Analysis and Algorithm for Multi-IRS Collaborative Localization via Hybrid Time–Angle Estimation

This paper proposes a novel multiple intelligent reflecting surfaces (IRSs) collaborative hybrid localization system, which involves deploying multiple IRSs near the target area and achieving target localization through joint time delay and angle estimation. Specifically, echo signals from all reflective elements are received by each sensor and jointly processed to estimate the time delay and angle parameters. Based on the above model, we derive the Fisher information matrix (FIM) for cascaded delay, angle of arrival (AOA), and angle of departure (AOD) estimation in semi-passive models, along with the corresponding Cramér-Rao bound (CRB). To achieve precise estimation close to the CRB, we design efficient algorithms for angle and location estimation. For angle estimation, reflective signals are categorized into three cases based on their rank, with different signal preprocessing. By constructing an atomic norm set and minimizing the atomic norm, the joint angle estimation problem is transformed into a convex optimization problem, and low-complexity estimation of multiple AOA and AOD pairs is achieved using the alternating direction method of multipliers (ADMM). For location estimation, we propose a three-stage localization algorithm that combines weighted least squares, total least squares, and quadratic correction to handle errors in the coefficient matrix and observation vector, thus improving accuracy. Numerical simulations demonstrate that the proposed collaborative system achieves an accuracy gain of approximately 7 dB compared to non-collaborative benchmarks, and the proposed estimation algorithms attain a mean squared error (MSE) within 4 dB of the CRB, verifying their robustness in low signal-to-noise ratio (SNR) conditions.