A Joint Localization and Clock Bias Estimation 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 CramerRao 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. Keywords—Clock bias estimation, localization, recursive nonlinear least squares, synchronization, time of arrival.