Multi-RIS-assisted mobile user positioning method and system

Abstract

The invention belongs to the technical field of wireless communication, and discloses a multi-RIS-assisted mobile user positioning method and system, and the method comprises the steps: constructing direct and indirect channel state information matrixes between a base station and each mobile user, and a cooperative link channel state information matrix between any two mobile users, the method comprises the following steps: estimating an initial position of a mobile user by using a maximum likelihood estimation method, iteratively updating an estimated value of mobile user positioning by using an unscented Kalman filter (UKF) algorithm according to an estimated value of the initial position of the mobile user, optimizing a mobile user positioning error by using a posterior Cramer-Rao bound PCRB algorithm, and carrying out iterative block coordinate descent algorithm. And gradually optimizing the RIS phase shift matrix, and obtaining the mobile user positioning based on the minimization posterior Cramer-Rao bound PCRB. According to the invention, the positioning precision of the mobile user can be effectively improved.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and in particular, to a multi-RIS-assisted mobile user positioning method and system. Background Art

[0002] In power systems, especially for large power facilities, substations, and power grids spanning wide areas, the positioning and tracking of mobile users (such as maintenance personnel, inspection robots, inspection drones, etc.) are crucial for ensuring the safety, reliability, and efficiency of power systems. Traditional positioning systems usually rely on deploying numerous base stations, multiple sensor arrays, or using advanced signal processing technologies, 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 for realizing intelligent radio environments, has been widely welcomed. Different from fixed scatterers in the wireless environment, RIS has the ability to control amplitude and adjust phase, and can be regarded as a controllable scatterer.

[0004] In the prior art, for the problem of mobile user tracking assisted by RIS, the patent with the publication number CN115308687A provides a multi-RIS-assisted positioning method, device, electronic device, and computer storage medium. The method includes: 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 RIS according to the measurement results, and repeatedly executes the above steps until the positioning condition is met. This method does not fully consider the impact of the cooperative links between mobile users on the multi-user positioning and tracking problem. At the same time, some noise will be introduced in the calculation process, ultimately reducing the accuracy of mobile user positioning performance. Summary of the Invention

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

[0006] In a first aspect, the present invention further provides a multi-RIS-assisted mobile user positioning method, which includes:

[0007] Step S1: Construct 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;

[0008] Step S2: Based on the direct and indirect channel state information matrices, the cooperative link channel state information matrix, and the positions of the base station and multiple RISs, establish the probability relationship between the received observations and the mobile user's position, and use the maximum likelihood estimation method to estimate the initial position of the mobile user;

[0009] Step S3: According to the initial position estimate of the mobile user, use the unscented Kalman filter (UKF) algorithm to iteratively update the estimate of the mobile user's location;

[0010] Step S4: Use the posterior Cramér-Rao bound (PCRB) algorithm to optimize the mobile user's location error;

[0011] Step S5: Use the iterative block coordinate descent algorithm to gradually optimize the RIS phase shift matrix and obtain the mobile user's location based on minimizing the posterior Cramér-Rao bound (PCRB).

[0012] Furthermore, 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 from the base station directly to the mobile user and the channel state information matrix of the NLOS path reflected by the RIS from the base station to the mobile user indirectly.

[0013] Furthermore, step S2 specifically includes:

[0014] Based on the direct and indirect channel state information matrices and the cooperative link channel state information matrix, construct the total channel state information matrix related to the mobile user's position;

[0015] Based on the total channel state information matrix related to the mobile user's position, establish the conditional probability likelihood function of the received observations;

[0016] Based on the conditional probability likelihood function, the positions of the base station and multiple RISs, use the maximum likelihood estimation method to determine the possible position area of the mobile user, divide the grid in this area, and obtain the mobile user's position that maximizes the likelihood function.

[0017] Furthermore, the specific formula for constructing the total channel state information matrix related to the mobile user's position based on the direct and indirect channel state information matrices and the cooperative link channel state information matrix is expressed as:

[0018]

[0019] where h(u) represents the total channel matrix related to the mobile user's position u, and H d (u) represents the direct channel matrix between the base station and the mobile user's position u, and 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 co-link channel state information matrix related to the j-th mobile user, and M represents the number of mobile users.

[0020] Furthermore, the specific steps of iteratively updating the estimated value of mobile user positioning using the unscented Kalman filter (UKF) algorithm according to the initial position estimate of the mobile user in step S3 include:

[0021] Set the state vector according to the two-dimensional coordinates of the initial position estimate of the mobile user and the initial velocity components. According to the state vector, set the initial state estimate value and the corresponding covariance matrix

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

[0023] Set the state transition function. According to the sigma points, obtain the predicted sigma point set, state estimate value, and covariance matrix;

[0024] Pass the predicted Sigma point set through the set measurement function to calculate the measurement prediction value, measurement prediction covariance matrix, cross-covariance matrix, Kalman filter gain, and further obtain the updated state estimate value and updated covariance matrix.

[0025] Furthermore, the specific steps of optimizing the positioning error of the mobile user using the posterior Cramér-Rao bound (PCRB) algorithm in step S4 include:

[0026] Set the initial Fisher information matrix according to the state estimate value of the mobile user at each time point, and iteratively obtain the Fisher information matrix using the posterior Cramér-Rao bound (PCRB) algorithm. Take the inverse of the Fisher information matrix to obtain the PCRB matrix;

[0027] According to the PCRB matrix, obtain the weighting matrix T, construct the matrix C of different predicted positions and velocities of the mobile user, optimize the positioning error of the mobile user, and obtain the positioning matrix C of the mobile user tr = C * T.

[0028] Furthermore, the positioning accuracy of RIS-assisted mobile users is positively correlated with the number of RISs and the number of reflecting element units arranged in the planar array of RISs.

[0029] Furthermore, the positioning accuracy of RIS-assisted mobile users is positively correlated with the number of co-links between mobile users.

[0030] Furthermore, the positioning accuracy of RIS-assisted mobile users is positively correlated with the base station transmission power.

[0031] In a second aspect, the present invention provides a multi-RIS assisted mobile user positioning system, including 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 runs, the processor communicates with the storage medium through the bus, and the processor executes the machine-readable instructions to perform the steps of any one of the above-mentioned methods.

[0032] Compared with the prior art, the beneficial effects of the present invention are at least as follows:

[0033] The multi-RIS assisted mobile user positioning method and system provided by the present invention deploy multiple RISs, avoiding the dependence of mobile users on LOS paths. At the same time, the cooperative link relationship between mobile users is considered to increase information for mobile user positioning. The unscented Kalman filter (UKF) algorithm is used to locate the cooperative position of mobile users assisted by multiple RISs, making the positioning accuracy better than that of the traditional Kalman filter (KF) algorithm and the extended Kalman filter (EKF) algorithm. At the same time, relying on the posterior Cramér-Rao lower bound (PCRB) and the RIS phase shift optimization based on block coordinate descent, the positioning accuracy of mobile users is greatly improved. Description of the Drawings

[0034] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained according to the provided drawings without creative efforts.

[0035] Figure 1 It is a flowchart of the multi-RIS assisted mobile user positioning method provided by the embodiment of the present invention;

[0036] Figure 2 It is a comparison diagram of the mobile user tracking and positioning errors achieved by different numbers of RISs provided by the embodiment of the present invention;

[0037] Figure 3 It is the influence of the number of cooperative links between mobile users on the posterior Cramér-Rao lower bound (PCRB) of mobile user positioning provided by the embodiment of the present invention. Detailed Embodiments

[0038] To make the objectives, technical solutions and advantages of the present invention more clearly understood, the following further details the present invention in conjunction with the accompanying drawings and embodiments. Obviously, the specific embodiments described herein are only used to explain the present invention, which are some but not all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0039] Figure 1 FIG. 4 is a flowchart of a multi-RIS assisted mobile user positioning method provided in Embodiment 1 of the present invention, which specifically includes:

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

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

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

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

[0044] In this embodiment, given the positions of the base station, RIS, the signals transmitted by the base station and adjacent user nodes, 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 conditional on u is:

[0045]

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

[0047] Given the observation value, the log-likelihood function of u is:

[0048] Λ(u) = -||r - h(u)||

[0049] In the formula, r represents the actually received signal observation value, h(u) represents the theoretical mean of the observation value r when the user's position is u, and Λ(u) represents the log-likelihood function of u.

[0050] Use the maximum likelihood estimator to find the parameter value that maximizes the log-likelihood function Λ(u) of u:

[0051]

[0052] In the formula, Λ(u) represents the log-likelihood function of u, arg max represents the parameter corresponding to the maximum value, represents the parameter value that maximizes the log-likelihood function Λ(u).

[0053] To make the search reach the maximum value, the approximate interval of the user's actual position needs to be known in advance. Generate a grid map that contains all possible candidate coordinate points, so as to quantify the search space. γ is the coordinate set of all points in the grid. On this basis, use the maximum likelihood estimation method to conduct a comprehensive grid search on each candidate point on the map, that is, an exhaustive search. The accuracy of the position depends on the resolution of the grid map. To achieve centimeter-level positioning, the size of the grid needs to be controlled within 0.1 m. The position error is expressed as:

[0054]

[0055] In the formula, represents the parameter value that maximizes the log-likelihood function Λ(u), u represents the true value of the user's position to be estimated, E represents taking the average of each measured value, and ε(u) represents taking the root mean square error of and u.

[0056] Further, according to the direct and indirect channel state information matrices, and the cooperative link channel state information matrix, construct the total channel state information matrix related to the mobile user position. The specific formula is expressed as:

[0057]

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

[0059] In this way, not only the channel signal of the direct LOS path from the base station to the mobile user is considered, but also the channel signal of the NLOS path reflected by the RIS from the base station to the mobile user is considered. At the same time, the cooperative link channel signal between mobile users is further considered, thereby providing data support for the accurate positioning of mobile users.

[0060] Step S3: According to the initial position estimate of the mobile user, use the unscented Kalman filter UKF algorithm to iteratively update the estimate of the mobile user's position.

[0061] Specifically, in step S3, according to the initial position estimate of the mobile user, using the unscented Kalman filter UKF algorithm to iteratively update the estimate of the mobile user's position includes: setting the state vector according to the two-dimensional coordinates of the initial position estimate of the mobile user and the initial velocity component, and setting the initial state estimate and the corresponding covariance matrix according to the state vector; obtaining 2L + 1 sigma points according to the state vector and the covariance matrix, where L is a positive integer; setting the state transition function, and obtaining the predicted sigma point set, state estimate, and covariance matrix according to the sigma points; passing the predicted Sigma point set through the set measurement function, calculating the measurement prediction value, measurement prediction covariance matrix, cross-covariance matrix, and Kalman filter gain, and further obtaining the updated state estimate and updated covariance matrix.

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

[0063] Define a k-1 to represent the mean value of the state at time k - 1, Q k-1 to represent the covariance matrix of the state estimate, and run to generate 2L + 1 sigma points. These points are selected to the left and right from the mean value and have 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 for constructing sigma points is as follows:

[0064]

[0065] In the formula, The state estimation mean at time k-1, where z0 represents the first sigma point, which is the state estimation mean itself at time k-1, i.e., the first sigma point, z i represents the sigma points when i takes values from 1 to L, z k represents the sigma points when i takes values from L + 1 to 2L, Q k-1 represents the covariance matrix of the state estimation. L and λ are the dimensions of the state and the scaling parameter respectively, represents the i-th column of the square root of the matrix Δ. Based on the current state estimation mean and covariance, a set of sigma points are generated, which can approximately represent the probability distribution of the state. When i = 0, it is the state estimation mean itself, while the sigma points when i = 1 to 2L are obtained by processing the covariance matrix based on the state estimation mean, and are used to capture the uncertainty and non-linear characteristics of the state.

[0066] The generated sigma points are propagated through the non-linear state function, and the prediction sigma point formula is constructed as follows:

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

[0068] In the formula, f(.) is the non-linear state transition function, u k-1 is the control input at time k-1, z k-1 represents the sigma point at time k-1, z k|k-1 represents the predicted sigma point at time k. In the formula, the sigma point z k-1 from the previous time is passed through the non-linear state transition function f(.), combined with the control input u k-1 , to obtain the predicted sigma point z k|k-1 , which is used to predict the state at the next time.

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

[0070]

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

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

[0073]

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

[0075] In the above formula, The mathematical calculation formula of

[0076]

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

[0078] Furthermore, 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 will be elaborated 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 this embodiment, the formula for calculating the mean of the measurement prediction is constructed as follows:

[0080]

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

[0082] The second step involves updating the state estimate and covariance with the actual measurement. To calculate the Kalman gain, it is first necessary to 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 constructed formula is as follows:

[0083]

[0084] Among them, is the sigma point generated at time k from the state predicted at time k - 1, and h(z k ) is the sigma point generated at time k from the measurement predicted 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, and its calculation formula is as follows:

[0086]

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

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

[0089]

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

[0091] The expression for updating the state estimate is further given as follows:

[0092]

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

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

[0095]

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

[0097] Step S4: Optimize the positioning error of mobile users using the posterior Cramér-Rao bound (PCRB) algorithm. Specifically, it includes setting an initial Fisher information matrix based on the state estimation values of mobile users at each time point, iteratively obtaining the Fisher information matrix using the posterior Cramér-Rao bound (PCRB) algorithm, and inverting the Fisher information matrix to obtain the PCRB matrix; according to the PCRB matrix, obtain the weighting matrix T, construct the matrix C of different positions and speeds predicted by mobile users, optimize the positioning error of mobile users, and obtain the positioning matrix C of mobile users tr = C * T.

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

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

[0100]

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

[0102]

[0103] In the formula, represents 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 , and can be decomposed and expressed 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 then be decomposed and 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 Cramer - Rao lower bound of the non - linear filtering algorithm shows that:

[0110]

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

[0112]

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

[0114]

[0115] Since the system depends on making predictions at the previous time, the diagonal elements of the PCRB include the lower bounds of the mean - square errors estimated for the user's position and velocity. The following regulations 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 \(C(u_1,\ldots,u m ,\ldots,u M )\) is a matrix related to the positions and velocities of multiple users, which is multiplied by the weighting matrix \(T\) to reflect the influence brought by different positions of each user in space. Therefore, \(\Xi=\text{diag}(\Xi_1,\ldots,\Xi m ,\ldots,\Xi M ).

[0119] Step S5: Use the iterative block coordinate descent algorithm to gradually optimize the RIS phase shift matrix and obtain the mobile user positioning based on minimizing the posterior Cramér-Rao bound (PCRB).

[0120] Specifically, in each iteration of the iterative block coordinate descent algorithm, all other variables are fixed, and only one (or several) variables are optimized. 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 objective function of the mobile user position, minimizing the objective function of the mobile user position, and thus achieving high-precision multi-user tracking and positioning based on minimizing the PCRB.

[0121] More specifically, define the set of phase shift matrices of \(S\) RISs as \(\delta = [\delta_1,\delta_2,\ldots,\delta S \), and the optimization function can be modeled as:

[0122]

[0123] The above formula is a non-convex function. In the formula, \(T(\delta)\) represents the optimization function of the RIS phase shift matrix, and the quantity to be optimized \(\delta\) is a set of discrete variables. Therefore, an iterative block coordinate descent (BCD) algorithm is introduced to find the local optimum. The basic idea of the block coordinate descent method is: 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, making each step of optimization focus on a smaller sub-problem.

[0124] At the \(i\)-th iteration, the phase shift of the \(n\)-th reflection element of the \(s\)-th RIS is expressed as and 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, through an alternating iterative approach, each discrete phase shift value on each RIS is optimized, gradually approaching the optimal solution. In each iteration, other variables are fixed, one discrete phase shift variable is optimized, and the value of the objective function is updated according to the current optimization result. Since the value of the objective function shows a monotonically decreasing trend in each round of iteration, this indicates that each optimization can improve the current solution. More importantly, since the PCRB provides a lower bound and the value of this lower bound is 0, it means that this optimization process can effectively approach the optimal solution and will not deteriorate infinitely, making the BCD algorithm have monotonic convergence.

[0127] In this embodiment, the preset number of base station antennas N b = 10, the number of reflection units of a single reconfigurable intelligent surface (RIS) N r = 20, the position coordinates of the base station b = [0, 0, 24] T m. Respectively, 1, 2, and 3 RISs are preset. When the position coordinates of the 3 preset RISs are r1 = [5, 45, 8] T m, r2 = [5, -45, 8] T m, r3 = [0, 20, 8] T m. Respectively, 0, 2, 3, and 5 mobile users are 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, the noise power The comparison of the mobile user tracking and positioning errors achieved by presetting 1, 2, and 3 RISs is shown in the appendix Figure 2 as shown. When 0, 2, 3, and 5 mobile users are preset, the influence on the posterior Cramér-Rao lower bound (PCRB) of mobile user positioning is shown in the appendix Figure 3 as shown.

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

[0129] According to another aspect of the embodiments of the present invention, a multi-RIS-assisted mobile user positioning system is provided, including 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 runs, the processor communicates with the storage medium through the bus, and the processor executes the machine-readable instructions to perform the multi-RIS-assisted mobile user positioning method of any one of the above.

[0130] The above embodiments only express the preferred implementation modes of the present invention. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the patent for the present invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several variations and improvements can still be made, and these all fall within the protection scope of the present invention. Therefore, the protection scope of the patent for the present invention shall be subject to the appended claims.

Claims

1. A multi-RIS assisted mobile user positioning method, characterized in that, It 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: According to the direct and indirect channel state information matrices, the cooperative link channel state information matrix, and the positions of the base station and multiple RISs, establish the probability relationship between the received observation value and the position of the mobile user, and use the maximum likelihood estimation method to estimate the initial position of the mobile user; Step S3: According to the initial position estimation value of the mobile user, use the unscented Kalman filter (UKF) algorithm to iteratively update the estimation value of the mobile user's location; Step S4: Use the posterior Cramér-Rao bound (PCRB) algorithm to optimize the positioning error of the mobile user; Step S5: Use the iterative block coordinate descent algorithm to gradually optimize the RIS phase shift matrix and obtain the mobile user positioning based on minimizing the posterior Cramér-Rao bound (PCRB).

2. The multi-RIS assisted mobile user positioning method according to claim 1, wherein, In step S1, constructing the direct and indirect channel state information matrices between the base station and each mobile user specifically includes: the channel state information matrix of the LOS path from the base station directly to the mobile user and the channel state information matrix of the NLOS path reflected by the RIS from the base station to the mobile user indirectly.

3. The multi-RIS assisted mobile user positioning method according to claim 1, characterized in that, In step S2, it specifically includes: According to the direct and indirect channel state information matrices and the cooperative link channel state information matrix, construct the total channel state information matrix related to the position of the mobile user; According to the total channel state information matrix related to the position of the mobile user, establish the conditional probability likelihood function of the received observation value; According to the conditional probability likelihood function, the positions of the base station and multiple RISs, use the maximum likelihood estimation method to determine the possible position area of the mobile user, divide the grid in this area, and obtain the position of the mobile user that maximizes the likelihood function.

4. The multi-RIS-assisted mobile user positioning method according to claim 3, wherein, The specific formula for constructing the total channel state information matrix related to the position of the mobile user according to the direct and indirect channel state information matrices and the cooperative link channel state information matrix is: Among them, h(u) represents the total channel matrix related to the location u of the mobile user, and H d (u) represents the direct channel matrix between the base station and the location u of the mobile user, and H i,i (u) represents the indirect channel matrix related to the i-th RIS, N represents the number of RISs, and H j,j (u) represents the channel state information matrix of the cooperative link related to 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, wherein, In step S3, according to the initial position estimation value of the mobile user, using the unscented Kalman filter (UKF) algorithm to iteratively update the estimation value of the mobile user's location specifically includes: Set the state vector according to the two-dimensional coordinates of the initial position estimation value of the mobile user and the initial velocity component. According to the state vector, set the initial state estimation value and the corresponding covariance matrix According to the state vector and the covariance matrix, obtain 2L + 1 sigma points, where L is a positive integer; Set the state transition function. According to the sigma points, obtain the predicted sigma point set, state estimation value, and covariance matrix; Pass the predicted Sigma point set through the set measurement function to calculate the measurement prediction value, measurement prediction covariance matrix, cross-covariance matrix, and Kalman filter gain, and further obtain the updated state estimation value and updated covariance matrix.

6. The multi-RIS assisted mobile user positioning method according to claim 1, wherein, In step S4, using the posterior Cramér-Rao bound (PCRB) algorithm to optimize the positioning error of the mobile user specifically includes: Set the initial Fisher information matrix according to the state estimation value of the mobile user at each time point, iteratively obtain the Fisher information matrix using the posterior Cramer-Rao bound (PCRB) algorithm, and invert the Fisher information matrix to obtain the PCRB matrix; According to the PCRB matrix, a weighted matrix T is obtained, a matrix C of different positions and speeds of the mobile user prediction is constructed, the positioning error of the mobile user is optimized, and the positioning matrix C of the mobile user is obtained tr = C * T.

7. The multi-RIS assisted mobile user positioning method according to claim 1, wherein, The positioning accuracy of RIS-assisted mobile users is positively correlated with the number of RISs and the number of reflecting element units arranged in the planar array of RISs.

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

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

10. The multi-RIS-assisted mobile user positioning system is characterized in that It 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 runs, the processor communicates with the storage medium through the bus, and the processor executes the machine-readable instructions to perform the steps of the method according to any one of claims 1-9.

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