A joint localization and synchronization technique using time of arrival at multiple antenna receivers

In this work, a system scheme is proposed for tracking a radio emitting target moving in two-dimensional space. The localization is based on the use of biased time-of-arrival (TOA) measurements obtained at two asynchronous receivers, each equipped with two closely spaced antennas. By exploiting the multi-antenna configuration and using all the TOA measurements up to current time step, the relative clock bias at each receiver and the target position are jointly estimated by solving a nonlinear least-squares (NLS) problem. To this end, a novel time recursive algorithm is proposed which fully takes advantage of the problem structure to achieve computational efficiency while using orthogonal transformations to ensure numerical reliability. The Cramer-Rao lower bound (CRLB) is also derived as a lower bound on the error in estimating the position and biases. Simulation results show that the mean-squared error (MSE) of the proposed method approaches the CRLB closely.