RIS-Aided Localization Algorithm and Analysis: Tackling Non-Gaussian Angle Estimation Errors

Reconfigurable intelligent surface (RIS)-aided localization systems are increasingly recognized for enhancing accuracy in internet of things (IoT) networks. However, prevailing studies tend to either assume a Gaussian distribution for angle estimation error (AEE) or directly neglect the impact of the AEE, overlooking its non-Gaussian nature in real-world scenarios, particularly with diverse estimation methods (e.g., 2D-DFT algorithm). Addressing this oversight, this paper explores the design and performance analysis of RIS-aided localization systems, specifically tackling non-Gaussian AEE. We adopt the classical two-step three-dimensional (3D) localization scheme to determine the position of mobile user (MU). Initially, we estimate angles of arrival (AoAs) and time differences of arrival (TDoAs) at the RIS using different methods, resulting in non-Gaussian and Gaussian errors, respectively. Subsequently, to accommodate the non-Gaussian nature of AoAs errors and the Gaussian character of TDoA errors, we design a multiple weighted least squares (mWLS) algorithm to accurately localize MU. Besides, our research also includes a unique bias analysis for evaluating the performance of the proposed localization algorithm under both Gaussian and non-Gaussian errors. Simulation results demonstrate the effectiveness of both the proposed mWLS algorithm and the bias analysis methodology.