A dual-based first-order algorithm for ToA asynchronous localization and synchronization

Joint ToA source localization and synchronization determines the location and time offset of a radiating source using time-of-arrival measurements collected from a time-synchronized array of sensors. Various approaches have been proposed to address this non-convex and non-smooth optimization problem, which usually transform the problem by applying convex relaxations or smooth approximations. In this paper, we focus on the original joint problem and show that it can be expressed as a sum of a quadratic function with multiple non-smooth functions. This type of problems cannot be solved using traditional proximal-based methods, and we develop a tailored dual-based first-order algorithm. We analyze the proposed method, and prove its convergence to critical points of the original problem under mild assumptions. Experimental results showcase advantages of the method in terms of convergence, RMSE, bias, and complexity.