For all All are optimization variables. Since the objective function in optimization problem (30) is non-convex, this embodiment considers applying the Particle Swarm Optimization (PSO) algorithm to solve it. PSO is a stochastic optimization method that attempts to mimic the social behavior of animal species with collective cooperative abilities. 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, swarm, velocity, position, and A "particle" is a possible solution to the optimization problem, representing a "position" in the search space. A "swarm" represents all possible solutions in the current iteration. "Velocity" is the speed at which a particle changes position in the search space, depending on... and . Define collective cognition, Define your own cognition. These parameters are obtained by calculating the position of each particle using a fitness function. Furthermore, each particle has its own... Value, all particles have the same Values. For each iteration, the velocity and position of each particle are updated based on the strategy proposed in reference

[97] . Figure 3 The diagram shows a flowchart of phase optimization using the PSO algorithm. Next, the specific steps for solving the optimization problem (30) based on PSO will be described in detail: 1) Initialize the particle swarm: randomly generate... One particle, This represents the position of each particle, i.e., one possible phase shift configuration of the RIS. Because the RIS has... If there are 1000 reflecting units, then the position vector dimension of each particle is 1000. 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.

[0065] 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 (30). The smaller the fitness value, the better the RIS phase shift configuration represented by the particle.

[0066] 3) For each particle, update its velocity and position according to the following formula.

[0067] Speed ​​update formula: In equation (31), It is a particle In the The velocity vector at the next iteration , This represents the maximum number of iterations for the algorithm. and It is a particle learning factor. and yes Random numbers between It is a particle The best location found so far It is the optimal position found so far for the entire particle swarm. It is a particle In the The position vector at the next iteration. It is the inertial weight, which is updated using the adaptive adjustment strategy in equation (4-32). (32) Position update formula:

[0068] (33) During the update process, it is necessary to ensure that the particle's 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 with the individual's optimal fitness value (i.e., the corresponding fitness value). (Fitness value), if the current value is better, then update the individual's optimal position. This is the current position. Compare the individual best fitness values ​​of all particles to find the global best fitness value and its corresponding global best position. 5) Determine the stopping condition: Set the maximum number of iterations. This serves as a stopping condition. The algorithm stops and outputs the globally optimal position when the condition is met. The RIS phase configuration corresponding to this position is the optimized result, and its corresponding PEB and OEB values ​​are the optimized performance indicators.

[0069] IV. Simulation Analysis

[0070] Based on the considered MIMO system, this section uses Matlab to conduct in-depth performance analysis and verification of the proposed RIS-assisted user positioning system in a near-field environment, thus providing a corresponding reference for the design of this mode in practical smart substations. Unless otherwise specified, the default values ​​for simulation parameters and data are set as follows: the number of antennas for the base station is... The number of antennas for the inspection equipment is The base station location coordinates are User location coordinates are The RIS location region is The carrier frequency is The system bandwidth is The subcarrier spacing is The speed of light is , wavelength is The antenna spacing is The antenna gain is The noise value and noise power spectral density are For weight coefficients and The determination of PEB and OEB reflects the system's positioning performance from different dimensions. Both are calculated based on the Cramer-Rao lower bound when deriving the lower limit of the system's positioning accuracy, and are equally important in comprehensively evaluating the system's positioning capabilities. In practical applications, the weights of the two are emphasized differently. For substation inspection processes, this embodiment focuses more on the specific location of the inspection equipment, which can better pinpoint the location of problems. Therefore, the experiment is set to... .

[0071] UE antenna rotation angle Using a single subcarrier, that is Phase shift control bit count As mentioned earlier, 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 outperforms random phase shift. Furthermore, under the optimized phase shift condition, the error gradually decreases with the increase of the number of RIS reflector units, while when… Over time, the error tends to slow down. Figure 4 The position and orientation errors under different numbers of RIS cells and different phase design strategies are depicted. The phase shift design strategies include those from 0 to... There are two methods: generating random phase shifts and optimizing phase shifts using the PSO algorithm. The simulation experiment sets the center coordinates of the RIS to [value missing]. UE antenna rotation angle Using a single subcarrier, that is Phase shift control bit count As mentioned earlier, 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 outperforms random phase shift. Furthermore, under the optimized phase shift condition, the error gradually decreases with the increase of the number of RIS reflector units, while when… As time progresses, the error tends to decrease slowly. Therefore, the number of reflection units on the RIS side can be increased while achieving good positioning performance.

[0072] Figure 5 Depicting different numbers of phase shift control bits To mitigate the impact of positioning error, the PSO algorithm was used in the simulation to optimize the RIS phase shift, and the user's transmit power was considered. Phase shift control bit count The number of RIS units is set to The remaining parameter settings are the same as in Experiment 1. The curves in the figure show that increasing the transmit power enhances the signal strength, which helps improve the quality of the RIS reflected signal and thus reduces the positioning error. Furthermore, the curves with 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 the 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 the transmit power and combining it with an optimized RIS phase shift control strategy can effectively improve positioning accuracy.

[0073] The simulation can be performed by moving the RIS along the y-axis and along the z-axis respectively. The simulation parameters are set as follows, fixing the positions of the BS and UE. , UE rotation angle When RIS moves along the y-axis, Figure 6 This demonstrates the impact of RIS placement on user orientation and positional error. The RIS is placed in the yz plane, and only needs to be considered... When RIS moves along the z-axis, Phase shift control bit count , the number of subcarriers RIS unit number As can be seen from 6(a), RIS is located at... At this point, the PEB value is at its minimum, indicating good system positioning performance. In synchronous communication scenarios, the system obtains additional positioning information dimensions through delay estimation, effectively enhancing the completeness of the position calculation. This mutual complementation between signal strength and time-domain information improves the overall positioning accuracy of the system. As shown in 6(b), RIS moves along the z-axis and reaches... When the PEB and OEB are minimized, the system performance is optimal. In a three-dimensional deployment, when the RIS is dynamically configured along the z-axis, an ideal geometric triangle can be formed between the base station, user terminal, and RIS. Since the system uses uplink signals for positioning, when the RIS is close to the BS, the optimization of the geometric structure and the reduction of path loss work together to further improve the positioning performance of the system. Analysis shows that an effective and near-optimal RIS is more effective when close to the BS because the signal is weaker near the terminal.

[0074] Simulation experiments were conducted using 8×8 and 12×12 RIS reflector arrays respectively 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 limit gradually stabilizes without significant fluctuations. This indicates that the PSO algorithm can effectively optimize the phase shift configuration of the RIS and stably achieve the optimal positioning and orientation error limits. Furthermore, a 12×12 RIS array provides a lower positioning error than an 8×8 RIS array because a larger RIS array can provide more reflection units, enabling finer signal conditioning and helping the system better cope with complex multipath propagation and signal occlusion problems.

[0075] This embodiment focuses on the indoor environment of substations, overcoming far-field limitations by introducing a near-field spherical wave model to study reliable positioning technology based on RIS in near-field communication scenarios. Using the user position error limit (PEB) and angle error limit (OEB) as performance evaluation indicators, the impact of phase shift optimization strategies and RIS placement location on system performance is analyzed. Simulation results show that, with a fixed number of RIS reflector units, the PSO optimization strategy adopted in this embodiment performs better than random phase shift. Furthermore, changing the RIS position implies a change in the number of line-of-sight paths; increasing the number of signal transmission paths improves system performance. In addition, increasing the number of RIS reflector units and the transmit power both improve system efficiency, but the performance improvement gradually diminishes after a certain point.

[0076] The above description only illustrates the preferred embodiments of the present invention. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention, and all such changes should be included within the protection scope of the present invention.

Claims

1. A RIS-aided wireless positioning method, characterized in that, The method comprises the following steps: S1, establishing a positioning system model: constructing a positioning system composed 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, the UE and the RIS, the BS, the RIS and the UE being located in a Fresnel region, wherein the RIS is placed in the y-z plane and the x coordinate is 0, determining the positions of the antennas of each device and the reflection units, defining a direction vector and a distance parameter; S2, constructing a signal model of an incident spherical wave front: based on a near-field propagation condition, establishing a signal transmission model of the UE to the RIS and then to the BS in an uplink, deducing channel matrices of a UE-RIS link and a RIS-BS link, constructing a RIS phase shift matrix, and considering spherical wave propagation characteristics and signal power and noise models; S3, performing positioning performance analysis: deducing a position error bound PEB and an orientation error bound OEB of the UE, constructing a Fisher information matrix FIM, establishing a relationship between channel parameters and the position and orientation of the UE through a transfer matrix, and solving an analytical expression of the PEB and the OEB; The method for deducing the position error bound PEB and the orientation error bound OEB of the UE and constructing the Fisher information matrix FIM in S3 is as follows: Receiving signal As a random vector, its joint probability density function is denoted as: as a function of the channel parameters of the received signal , the likelihood function of the received signal is the covariance matrix of the noise; therefore, according to the maximum likelihood estimation principle, the estimate of is given by A two-stage method is adopted to estimate the position and orientation of the UE, in the first step, a general form of system channel parameters is determined, which is represented as follows: wherein, the gain, elevation angle, azimuth angle and time delay channel information are included; In a second step, the position and direction of the UE are estimated by the channel parameters , and the estimates of the position and direction are denoted by and , respectively. wherein denotes and a function between denotes an unbiased estimate of ; the CRLB is minimized over the UE position and orientation, referred to as the position error bound PEB and the orientation error bound OEB, respectively; where denotes the covariance; the Fisher information matrix is first derived from the channel parameters Based on the Cramer-Rao theorem, the lower bound of the error is expressed as: wherein is the Fisher information matrix, is defined as follows: In generalized stationary processes is 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 transition matrix and is expressed as: In the formula, the transfer matrix As a bridge to build the positioning system parameter relationship, its physical meaning lies in the characterization of the conversion characteristics between different state variables in the system, which is specifically expressed as: ； S4, optimizing RIS phase shift configuration: adopting particle swarm optimization (PSO) algorithm, optimizing the phase shift matrix of RIS with the weighted joint PEB and OEB minimization as the target, the weighted joint optimization satisfies min, wherein , and is a weighted coefficient; S4.1, initialize the particle swarm: randomly generate particles, representing the position of each particle, i.e. a possible phase shift configuration of the RIS; since the RIS has reflective elements, the position vector of each particle has a dimension of whose elements take phase shift values from the phase shift set ; at the same time, initialize a velocity vector for each particle; S4.2, evaluating the fitness of a particle: for each particle, the fitness value of each particle is calculated according to the RIS phase shift configuration represented by the particle and the optimization objective function, and the smaller the fitness value, the more optimal the RIS phase shift configuration represented by the particle; S4.3, for each particle, the speed and position thereof are updated according to the following formulae: Speed update formula: In the formula, It is a particle In the The velocity vector at the next iteration , This represents the maximum number of iterations for the algorithm. and It is a particle learning factor. and yes Random numbers between It is a particle The best location found so far It is the optimal position found so far for the entire particle swarm. It is a particle In the The position vector at the next iteration. It is an inertial weight, which is updated using an adaptive adjustment strategy; Position update formula: In the updating process, it is necessary to ensure that the position of the particle, i.e. the phase shift value of the RIS, is within the value range of the given condition; S4.4, update individual best and global best: for each particle , compare its current fitness value and individual best fitness value, i.e. the fitness value corresponding to the individual best position, if the current value is better, update the individual best position to the current position; compare the individual best fitness values of all particles, find the global best fitness value and the corresponding global best position ; S4.5, judge stop condition: set the maximum number of iterations As a stop condition, stop the algorithm when the condition is met, output the global optimal position The RIS phase configuration corresponding to this position is the optimized result, and the PEB and OEB values corresponding to it are the optimized performance indicators.

2. The RIS-assisted wireless positioning method of claim 1, wherein, The method for defining the coordinates of the BS, the UE and the RIS in the S1 is as follows: the coordinate of the center position of the BS is defined as , the coordinate of the first antenna of the BS is defined as , , the coordinate of the center position of the UE is defined as , and the coordinate of the first antenna of the UE is defined as . The RIS is composed of reflective units, the central position coordinates of which are , the position coordinates of the th unit are , ; from the placement position of the RIS, it can be known that ; The rotation angle of the UE antenna is defined as ; the BS, RIS and UE are located in the Fresnel region, i.e. the distance is located in the interval , where represents the aperture size of the RIS, represents the wavelength of the signal, represents the distance between the elements.

3. The RIS-assisted wireless positioning method of claim 1, wherein, The method for defining the direction vector and the distance parameter in S1 is as follows: The direction vector is defined as follows: wherein and denote the elevation and azimuth angles; with the BS as the center of the three-dimensional coordinate system, the UE and RIS center coordinates are represented as: wherein , , and denote the distance, elevation and azimuth angle with respect to the BS; for and its corresponding antenna array or reflecting unit the antenna coordinates of each array are denoted as: The distance between each unit is expressed as: , , , .

4. The RIS-assisted wireless positioning method of claim 1, wherein, The method for establishing the signal transmission model of the UE to the RIS and then to the BS in an uplink in S2 is as follows: In the uplink, the system operates at a wavelength corresponding carrier frequency The signal bandwidth is The UE transmits orthogonal frequency division multiplexing, OFDM, subcarriers, for the first subcarrier, is described as: is the normalized data signal corresponding to the th subcarrier, satisfying the condition , is the beamforming matrix, satisfying and .

5. The RIS-assisted wireless positioning method of claim 1, wherein, The method for deducing the channel matrices of the UE-RIS link and the RIS-BS link and constructing the RIS phase shift matrix in S2 is as follows: The BS estimates the UE position and its direction by exploiting the distance and angle information in the spherical wave model; assuming the LOS path from the UE to the BS is blocked, the BS can only receive the signal that has passed through the cascaded link UE-RIS-BS; therefore, the received signal associated with the mthsubcarrier is represented as: ​ wherein is the signal power, is the system transmitted signal vector, is the observation noise, which is modeled as independent and identically distributed additive white Gaussian noise with mean zero and variance and are the channel matrices of the UE-RIS and RIS-BS links, respectively, is the RIS phase shift matrix;​ wherein: G is the gain of a single UE antenna element, G is the gain of a single BS antenna element.

6. The RIS-assisted wireless positioning method of claim 1, wherein, The method in S2 considering the spherical wave propagation characteristics and the signal power and noise model is: for the phase shift of the reflection unit , that is, assuming that each reflection element can only take a limited discrete phase shift, The number of phase shift control bits of each reflection element of the RIS is obtained by uniformly quantizing in the interval to obtain a discrete phase shift value, which is: In the analysis, it is assumed that the synchronization procedure between the BS and the UE is always performed, and after synchronization, the time and angle information of the received signal is investigated by joint processing. The general model of the received signal associated with the first subcarrier is rewritten to obtain a scalar representation of the received signal: After removing the noise, the useful part of the signal is , denotes the gain of the RIS reflection path, denotes the considered subcarrier, and denote the time delay of the UE’s 1st antenna to the RIS’s 1st element and the RIS’s 1st element to the BS’s 1st antenna, respectively, denotes the light speed, the distance between the UE’s 1st antenna and the RIS’s 1st reflection element is given by In the formula, , wherein the angle information of the signal is contained, , ; Similarly, the first The RIS reflection unit and the first Distance between BS antennas in accordance with To express.

7. The RIS-assisted wireless positioning method of claim 1, wherein, The method for establishing the relationship between the channel parameters and the position and orientation of the UE through the transfer matrix and solving the analytical expression of the PEB and the OEB in S3 is as follows: On the solution of elements of a matrix given a set and there exists the following equality relationship: By obtaining PEB and OEB, PEB is the first sub-matrix trace square root: OEB is the square root of the sub-matrix trace of lines 4 to 6 and columns 4 to 6 of 。 8. The RIS-assisted wireless positioning method of claim 1, wherein, The method for optimizing the RIS phase shift configuration in S4 is as follows: A weighted joint optimization strategy is adopted, i.e. the PEB and the OEB are simultaneously optimized in the manner of balancing the position error and the angle error by introducing a weighting coefficient, the selection of the weighting coefficient being adjusted according to the demand of the system for positioning accuracy and orientation accuracy, and the optimization problem being represented as follows: In the formula, For all All of these are optimization variables.

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