A RIS-assisted ISAC system beam tracking method based on cubature Kalman filter

Abstract

The present application belongs to the technical field of beam tracking under the Internet of Vehicles scene, and specifically relates to a kind of RIS auxiliary ISAC system beam tracking method based on cubature Kalman filtering, step 1: construct Internet of Vehicles ISAC system, and construct multiple model motion state set;Step 2: based on multiple model motion state set, design state vector and state transition matrix, and then design nonlinear base station-ISAC observation model;Step 3: design adaptive strong tracking cubature Kalman filter, generate a set of cubature points using third-order spherical radial cubature criterion, obtain hybrid state estimation and hybrid covariance matrix through the process of multiple model in interactive multiple model motion state set;Step 4: calculate the correlation measure, and assign the optimal vector to the most relevant target, and finally perform accurate beam tracking.The present application solves the problem of existing single motion model, and simultaneously solves the error of EKF in nonlinear system and the filter divergence problem prone to occur in high-dimensional system of UKF.

Description

Technical Field

[0001] This invention belongs to the field of beam tracking technology in the context of vehicle networking, specifically relating to a beam tracking method for a RIS-assisted ISAC system based on capacitive Kalman filtering. Background Technology

[0002] Predictive beam tracking techniques based on Kalman filtering have been extensively studied, with the vast majority of related works employing radar-assisted schemes based on the Extended Kalman Filter (EKF), fusing measurement data from vehicles and roadside infrastructure. However, EKF requires the computation of complex Jacobian matrices and can introduce errors in nonlinear systems. Furthermore, the Unscented Kalman Filter (UKF) is prone to filter divergence problems in high-dimensional systems.

[0003] Most existing beam tracking studies are based on single motion model scenarios, which cannot adapt to nonlinear driving scenarios including curves, roundabouts, lane changes, and acceleration / deceleration maneuvers. When the vehicle's direction of motion changes, the state evolution model suffers severe mismatch, ultimately leading to tracking failure. Although existing research has designed adaptive curve coordinate systems for arbitrary road geometry scenarios and proposed the Interacting Multiple Model (IMM) framework, the system scenarios it considers still have inherent limitations. Furthermore, building obstruction and severe signal attenuation in urban environments also significantly impact millimeter-wave vehicle-to-infrastructure (V2I) links. Reconfigurable Intelligent Surfaces (RIS) can reconstruct the wireless propagation environment through passive reflection, providing a highly promising solution for improving link reliability and enriching sensing dimensions.

[0004] To address the aforementioned challenges, this invention proposes a RIS-assisted interactive multiple model-adaptive strong trackingcubature Kalman filter (IMM-ASTCKF) scheme. Specifically, this invention provides a RIS-assisted beam tracking method for ISAC systems based on volumetric Kalman filtering. Summary of the Invention

[0005] The purpose of this invention is to propose a RIS-assisted interactive multiple model-adaptive strong tracking capacitive Kalman filter (IMM-ASTCKF) scheme. Specifically, this invention provides a RIS-assisted beam tracking method for ISAC systems based on capacitive Kalman filtering, which can solve the beam tracking problem in integrated sensing and communication (ISAC) systems for vehicle-to-everything (V2X) networks. It addresses the problems of existing single motion models, while simultaneously resolving the errors of EKF in nonlinear systems and the filtering divergence problem that easily occurs with UKF in high-dimensional systems.

[0006] The specific technical solution adopted by this invention is as follows: Step 1: Construct a vehicle-to-everything (V2X) ISAC system, and build a multi-model motion state set within the V2X ISAC system; Step 2: Based on the multi-model motion state set, design the state vector and state transition matrix, and then design the nonlinear base station-ISAC observation model of the vehicle-to-everything (V2X) ISAC system; Step 3: Design an adaptive strong tracking capacitive Kalman filter, generate a set of capacitive points using the third-order spherical radial capacitive criterion, and obtain the mixed state estimate and mixed covariance matrix through the multi-model process of the multi-model motion state set mentioned above. Step 4: Calculate the correlation metric and assign the optimal vector to the most relevant target, and finally perform accurate beam tracking.

[0007] The technical effects achieved by this invention are as follows: This invention solves the beam tracking problem in integrated sensing and communication (ISAC) systems for vehicle-to-everything (V2X) networks. It addresses the limitations of existing single motion models, while also resolving the errors of the Extensive Kinematic Filter (EKF) in nonlinear systems and the filtering divergence problem that easily occurs with the Underlying Kinematic Filter (UKF) in high-dimensional systems. Attached Figure Description

[0008] Figure 1 This is a schematic diagram of the RIS-assisted vehicle networking ISAC system scenario in this invention. Figure 2 This is a schematic diagram of trajectory tracking under the RIS-assisted vehicle networking ISAC system in this invention. Figure 3 This is a schematic diagram of the instantaneous distance prediction error of three targets in this invention; Figure 4This is a schematic diagram of the instantaneous angle prediction error of three targets in this invention; Figure 5 This is a schematic diagram comparing the average distance error of IMM-ASTCKF with EKF and UKF in this invention; Figure 6 This is a schematic diagram comparing the average angle error of IMM-ASTCKF with EKF and UKF in this invention. Detailed Implementation

[0009] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to embodiments. It should be understood that the following text is merely used to describe one or more specific embodiments of the invention and does not strictly limit the scope of protection specifically claimed by the invention.

[0010] like Figures 1-5 As shown, a RIS-assisted interactive multiple model-adaptive strong trackingcubature Kalman filter (IMM-ASTCKF) method is proposed. Specifically, this invention provides a RIS-assisted beam tracking method for an ISAC system based on capacitive Kalman filtering, which includes the following steps: Step 1: Construct a vehicle-to-everything (V2X) ISAC system, and build a multi-model motion state set within the V2X ISAC system; The state vector corresponding to the uniform motion model contains position and velocity information, and can be represented as follows: ; in and This represents the Cartesian position coordinates of vehicle k at discrete time k. and These represent the velocity vector components in the corresponding coordinate axis directions.

[0011] The state evolution equation of the uniform motion model is: ; in Represents the process noise vector. Indicates the sampling period.

[0012] The uniformly accelerated motion model assumes that the vehicle moves along a straight line with constant acceleration over a short time interval, and its corresponding state vector can be represented as follows: ; in and Let x and y represent the acceleration components of the vehicle along the x-axis and y-axis at time k, respectively. The state evolution equation for the uniformly accelerated motion model is: ; in This indicates process noise.

[0013] The turning model assumes that the vehicle turns at a constant turning rate over a short time interval, and its corresponding state vector can be represented as follows: ; in Let k represent the turning speed of the vehicle at time k. The state evolution equation for the turning model is: ; in This represents the corresponding process noise. Unlike uniform motion and uniformly accelerated motion models, the state transition matrix of the turning model is nonlinear and depends on the current turning speed. , can be represented as ; In step 1, the constructed multi-model motion state set includes a uniform linear motion model, a uniformly accelerated linear motion model, and a turning model.

[0014] In the constructed vehicle-to-everything (V2X) ISAC system, when obstacles obstruct communication, a reconfigurable intelligent metasurface (RIS)-assisted communication is introduced; the phase shift matrix of the RIS is represented as: ; A semi-positive definite relaxation method is used to achieve near-optimal phase shift alignment of RIS.

[0015] Step 2: Based on the multi-model motion state set, design the state vector and state transition matrix, and then design the nonlinear base station-ISAC observation model of the vehicle-to-everything (V2X) ISAC system. Since the positions of the base station and the target vehicle can be represented by coordinates in the Cartesian coordinate system, the distance from the base station to the vehicle, the vehicle speed observed by the base station, and the base station side angle can be obtained from the coordinates and the instantaneous vehicle speed extracted from the echo. Based on the distance from the base station to the vehicle, the vehicle speed observed by the base station, and the base station side angle, the base station-ISAC observation model is constructed. The position and speed of the target vehicle can be expressed as follows: and The integrated sensing and communication system enables the base station to directly determine the distance to the target by analyzing the received echo. radial velocity and azimuth Therefore, the observation vector of base station at time k is ; in and These represent the distance, velocity, and angle observation noise, respectively, and are typically modeled as a zero-mean Gaussian white noise process with variances of... , and The covariance matrix of the observation noise is: ; Because there is a nonlinear relationship between the observed values ​​(distance, radial velocity, azimuth) and the vehicle state vector (position, velocity, angular velocity) in Cartesian coordinates, the observation equation is modeled as follows: ; in Represents a nonlinear observation mapping. Let k be the state vector of the vehicle at time k (its specific dimensions and composition depend on the chosen kinematic model). This represents the observation noise vector corresponding to time k. (Nonlinear observation function) The following unified representation is maintained under the three kinematic models: ; This enables a nonlinear transformation from vehicle state in Cartesian coordinates to observations in the ISAC system.

[0016] Step 3: Design an adaptive strong tracking capacitive Kalman filter. Utilize the third-order spherical radial volume criterion to generate a set of volume points to approximate the mapping relationship of the state distribution under nonlinear transformations. Let... Let the state vector be n-dimensional, and its mean be denoted as . The Cholesky square root factor of the covariance matrix is ​​denoted as ,satisfy Based on the third-order spherical-radial volume criterion, the following is generated: Each equally weighted volume point, specifically expressed as follows: ; in The fundamental volume point set is constructed from the identity matrix and its negative matrix, i.e. All volume points share the same weight, expressed as: ; After generating a set of volume points, the square root matrix of the covariance is passed through orthogonal triangulation to ensure the numerical stability of the filter; then, an adaptive factor is introduced to improve the stability against noise. Through the process of interacting with the uniform linear motion model, the uniformly accelerated linear motion model, and the turning model in the multi-model motion state set, a mixed state estimate and a mixed covariance matrix are obtained. Also calculate the mixture probability In the formula, r is the normalization factor, and r is the total number of models; When calculating the mixed probability, the mixed initial state and mixed initial covariance matrix of each uniform linear motion model, uniformly accelerated linear motion model and turning model are calculated, where T and G are dimension change matrices.

[0017] ; .

[0018] Then, prediction and updates are performed based on the mixed initial states. Specifically, the following steps are included: A: The predicted points are obtained by nonlinear propagation of the volume points generated using capacitive Kalman filtering. ; B: Calculate the predicted state estimate, the predicted covariance matrix, the measured state estimate, and the measured covariance matrix.

[0019] ; in The square root of the process noise covariance matrix of model j is given by the expression. Represents the square root of the measurement noise covariance matrix of model j; C: Similarly, calculate the measurement mean and measurement covariance matrix; D: Calculate the cross-covariance matrix between the predicted state points and the predicted measurement points. ; E: Define the measurement residual vector as The adaptive factor is defined as follows: ; F: Calculate the Kalman gain to complete state estimation and covariance update; .

[0020] The probabilities of each model at the current time are corrected based on the latest measurement data. Based on the updated model probabilities, the posterior state estimates and covariance matrices of each model are weighted and fused.

[0021] The likelihood function can be expressed as the likelihood function in a given model. and historical observations from time 1 to k-1 Under the conditions, observation Conditional probability density: ; Under the Gaussian observation noise assumption, the expression for the likelihood function is: ; Where m represents the dimension of the observation vector, the corrected probability of each model can be calculated based on the likelihood function and the predicted model probability using the following formula, thereby completing the model probability update.

[0022] ; Step 4: Calculate the correlation metric and assign the optimal vector to the most relevant target, and finally perform accurate beam tracking.

[0023] In step 4, an additional prediction step is introduced at each time interval to advance the state prediction by one time step; the correlation metric is calculated using Mahalanobis distance to assign the optimal result to the most relevant target.

[0024] The working principle of this invention is as follows: The experimental scenario of this invention involves three vehicles on a highway, moving at a constant speed, accelerating uniformly, and turning, respectively. Their movements are obstructed by roadside obstacles in a certain area. For example... Figure 1 As shown, based on the problems involved in this vehicle-to-everything (V2X) scenario, this invention proposes a RIS-assisted interactive multi-model-adaptive strong tracking capacitive Kalman filter scheme for beam tracking.

[0025] like Figures 2 to 6 As shown, the IMM-ASTCKF method proposed in this invention achieves excellent beam tracking accuracy in both scenarios involving direct beam transmission from the base station to the target and RIS-assisted beam alignment. Although a small estimation error exists in the initial stage, this error rapidly decays as the filter converges, enabling rapid target lock and stable, continuous tracking. While model switching and target entry / exit from blind zones may cause a slight decrease in tracking performance and fluctuations in the error curve, the overall distance and angle errors remain at low levels, fully validating the accuracy of the proposed beam tracking method. Comparing this invention with existing EKF and UKF methods, the tracking error of this invention is significantly lower than the other two methods, fully demonstrating its outstanding advantage in target tracking accuracy.

[0026] The above description is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention. Structures, devices, and operating methods not specifically described or explained in this invention are implemented according to conventional methods in the art unless otherwise specified or limited.

Claims

1. A beam tracking method for a RIS-assisted ISAC system based on capacitive Kalman filtering, characterized in that: Includes the following steps: Step 1: Construct a vehicle-to-everything (V2X) ISAC system, and build a multi-model motion state set within the V2X ISAC system; Step 2: Based on the multi-model motion state set, design the state vector and state transition matrix, and then design the nonlinear base station-ISAC observation model of the vehicle-to-everything (V2X) ISAC system. Since the positions of the base station and the target vehicle can be represented by coordinates in the Cartesian coordinate system, the distance from the base station to the vehicle, the vehicle speed observed by the base station, and the base station side angle can be obtained from the coordinates and the instantaneous vehicle speed extracted from the echo. Based on the distance from the base station to the vehicle, the vehicle speed observed by the base station, and the base station side angle, the base station-ISAC observation model is constructed. Step 3: Design an adaptive strong tracking capacitive Kalman filter, generate a set of capacitive points using the third-order spherical radial capacitive criterion, and obtain the mixed state estimate and mixed covariance matrix through the multi-model process of the multi-model motion state set mentioned above. Step 4: Calculate the correlation metric and assign the optimal vector to the most relevant target, and finally perform accurate beam tracking.

2. The beam tracking method for a RIS-assisted ISAC system based on capacitive Kalman filtering according to claim 1, characterized in that: In step 1, the constructed multi-model motion state set includes a uniform linear motion model, a uniformly accelerated linear motion model, and a turning model.

3. The beam tracking method for a RIS-assisted ISAC system based on capacitive Kalman filtering according to claim 2, characterized in that: In the constructed vehicle-to-everything (V2X) ISAC system, when obstacles obstruct communication, a reconfigurable intelligent metasurface (RIS)-assisted communication is introduced; the phase shift matrix of the RIS is represented as: ； in This represents the phase shift introduced by the nth reflection unit, and then a semi-definite relaxation method is used to align the RIS to approximately optimal phase shift.

4. The beam tracking method for a RIS-assisted ISAC system based on capacitive Kalman filtering according to claim 2, characterized in that: In step 3, after generating a set of volume points, the square root matrix of the covariance is passed through orthogonal triangulation. Then, an adaptive factor is introduced.

5. The beam tracking method for a RIS-assisted ISAC system based on capacitive Kalman filtering according to claim 4, characterized in that: In step 3, the mixing probability is also calculated. In the formula, This represents the probability of model i at time k-1. This represents the conditional probability of the system transitioning from model i to model j; r is the normalization factor, and r is the total number of models; Then, prediction and updates are performed based on the mixed initial state. The probabilities of the uniform linear motion model, uniformly accelerated linear motion model, and turning model at the current moment are corrected according to the latest measurement data. Based on the updated model probabilities, the posterior state estimates and covariance matrices of the uniform linear motion model, uniformly accelerated linear motion model, and turning model are weighted and fused to obtain the mixed state estimate and mixed covariance matrix.

6. The beam tracking method for a RIS-assisted ISAC system based on capacitive Kalman filtering according to claim 5, characterized in that: When calculating the mixing probability, the initial mixing state and initial mixing covariance matrix of each uniform linear motion model, uniformly accelerated linear motion model and turning model are calculated, where T and G are dimension change matrices. ； ； in express k Time of the first i The state estimates corresponding to each model express k Time of the first i The state covariance matrix corresponding to each model express k Time of the first i Model probability of each model Indicates that the system is in k From the model at all times i Transfer to model j The conditional transition probability.

7. A beam tracking method for a RIS-assisted ISAC system based on capacitive Kalman filtering according to claim 6, characterized in that: The prediction and update process based on a mixed initial state specifically includes the following steps: A: Volume points generated using capacitive Kalman filtering After nonlinear propagation Obtain the predicted point, This represents the change from time k-1 to time k, determined by the vehicle's motion: ； B: Calculate the weight of each volume point: ； Calculate the predicted state estimate at time l: ； Calculate the prediction covariance matrix: ； Calculate the measurement state estimate: ； Calculate the measurement covariance matrix: ； in , For the predicted points and predicted states projected onto the observation space, The square root of the process noise covariance matrix of model j is given by the given expression. Represents the square root of the measurement noise covariance matrix of model j; C: Similarly, calculate the measurement mean and measurement covariance matrix; D: Based on the derivation process above, the cross-covariance matrix between the predicted state point and the predicted measurement point can be calculated. ； E: Define the measurement residual vector as , For measurements received by the base station, the adaptive factor is defined as follows: ； F: Calculate the Kalman gain based on the previous derivation: ； Based on the Kalman gain, the state estimation update is completed: ； Complete covariance update: ； 。 8. A beam tracking method for a RIS-assisted ISAC system based on capacitive Kalman filtering according to claim 7, characterized in that: In step 4, an additional prediction step is introduced at each time interval to advance the state prediction by one time step; the correlation metric is calculated using Mahalanobis distance to assign the optimal result to the most relevant target.

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