  In a time division broadcast positioning system (TDBPS), a user device (UD)
determines its position by obtaining sequential time-of-arrival (TOA) or
pseudorange measurements from signals broadcast by multiple synchronized base
stations (BSs). The existing localization method using sequential pseudorange
measurements and a linear clock drift model for the TDPBS, namely LSPM-D, does
not compensate the position displacement caused by the UD movement and will
result in position error. In this paper, depending on the knowledge of the UD
velocity, we develop a set of optimal localization methods for different cases.
First, for known UD velocity, we develop the optimal localization method,
namely LSPM-KVD, to compensate the movement-caused position error. We show that
the LSPM-D is a special case of the LSPM-KVD when the UD is stationary with
zero velocity. Second, for the case with unknown UD velocity, we develop a
maximum likelihood (ML) method to jointly estimate the UD position and
velocity, namely LSPM-UVD. Third, in the case that we have prior distribution
information of the UD velocity, we present a maximum a posteriori (MAP)
estimator for localization, namely LSPM-PVD. We derive the Cramer-Rao lower
bound (CRLB) for all three estimators and analyze their localization error
performance. We show that the position error of the LSPM-KVD increases as the
assumed known velocity deviates from the true value. As expected, the LSPM-KVD
has the smallest position error while the LSPM-PVD and the LSPM-UVD are more
robust when the prior knowledge of the UD velocity is limited. Numerical
results verify the theoretical analysis on the optimality and the positioning
accuracy of the proposed methods.
