Novel Iterative Approach for Time-of-Arrivals-Based Localization With Maximum Likelihood Estimation

In this letter, the problem of localizing in a wireless environment with non-line-of-sight (NLoS) propagation without strict time synchronization is being considered. This problem utilizes maximum likelihood (ML) estimation based on time-of-arrival (TOA) measurements. However, the original form of this problem is not convex and cannot be directly solved using standard convex optimization techniques. To overcome this issue, we decompose the original non-convex localization problem into two convex sub-problems: quadratic programming (QP) and linear regression (LR). The QP sub-problem is formulated by converting the numerator of ML expression into the quadratic form and regarding the nonlinear denominator as a weight. In contrast, the LR sub-problem is built using the nonlinear relation among the defined variables. Through a dynamic adjustment of the objective function in the QP sub-problem, we develop an iterative algorithm to solve the original localization problem. The simulation results demonstrate that the proposed algorithm achieves the same localization accuracy with reduced computational complexity compared to the ML estimation-based localization.