Performance limit and phase design for near-field tracking with reconfigurable intelligent surface

Localization and tracking technique is one of the key technologies in the field of signal processing. Traditional methods use range-based techniques for target localization and tracking, but the algorithm's accuracy can degrade or even fail when the line of sight (LOS) link is obstructed. Reconfigurable intelligent surface (RIS), as a low-cost and flexibly deployable hardware material, can reflect incoming signals in a directional manner, which provides additional virtual line of sight (VLOS) links to enhance the accuracy of target localization and tracking. In this paper, we investigate the near-field target tracking problem with RIS, while analyzing the performance limit for the scenario and designing the phase of the RIS. Specifically, we establish a scene of near-field RIS-assisted tracking system and derive the posterior Cramér-Rao lower bound (PCRLB) as the tracking performance metric. By handling the Fisher information matrix (FIM), we illustrate that RIS-assisted target tracking system can effectively reduce the blind spot range of target velocity estimation compared to the traditional antenna array. Furthermore, we formulate an optimization problem by minimizing PCRLB to seek the optimal phase design under two scenes. For the prior target scenario, we process the original problem as a semidefinite program (SDP) problem by releasing it. In the unknown target scenario, we process the area of interest into an uncertain set and ultimately solve the problem through robust alternating optimization. Finally, the simulation experiments prove the effectiveness of the RIS-assisted target tracking algorithm.