Parametric and posterior Cramér-Rao lower bounds for extended target tracking in a random matrix framework

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2015
Sarıtaş, Elif
This thesis presents the parametric and posterior Cramér-Rao lower bounds (CRLB) for extended target tracking (ETT) in a random matrix framework. ETT is an area of target tracking in which the common assumption of point targets does not hold due to the recent improvements in sensor technology. With the increased sensor capability, targets can generate more than one measurement in a single scan depending on their size. Therefore, not only the target’s kinematical state but also its extension can be estimated. Although there are different methods in literature that deals with ETT, random matrix based ETT algorithms are the subject of this thesis. In this Bayesian approach, the extents of the targets are assumed to be ellipsoidal and they are represented with positive definite matrices which are called as the extent states. The kinematic and extent states are estimated recursively in a Bayesian framework. When these estimators are applied, their performances come into question. Cramér-Rao Lower Bound (CRLB) which gives a lower bound on the achievable mean-square-error (MSE) of an unbiased estimator is a commonly used method to evaluate estimator performance in estimation theory. CRLB is the inverse of the Fisher Information which is a measure of information that a measured random variable carries about the parameter to be estimated; and in this study, it is applied for ETT algorithms. First, parametric and posterior CRLBs for ETT in a random matrix framework are obtained. Formulae for CRLBs for both kinematic and extent states are computed by using both analytical and numerical tools, and then compared with the performance of a state-of-the-art random matrix based ETT algorithm.
Citation Formats
E. Sarıtaş, “Parametric and posterior Cramér-Rao lower bounds for extended target tracking in a random matrix framework,” M.S. - Master of Science, Middle East Technical University, 2015.