Method and system for mobile user positioning with multi-ris assistance

Abstract

The application belongs to the technical field of wireless communication, and discloses a multi-RIS assisted mobile user positioning method and system.The method comprises the following steps: constructing a direct and indirect channel state information matrix between a base station and each mobile user, and a cooperative link channel state information matrix between any two mobile users, using a maximum likelihood estimation method to estimate the initial position of the mobile user, using an unscented Kalman filter (UKF) algorithm to iteratively update the estimation value of the mobile user positioning according to the initial position estimation value of the mobile user, using a posterior Cramer-Rao bound (PCRB) algorithm to optimize the positioning error of the mobile user, and using an iterative block coordinate descent algorithm to gradually optimize the RIS phase shift matrix, so as to obtain the mobile user positioning based on the minimum posterior Cramer-Rao bound (PCRB). The application can effectively improve the positioning accuracy of the mobile user.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless communication, in particular to a multi-RIS assisted mobile user positioning method and system. BACKGROUND

[0002] In power systems, especially for large power facilities, substations and power networks spanning extensive areas, the positioning and tracking of mobile users (such as maintenance personnel, repair robots, inspection drones, etc.) are crucial to ensuring the safety, reliability and efficiency of the power system. Traditional positioning systems usually rely on deploying numerous base stations, multiple sensor arrays or using advanced signal processing techniques, resulting in complex and expensive infrastructure. Or rely on radio-based signal positioning, however, wireless high-frequency signals are very sensitive and are easily affected by obstacles due to their poor penetration.

[0003] Reconfigurable Intelligent Surfaces (RIS) as a low-power technology to realize intelligent radio environment is widely welcomed. Unlike fixed scatterers in wireless environments, RIS has the ability to control amplitude and adjust phase, which can be considered as controllable scatterers.

[0004] In the prior art, for the problem of mobile user tracking assisted by RIS, a patent with publication number CN115308687A provides a multi-RIS assisted positioning method, device, electronic equipment and computer storage medium, the method comprising: receiving multiple reference signals forwarded by multiple reconfigurable intelligent surfaces RIS, processing the reference signals to generate measurement results, and sending the measurement results to a network side device, so that the network side device adjusts the reflection parameters of the RIS according to the measurement results, and the above steps are executed cyclically until the positioning condition is met. This method does not fully consider the influence of the cooperative link between mobile users on the multi-user positioning and tracking problem, and at the same time, some noise is introduced in the calculation and processing, which ultimately reduces the accuracy of the mobile user positioning performance. SUMMARY

[0005] In view of the above technical problems, the present application provides a multi-RIS assisted mobile user positioning method and system.

[0006] In a first aspect, the present application also provides a multi-RIS assisted mobile user positioning method, which comprises:

[0007] Step S1: Constructing the direct and indirect channel state information matrix between the base station and each mobile user, and the cooperative link channel state information matrix between any two mobile users;

[0008] Step S2: According to the direct and indirect channel state information matrices, the cooperative link channel state information matrix, the positions of the base station and the plurality of RISs, a probability relationship between a received observation value and a mobile user position is established, and an initial position of the mobile user is estimated by using a maximum likelihood estimation method;

[0009] Step S3: According to the initial position estimation value of the mobile user, an estimated value of the mobile user positioning is iteratively updated by using an unscented Kalman filter (UKF) algorithm;

[0010] Step S4: A positioning error of the mobile user is optimized by using a posteriori Cramer-Rao bound (PCRB) algorithm;

[0011] Step S5: An RIS phase shift matrix is gradually optimized by using an iterative block coordinate descent algorithm, and a mobile user positioning based on a minimized posteriori Cramer-Rao bound (PCRB) is obtained.

[0012] Further, the direct and indirect channel state information matrices between the base station and each mobile user in the step S1 specifically include a channel state information matrix of a LOS path directly from the base station to the mobile user and a channel state information matrix of an NLOS path from the base station to the mobile user through reflection of the RIS.

[0013] Further, the step S2 specifically includes:

[0014] According to the direct and indirect channel state information matrices, the cooperative link channel state information matrix, a total channel state information matrix related to the mobile user position is constructed;

[0015] According to the total channel state information matrix related to the mobile user position, a conditional probability likelihood function of a received observation value is established;

[0016] According to the conditional probability likelihood function, the positions of the base station and the plurality of RISs, a maximum likelihood estimation method is used to determine a position region in which the mobile user may exist, a grid is divided in the region, and a mobile user position that maximizes the likelihood function is obtained.

[0017] Further, according to the direct and indirect channel state information matrices, the cooperative link channel state information matrix, a total channel state information matrix related to the mobile user position is constructed specifically as follows:

[0018]

[0019] wherein h (u) represents a total channel matrix related to the mobile user position u, H d (u) represents a direct channel matrix related to the base station and the mobile user position u, H i,i(u) represents an indirect channel matrix related to the i-th RIS, N represents the number of RISs, H j,j (u) represents a cooperative link channel state information matrix related to the j-th mobile user, and M represents the number of mobile users.

[0020] Further, the step S3 of iteratively updating the estimation value of the mobile user positioning according to the initial position estimation value of the mobile user using the unscented Kalman filter (UKF) algorithm specifically comprises:

[0021] According to the initial position estimation value of the mobile user two-dimensional coordinate and the initial velocity component, a state vector is set, and according to the state vector, an initial state estimation value and a corresponding covariance matrix are set

[0022] According to the state vector and the covariance matrix, 2L+1 sigma points are obtained, where L is a positive integer;

[0023] A state transition function is set, and according to the sigma points, a predicted sigma point set, a state estimation value, and a covariance matrix are obtained;

[0024] The predicted sigma point set is calculated through the set measurement function, and the measurement prediction value, the measurement prediction covariance matrix, the cross-covariance matrix, and the Kalman filter gain are further obtained. The update state estimation value and the update covariance matrix are further obtained.

[0025] Further, the step S4 of optimizing the mobile user positioning error using the posterior Cramer-Rao bound (PCRB) algorithm specifically comprises:

[0026] An initial Fisher information matrix is set according to the state estimation value of each time point of the mobile user, and the Fisher information matrix is iteratively obtained using the posterior Cramer-Rao bound (PCRB) algorithm. The PCRB matrix is obtained by inverting the Fisher information matrix;

[0027] According to the PCRB matrix, a weighting matrix T is obtained, a matrix C of different positions and velocities of the mobile user is constructed, the mobile user positioning error is optimized, and a positioning matrix C of the mobile user is obtained tr =C*T.

[0028] Further, the positioning accuracy of the mobile user assisted by the RIS is positively related to the number of RISs and the number of reflecting element units in the planar array arrangement of the RIS.

[0029] Further, the positioning accuracy of the mobile user assisted by the RIS is positively related to the number of cooperative links between the mobile users.

[0030] Further, the positioning accuracy of the mobile user assisted by the RIS is positively related to the base station transmission power.

[0031] In a second aspect, the present application provides a multi-RIS assisted mobile user positioning system, comprising a processor, a storage medium and a bus, the storage medium storing machine readable instructions executable by the processor, the processor and the storage medium communicating through the bus when an electronic device of the positioning system is running, and the processor executing the machine readable instructions to perform the steps of any of the above methods.

[0032] Compared with the prior art, the present application has at least the following advantages:

[0033] The multi-RIS assisted mobile user positioning method and system provided by the present application deploy multiple RIS, avoid the dependence of mobile users on the LOS path, consider the cooperative link relationship between mobile users to increase information for mobile user positioning, and use the unscented Kalman filter (UKF) algorithm to position the cooperative position of mobile users assisted by multiple RIS, so that the positioning accuracy is better than that of the traditional Kalman filter (KF) algorithm and extended Kalman filter (EKF) algorithm, and the positioning accuracy of mobile users is greatly improved by relying on the posterior Cramer-Rao lower bound (PCRB) and RIS phase shift optimization based on block coordinate descent. BRIEF DESCRIPTION OF DRAWINGS

[0034] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only embodiments of the present application, and those skilled in the art can obtain other drawings according to the provided drawings without creative labor.

[0035] Figure 1 A multi-RIS assisted mobile user positioning method flowchart is provided for the embodiments of the present application.

[0036] Figure 2 A mobile user tracking positioning error comparison chart realized by different numbers of RIS is provided for the embodiments of the present application.

[0037] Figure 3 The influence of the number of cooperative links between mobile users on the posterior Cramer-Rao lower bound (PCRB) of mobile user positioning is provided for the embodiments of the present application. DETAILED DESCRIPTION

[0038] In order to make the purposes, technical solutions and advantages of the present application clearer, the present application will be further described in detail below in combination with the drawings and examples. Obviously, the specific examples described here are only used to explain the present application and are a part of the examples of the present application, but not all the examples. Based on the examples in the present application, all the other examples obtained by those skilled in the art without creative work belong to the protection scope of the present application.

[0039] Figure 1 A multi-RIS assisted mobile user positioning method flow chart is provided for the embodiment 1 of the present application, which specifically includes:

[0040] Step S1: constructing the direct and indirect channel state information matrix between the base station and each mobile user, and the cooperative link channel state information matrix between any two mobile users.

[0041] Specifically, step S1 mainly includes the channel state information matrix of the LOS (Line of Sight) path from the base station to the mobile user directly and the channel state information matrix of the NLOS (Non Line of Sight) path from the base station to the mobile user through the reflection of RIS.

[0042] Step S2: according to the direct and indirect channel state information matrix, the cooperative link channel state information matrix, the positions of the base station and the multiple RIS, establishing the probability relationship between the received observation value and the mobile user position, and using the maximum likelihood estimation method to estimate the initial position of the mobile user.

[0043] Specifically, step S2 includes: according to the direct and indirect channel state information matrix and the cooperative link channel state information matrix, constructing the total channel state information matrix related to the mobile user position; according to the total channel state information matrix related to the mobile user position, establishing the conditional probability likelihood function of the received observation value; according to the conditional probability likelihood function and the positions of the base station and the multiple RIS, using the maximum likelihood estimation method to determine the possible position area of the mobile user, dividing the grid in the area, and obtaining the mobile user position that makes the likelihood function maximum.

[0044] In the embodiment, the positions of the base station and the RIS, the signals transmitted by the base station and the adjacent user nodes are given, and the position u of the user is estimated according to the observation. The probability density function Pr(r;u) of the received observation value r under the condition of u is:

[0045]

[0046] In the formula, r represents the actual received signal observation value, u represents the user position to be estimated, L represents the dimension of the state parameter, σ 2where σ2 represents the variance of the observation noise, h(u) represents the theoretical mean of the observation r when the user position is u, and Pr(r;u) represents the probability density function of receiving the observation r given the condition u.

[0047] The log-likelihood function of u given the observation r is:

[0048] Λ(u) = -||r - h(u)|

[0049] where r represents the actual received signal observation, h(u) represents the theoretical mean of the observation r when the user position is u, and Λ(u) represents the log-likelihood function of u.

[0050] The parameter value maximizing the log-likelihood function Λ(u) of u is found using the maximum likelihood estimator:

[0051]

[0052] where Λ(u) represents the log-likelihood function of u, arg max represents the parameter corresponding to the maximum value, represents the parameter value maximizing the log-likelihood function Λ(u).

[0053] To maximize the search, the approximate interval of the actual position of the user needs to be known in advance. A grid map is generated, which contains all possible candidate coordinate points, so that the search space can be quantized, and γ is the coordinate set of all points in the grid. On this basis, the maximum likelihood estimation method is used to conduct a comprehensive grid search of each candidate point on the map, i.e., an exhaustive search. The accuracy of the position depends on the resolution of the grid map, and to achieve centimeter-level positioning, the size of the grid needs to be controlled within 0.1 m. The position error is represented as:

[0054]

[0055] where represents the parameter value maximizing the log-likelihood function Λ(u), u represents the true value of the user position to be estimated, and E represents the average of each measured value, and ε(u) represents the root mean square error of and u.

[0056] Further, according to the direct and indirect channel state information matrix, the cooperative link channel state information matrix, a total channel state information matrix related to the position of the mobile user is constructed, and the specific formula is represented as:

[0057]

[0058] where h(u) represents the total channel matrix related to the position u of the mobile user, H d(u) represents the direct channel matrix of the base station related to the location of the mobile user u, H i,i (u) represents the indirect channel matrix related to the i-th RIS, N represents the number of RISs, H j,j (u) represents the cooperative link channel state information matrix related to the j-th mobile user, and M represents the number of mobile users.

[0059] In this way, not only the channel signals of the base station direct-to-mobile user LOS path are considered, but also the channel signals of the base station indirect-to-mobile user NLOS path reflected by the RIS, and at the same time, the cooperative link channel signals between the mobile users are further considered, thereby providing data support for realizing accurate positioning of the mobile users.

[0060] Step S3: iteratively updating the estimated value of the mobile user positioning using the unscented Kalman filter (UKF) algorithm according to the initial position estimated value of the mobile user.

[0061] Specifically, the step S3 of iteratively updating the estimated value of the mobile user positioning using the unscented Kalman filter (UKF) algorithm according to the initial position estimated value of the mobile user includes: setting a state vector according to the two-dimensional coordinate of the initial position estimated value of the mobile user and the initial velocity component, setting an initial state estimated value and a corresponding covariance matrix according to the state vector; obtaining 2L+1 sigma points according to the state vector and the covariance matrix, wherein L is a positive integer; setting a state transition function, obtaining a predicted sigma point set, a state estimated value, and a covariance matrix according to the sigma points; calculating a measurement predicted value, a measurement predicted covariance matrix, a cross-covariance matrix, and a Kalman filter gain by passing the predicted sigma point set through a set measurement function, and further obtaining an updated state estimated value and an updated covariance matrix.

[0062] More specifically, in the time update phase of the unscented Kalman filter (UKF) algorithm, this phase predicts the next state and updates the corresponding covariance by propagating a set of sigma points through a nonlinear system, which are selected to the left and right of the mean with the same distance on the coordinate axis.

[0063] Define a k-1 , which represents the mean value of the state at time k-1, Q k-1 , which represents the covariance matrix of the state estimate, runs to generate 2L+1 sigma points, which are selected to the left and right of the mean with the same distance on the coordinate axis. The purpose of generating sigma points is to accurately estimate the mean value and covariance of the state estimate. In this embodiment, the mathematical calculation formula of the sigma points is constructed as follows:

[0064]

[0065] In the formula, Let z0 be the mean state estimate at time k-1, indicating that the first sigma point is the mean state estimate at time k-1 itself, i.e., the first sigma point. i Let z represent the sigma point when the i-th value is i = 1, ..., L. k Let Q represent the sigma point when the i-th value is i = L+1, ..., 2L. k-1 Let L represent the covariance matrix of the state estimate, where L and λ are the dimensions of the state and scaling parameters, respectively. This represents the i-th column of the square root of matrix Δ. Based on the current state estimate mean and covariance, a set of sigma points is generated. These sigma points approximate the probability distribution of the state. The sigma points for i=0 are the state estimate mean itself, while the sigma points for i=1,...2L are obtained by processing the covariance matrix based on the state estimate mean, used to capture the uncertainty and nonlinearity of the state.

[0066] The generated sigma points are propagated through a nonlinear state function, and the formula for predicting sigma points is as follows:

[0067] z k|k-1 =f(z) k-1 ,u k-1 )

[0068] In the formula, f(.) is the nonlinear state transition function, u k-1 It is the control input at time k-1, z k-1 Let z represent the sigma point at time k-1. k|k-1 This represents the predicted sigma point at time k. In the formula, the sigma point z from the previous time step is used. k-1 By using the nonlinear state transition function f(.) and combining it with the control input u k-1 The predicted sigma point z is obtained. k|k-1 It is used to predict the state at the next moment.

[0069] Based on the propagation of these sigma points, the mean state at time k can be predicted as:

[0070]

[0071] In the formula, Indicates weight, This represents the predicted sigma point at time k-1. This represents the mean of the predicted state at time k, which is a preliminary estimate of the next state.

[0072] The formula for the predicted state covariance at time k can be expressed as:

[0073]

[0074] where W i m and W i c respectively define the weights of the state mean and covariance, P k is the process noise covariance, represents the predicted sigma points at time k-1, represents the predicted state mean at time k, represents the predicted state covariance at time k, which is used to measure the uncertainty of the predicted state.

[0075] In the above formula, The mathematical formula of can be expressed as:

[0076]

[0077] In the above formula, The distribution state of the surrounding Sigma points is determined by a, adjusting a can reduce the influence of high order terms, and a small positive number is usually assumed, 0≤a≤1; set β≥0 to improve the accuracy of variance; λ=a 2 (L+κ)-L, a determines the distribution range of sigma, set κ=3-n, which is an auxiliary parameter, to ensure that (L+λ)Q is a semi-definite matrix.

[0078] Further, in the measurement update stage of the Unscented Kalman Filter (UKF) algorithm, the latest measurement is used to refine the predicted state and enhance the estimation. This includes several steps: measurement prediction, Kalman gain calculation, state and covariance update, which are described in detail below.

[0079] This stage also has two main steps. The first step is to predict the measurement result by propagating the sigma points through the measurement model, in the present embodiment, the formula for calculating the measurement prediction mean is constructed as follows:

[0080]

[0081] In the above formula, represents the corresponding weight of the measurement prediction value h(z k ), h(z k ) represents the measurement prediction value, represents the measurement prediction value mean.

[0082] The second step involves updating the state estimation and covariance with the actual measurement. In order to calculate the Kalman gain, it is necessary to first calculate the cross-covariance matrix and the measurement prediction covariance, respectively. The cross-covariance matrix represents the correlation between the state and the measurement prediction, and the formula is constructed as follows:

[0083]

[0084] wherein, is a sigma point generated at time k from the predicted state at time k-1, h(z k ) is a sigma point generated at time k from the predicted measurement at time k-1, is the predicted state vector, is the predicted measurement vector.

[0085] measurement prediction covariance also represents the expected accuracy of the measurement prediction, which is calculated as follows:

[0086]

[0087] wherein, R k is the measurement noise covariance matrix at time k. Considering the difference between the measurement prediction and the measurement prediction mean, as well as the influence of the measurement noise, the measurement prediction covariance at time k is calculated by the formula which is used to measure the uncertainty of the measurement prediction.

[0088] The Kalman gain expression is given as follows:

[0089]

[0090] wherein, the Kalman gain is calculated according to the cross-covariance matrix and the measurement prediction covariance , which is used to determine how to update the state estimate according to the measurement value, and it determines the degree of influence of the measurement value on the state update.

[0091] The update state estimate expression is further given as follows:

[0092]

[0093] wherein, the Kalman gain is used to update the state prediction mean obtained in the time update stage by combining the difference between the actual measurement value and the measurement prediction mean, to obtain a more accurate state estimate value.

[0094] The further state covariance matrix expression is as follows:

[0095]

[0096] wherein, the Kalman gain and the measurement prediction covariance are used to update the state prediction covariance obtained in the time update stage, to obtain the updated state covariance, which is used to reflect the uncertainty of the updated state estimate.

[0097] Step S4: using the posterior Cramér-Rao bound PCRB algorithm to optimize the positioning error of the mobile user. Specifically, including setting the initial Fisher information matrix according to the state estimation value of each time point of the mobile user, using the posterior Cramér-Rao bound PCRB algorithm to obtain the Fisher information matrix, and obtaining the PCRB matrix by inverting the Fisher information matrix; according to the PCRB matrix, obtaining the weighting matrix T, constructing the matrix C of the predicted different positions and speeds of the mobile user, optimizing the positioning error of the mobile user, and obtaining the positioning matrix C of the mobile user tr =C*T.

[0098] The posterior Cramér-Rao bound (PCRB) is an important concept in parameter estimation theory for measuring the estimation accuracy. PCRB is based on Bayesian estimation theory and is used to describe the lower limit of the minimum mean square error (MSE) that can be achieved when estimating unknown parameters given observation data and prior information. It provides a benchmark for evaluating the performance of various estimators, i.e. the mean square error of any unbiased estimator cannot be lower than PCRB. PCRB can be used to evaluate the precision limit of user position estimation based on a given observation model and prior information. By calculating PCRB, the optimal positioning accuracy that can be theoretically achieved under the current system settings and observation conditions can be known, thereby providing a basis for designing positioning algorithms and evaluating algorithm performance.

[0099] More specifically, the estimated state of the user is represented as The estimate of the state a k+1 is a function of the observation vector r k+1 . PCRB can be represented as:

[0100]

[0101] where, denotes the mathematical expectation of the user state and the measurement value, J(a k+1 ) is the posterior information matrix of the user state a k . J(a k+1 ) can be represented as:

[0102]

[0103] where, denotes the second-order partial derivative matrix operation, p(r k+1 ,a k+1 ) is the joint probability density function of a k+1 and r k+1 , which can be decomposed as:

[0104] p(rk+1 a k+1 )=p(a k+1 )p(r k+1 |a k+1 )

[0105] Based on this, J(a k+1 ) can be further expressed as:

[0106] J(a k+1 )=J P (a k+1 )+J D (a k+1 )

[0107] where J P (a k+1 ) and J D (a k+1 ) are the FIMs related to the user's prior information and the target state observation data, respectively. Their specific forms are:

[0108]

[0109] Further derivation of the nonlinear filtering algorithm Cramer-Rao lower bound can be known:

[0110]

[0111] where, J P (a k+1 ) and J D (a k+1 ) can be further simplified as:

[0112]

[0113] Given the initialization J(a0), the Cramer-Rao information matrix at time k+1 can be recursively calculated, and the PCRB of the user state estimation error can be obtained by the following formula:

[0114]

[0115] Since the system depends on the prediction made at the previous time, the diagonal elements of the PCRB include the lower bound of the estimated mean square error of the user's position and velocity, and the following provisions are made for the measurement of the tracking accuracy of the mobile user:

[0116] T(a k )=tr(C(u1,...,u m ,...,u M ))

[0117] =tr(ΞC)

[0118] where C(u1,...,u m ,...,u M ) is a matrix with respect to the positions and velocities of multiple users, multiplied by a weighting matrix T to reflect the influence of each user at different positions in space, so Ξ = diag(Ξ1,...,Ξ m ,...,Ξ M ),

[0119] Step S5: using the iterative block coordinate descent algorithm, step by step optimizing the RIS phase shift matrix, obtaining the mobile user positioning based on minimizing the posterior Cramer-Rao bound PCRB.

[0120] Specifically, the iterative block coordinate descent algorithm fixes all other variables in each iteration, and only optimizes one (or several) variables. This strategy can decompose the originally complex high-dimensional optimization problem into a series of relatively simple low-dimensional sub-problems, reducing the difficulty of solving the target function of the mobile user position, minimizing the target function of the mobile user position, thereby achieving high-precision multi-user tracking positioning based on minimizing PCRB.

[0121] More specifically, define the phase shift matrix set of S RIS as δ = [δ1, δ2,..., δ S ], and the optimization function can be modeled as:

[0122]

[0123] The above formula is a non-convex function, where T(δ) represents the optimization function of the RIS phase shift matrix, and the to-be-optimized quantity δ is a set of discrete variables. Therefore, the iterative block coordinate descent (BCD) algorithm is introduced to find the local optimum. The basic idea of the block coordinate descent method is that in each iteration, all other variables are fixed, and only one (or several) variables are optimized. The advantage of this method is that it can effectively simplify complex optimization problems, so that the optimization of each step can focus on a smaller sub-problem.

[0124] At the i-th iteration, the phase shift of the n-th reflecting element of the s-th RIS is represented as Its optimization problem can be written as:

[0125]

[0126] Based on this, the solution to the problem can be obtained by enumerating all possible discrete phase shift values in the set χ. Specifically, by means of alternating iteration, each discrete phase shift value on each RIS is optimized to gradually approach the optimal solution. In each iteration, fix other variables, optimize one discrete phase shift variable, and update the value of the objective function according to the current optimization result. Since the value of the objective function presents a monotonically decreasing trend in each iteration, it indicates that each optimization can improve the current solution. More importantly, since the PCRB provides a lower bound, and the value of the lower bound is 0, it means that the optimization process can effectively approach the optimal solution, and will not deteriorate indefinitely, so that the BCD algorithm has a monotonic convergence.

[0127] In this embodiment, the preset number of base station antennas N b = 10, the number of reflecting elements of a single smart reflecting surface RIS N r = 20, the position coordinates of the base station b = [0, 0, 24] T m, 1, 2, and 3 RISs are respectively preset, and when 3 RISs are preset, the position coordinates of the RISs are respectively r1 = [5, 45, 8] T m, r2 = [5, -45, 8] T m, and r3 = [0, 20, 8] T m, 0, 2, 3, and 5 mobile users are respectively preset, the number of RIS phase shift control bits R = 3, the system bandwidth B = 15 MHz, the signal frequency f c = 5.4 GHz, the number of subcarriers L = 10, and the noise power The comparison of mobile user tracking positioning errors achieved by 1, 2, and 3 RISs is shown in FIG. 8. Figure 2 The influence of the posterior Cramer-Rao lower bound PCRB on mobile user positioning when 0, 2, 3, and 5 mobile users are preset is shown in FIG. 9. Figure 3

[0128] Therefore, further, the RIS-aided mobile user positioning accuracy is positively correlated with the number of RISs, the number of reflecting element units of the planar array arrangement of the RIS, the number of cooperative links between mobile users, and the base station transmission power.

[0129] According to another aspect of the embodiment of the present application, a multi-RIS-aided mobile user positioning system is provided, which includes a processor, a storage medium, and a bus. The storage medium stores machine-readable instructions executable by the processor. When the electronic device of the positioning system is running, the processor communicates with the storage medium through the bus. The processor executes the machine-readable instructions to perform the multi-RIS-aided mobile user positioning method of any one of the above. ​

[0130] The above embodiments only express the preferred modes of implementing the present application, which are described in a more specific and detailed manner, but should not be understood as limiting the scope of the patent of the present application. It should be noted that for those of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present application, which all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application should be subject to the appended claims.

Claims

1. A multi-RIS-assisted mobile user positioning method, characterized in that, Includes the following steps: Step S1: Construct the direct and indirect channel state information matrices between the base station and each mobile user, and the cooperative link channel state information matrix between any two mobile users; Step S2: Based on the direct and indirect channel state information matrix, the cooperative link channel state information matrix, the location of the base station and multiple RIS, establish the probability relationship between the received observation value and the location of the mobile user, and use the maximum likelihood estimation method to estimate the initial location of the mobile user; Step S3: Based on the initial location estimate of the mobile user, use the Unscented Kalman Filter (UKF) algorithm to iteratively update the estimated location of the mobile user; Step S4: Use the posterior Cramer-Rao bound PCRB algorithm to optimize the positioning error of mobile users; Step S5: Use the iterative block coordinate descent algorithm to progressively optimize the RIS phase shift matrix and obtain the mobile user location based on minimizing the posterior Cramer-Rao bound PCRB.

2. The multi-RIS-assisted mobile user positioning method according to claim 1, characterized in that, The construction of the direct and indirect channel state information matrices between the base station and each mobile user in step S1 specifically includes: the channel state information matrix of the LOS path directly from the base station to the mobile user and the channel state information matrix of the NLOS path indirectly from the base station to the mobile user via RIS reflection.

3. The multi-RIS-assisted mobile user positioning method according to claim 1, characterized in that, Step S2 specifically includes: Based on the direct and indirect channel state information matrices and the cooperative link channel state information matrix, a total channel state information matrix related to the mobile user's location is constructed. Based on the total channel state information matrix related to the mobile user's location, establish the conditional probability likelihood function of the received observations; Based on the conditional probability likelihood function, the location of the base station and multiple RIS, the maximum likelihood estimation method is used to determine the possible location area of ​​the mobile user. Within this area, a grid is divided to obtain the mobile user location that maximizes the likelihood function.

4. The multi-RIS-assisted mobile user positioning method according to claim 3, characterized in that, Based on the direct and indirect channel state information matrices and the cooperative link channel state information matrix, the specific formula for constructing the total channel state information matrix related to the mobile user's location is as follows: Where h(u) represents the total channel matrix associated with the mobile user's location u, H d (u) represents the direct channel matrix related to the location u of the base station and the mobile user. H i,i (u) represents the indirect channel matrix associated with the i-th RIS, N represents the number of RIS, and H j,j (u) represents the cooperative link channel state information matrix associated with the j-th mobile user, and M represents the number of mobile users.

5. The multi-RIS-assisted mobile user positioning method according to claim 1, characterized in that, Step S3, which iteratively updates the estimated location of the mobile user using the Unscented Kalman Filter (UKF) algorithm based on the initial location estimate, specifically includes: A state vector is set based on the mobile user's initial position estimate (two-dimensional coordinates) and initial velocity components. Based on this state vector, initial state estimates and their corresponding covariance matrices are then set. Based on the state vector and covariance matrix, obtain 2L+1 sigma points, where L is a positive integer; Define a state transition function, and obtain the predicted sigma point set, state estimate, and covariance matrix based on the sigma points; The predicted Sigma point set is used to calculate the measurement prediction value, measurement prediction covariance matrix, cross covariance matrix, and Kalman filter gain through a set measurement function, and then the updated state estimate and updated covariance matrix are obtained.

6. The multi-RIS-assisted mobile user positioning method according to claim 1, characterized in that, Step S4 uses the posterior Cramer-Rao bound algorithm (PCRB) to optimize the mobile user positioning error, specifically including: An initial Fell information matrix is ​​set based on the state estimate of the mobile user at each time point. The Fell information matrix is ​​obtained iteratively using the posterior Cramer-Rao bound PCRB algorithm. The PCRB matrix is ​​obtained by inverting the Fell information matrix. Based on the PCRB matrix, a weighting matrix T is obtained, and a matrix C is constructed to predict different positions and velocities for the mobile user. The positioning error of the mobile user is then optimized to obtain the positioning matrix C of the mobile user. tr =C*T.

7. The multi-RIS-assisted mobile user positioning method according to claim 1, characterized in that, The accuracy of RIS-assisted mobile user positioning is positively correlated with the number of RIS and the number of reflective element units in the planar array arrangement of the RIS.

8. The multi-RIS-assisted mobile user positioning method according to claim 1, characterized in that, The accuracy of RIS-assisted mobile user positioning is positively correlated with the number of collaborative links between mobile users.

9. The multi-RIS-assisted mobile user positioning method according to claim 1, characterized in that, The accuracy of RIS-assisted mobile user positioning is positively correlated with the base station's transmit power.

10. A multi-RIS-assisted mobile user positioning system, characterized in that, The device includes a processor, a storage medium, and a bus. The storage medium stores machine-readable instructions executable by the processor. When the electronic device of the positioning system is running, the processor communicates with the storage medium via the bus, and the processor executes the machine-readable instructions to perform the steps of the method as described in any one of claims 1-9.

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