Improved SOCP Relaxation for SRI-Unknown Emitter Localization Using a Moving Receiver

Employing a single moving receiver for emitter localization offers numerous advantages, including low cost, ease of implementation, and elimination of clock synchronization. A novel localization method is proposed for a stationary emitter with an unknown Signal Repetition Interval (SRI). We first construct a localization model based on time-of-arrival, taking into account potential missed detections, and then derive the Cramér-Rao Lower Bound. Given that the established model is non-convex, we reformulate the problem into a convex form and convert it to Second-order Cone Programming (SOCP) format. However, the SOCP formulation encounters convex hull issues, which may hinder far-field localization. To address this challenge, we introduce a penalty term to alleviate the convex hull problem for the first time. Simulation results demonstrate the effectiveness of the proposed approach in comparison to existing methods, and the validity of the penalty term is also confirmed.