Localization and tracking of the ground moving target (GMT) are investigated based on measurements of TDOA
(time-difference of arrival) and AOA (angle of arrival) in which the measurement noises are assumed to be
uncorrelated and Gaussian distributed. An approximate MMSE algorithm is proposed via developing constrained
Kalman filtering based on the pseudo-measurement model in the existing literature that leads to a nonlinear
constraint imposed on the state vector for the GMT model. Randomization of the state vector suggests to replace
the hard constraint by its expectation. We first derive a solution to a similar constrained MMSE problem that
is used to extend the Kalman filtering to develop a linear recursive MMSE estimator subject to the nonlinear
constraint as mentioned earlier which is termed as constrained Kalman filtering.
Source localization is investigated based on noisy measurements of TDOA (time-difference of arrival) in which the
measurement noises are assumed to be Gauss distributed. The solution to the constrained WLS (weighted leastsquares)
is derived and applied to the source localization problem based on TDOAs. The proposed algorithm is
shown to be an approximate MLE (maximum likelihood estimation) algorithm under some mild condition. The
simulation results show that the proposed approximate MLE algorithm compares favorably with the existing
solution methods for source localization based on TDOA measurements.
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