In target tracking problem, two important considerations for estimating the position of the target are firstly the optimal formation of sensors that receive the target information and secondly the estimation method based on the received information. In this thesis we studied target localization problem based on the time difference of arrival (TDOA) data. This thesis propose two methods to improve the performance of the target tracking problem.
In the first part, we discussed the optimal sensor formation problem in terms of Fisher information. The estimators of the target location expressed in terms of the spherical coordinates are found to be uncorrelated when the sensors are arranged in a concentric ring formation. The proposed optimal formation of sensors is in the concentric ring formation and is shown to change in accordance with sensors' angular positions with respect to the line-of-sight vector from the reference sensor to the target.
In the second part, we present a estimation method for the linear state space model with an unknown measurement matrix using a Bayesian method. We explored availability of the Bayes method for parameter estimation with no constraints on the parameter space and found that the estimation for the state vector is acceptable as long as the priors are not vague on both the state and the measurement matrix. We also investigated the model where the measurement matrix is contaminated with noise and found that the estimates for the state vector were more accurate than those by the methods in literature.