A Diffusion-Based Distributed Time Difference Of Arrival Source Positioning

We propose a distributed time difference of arrival method for estimating a source using a multi-agent network. By exchanging information with the agents in its local neighborhood, each agent estimates the source position by minimizing a local cost function which is obtained by linearizing the local time difference of arrival measurements. The local minimization is performed using the diffusion approach where at the first step each agent determines a local estimate by combining the weighted source position estimates received from its neighbors, and then adapt the local gradient of its local cost function. We propose to use adaptive weights which are time-varying and depends on the fit errors of each agent in the network. Numerical results and real data experiments demonstrate that such an approach produces close position estimates compared to the centralized method and the theoretical Cramer-Rao lower bounds.