| The symmetric measurement equation (SME) filter for track maintenance in multiple target tracking is extended to the general case when there are an arbitrary unknown number of false and missing position measurements in the measurement set at any time point. The key idea of the developed algorithm in this thesis is to combine all the feasible innovation vectors that pass a thresholding operation defined in the range space of a symmetric function to carry out target state estimation at a time point. It is shown that, via this algorithm, the target/measurement association problem is avoided, and, in addition, there is no need to identify which target measurements may correspond to false returns or which target measurements may be missing. As a result, the new extended SME filter algorithm requires the consideration of a significantly smaller number of hypotheses in comparison to other existing approaches to multiple target tracking, and there is a reduction in the computational complexity of the multiple target tracking problem. Various analytical properties of the extended SME filter algorithm are studied and the performances of the filter are tested via computer simulations. The performance evaluations of the extended SME filter include a comparison with the joint probabilistic data association (JPDA) filter which is one of the most successful approaches in multiple target tracking to date. |
