Algebraic Solution for Unified Near-Field and Far-Field Direction-Finding Using TOA

This paper addresses the challenge of model mismatch in traditional time-of-arrival (TOA)-based localization methods for near-field or far-field source. We propose a unified TOA-based localization model that operates effectively in both scenarios. To estimate source direction, we introduce an algebraic closed-form solution, the two-step weighted least squares based on the modified polar representation (TSWLSMPR) method, which mitigates the issues associated with model mismatch. Additionally, we derive the Cramér-Rao Lower Bound (CRLB) as a benchmark to assess the performance of the proposed method. Simulation results demonstrate that the TSWLS-MPR method achieves the CRLB under varying levels of measurement noise, source distance, and source direction, confirming its accuracy and efficiency.