  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. Simulations show
that the mean-squared error (MSE) of the proposed method is much smaller than
that of existing methods with the same antenna scheme, and approaches the
Cramer-Rao lower bound (CRLB) closely.
