This paper investigates the cell-free multi-user integrated sensing and communication (ISAC) system, where multiple base stations collaboratively track the users and detect their signals. Moreover, reconfigurable intelligent surfaces (RISs) are deployed to serve as additional reference nodes to overcome the line-of-sight blockage issue of mobile users for accomplishing seamless sensing. Due to the high-speed user mobility, the multi-user tracking and signal detection performance can be significantly deteriorated without elaborated online user kinematic state updating principles. To tackle this challenge, we first manage to establish a probabilistic signal model to comprehensively characterize the interdependencies among user states, transmit signals, and received signals during the tracking procedure. Based on the Bayesian problem formulation, we further propose a novel hybrid variational message passing (HVMP) algorithm to realize computationally efficient joint estimation of user states and transmit signals in an online manner, which integrates VMP and standard MP to derive the posterior probabilities of estimated variables. Furthermore, the Bayesian Cramer-Rao bound is provided to characterize the performance limit of the multi-user tracking problem, which is also utilized to optimize RIS phase profiles for tracking performance enhancement. Numerical results demonstrate that the proposed algorithm can significantly improve both tracking and signal detection performance over the representative Bayesian estimation counterparts.

翻译：本文研究无蜂窝多用户集成感知与通信系统，其中多个基站协同跟踪用户并检测其信号。此外，系统部署可重构智能表面作为额外参考节点，以克服移动用户视距链路阻塞问题，实现无缝感知。由于用户高速移动性，若缺乏精细的在线用户运动状态更新机制，多用户跟踪与信号检测性能将显著恶化。为应对这一挑战，我们首先建立概率信号模型，以全面刻画跟踪过程中用户状态、发射信号与接收信号之间的相互依赖关系。基于贝叶斯问题建模，我们进一步提出一种新型混合变分消息传递算法，以在线方式实现用户状态与发射信号的联合高效估计。该算法融合VMP与标准MP来推导估计变量的后验概率。此外，本文推导了贝叶斯克拉美-罗界以刻画多用户跟踪问题的性能极限，并利用该界限优化RIS相位配置以提升跟踪性能。数值结果表明，相较于代表性贝叶斯估计方法，所提算法能显著提升跟踪与信号检测性能。