Efficient local optimisation‐based approach for non‐convex and non‐smooth source localisation problems

Abstract

This study proposes a novel approach to solve the source localisation problem with noisy range measurements. Since the objective function of the range-based least square problem is non-convex and non-smooth, it is challenging to achieve an accurate estimation. Unlike previous methods that took non-convexity property of the objective function into account, this approach addresses the problem considering the non-smoothness property of the objective function. The problem is solved by a two-stage local optimisation technique which is based on a smooth non-convex approximation of the original objective function. First, the least square method is utilised to obtain a coarse estimation of the problem. Then, the estimation is refined by the trust region method which converges quadratically. Simulation results are presented to show that the proposed approach outperforms other existing methods in terms of the mean squared localisation error and convergence speed.