Finite-Set Statistics Based Multiple Target Tacking

Multitarget tracking is a class of dynamic state estimation problems based on a sequence of measurement, in which the entity of interest is a finite set that is random in the number of elements as well as the values of individual elements. There are two types of multitarget tracking approaches. One is multitarget tracking based on data association, and other is multitarget tracking based on Finite Set Statistics (FISST). In the Random Finite Set (RFS) formulation for multitarget tracking, multitarget state and multitarget measurement are naturally modeled by random finite sets. So, the mathematical tools provided by FISST can be used to extend the Bayesian inference to multitarget tracking problem. Compared with the traditional association-based mutlitarget tracking approaches, the difficulties caused by data association are avoided. Though the multitarget tracking approach based on FISST was introduced a decade ago, and theoretically solid, the multitarget Bayes recursion proposed by R. Mahler is intractable in most practical applications and abandoned by many tracking researchers. The appearance of Probability Hypothesis Density (PHD) filter and its Gaussian Mixture implementation make things significant, and the gap between engineering and theory of FISST becomes trivial.In this dissertation, based on FISST for multitarget tracking, several problems of multitarget tracking are studied. The main contributions of the work are summarized as follows:1. The localization of multiple emitters from passive angle measurements is a widely investigated problem. Traditionally, the central problem of state estimation for multiple targets by multiple passive sensors is data association. Mathematically, the formulation of the data association problem leads to a generalization of S-dimensional (S-D) assignment problem. Unfortunately, the complexity of solving the S-D assignment problem for S≥3 is NP hard. Additionally, it can not give satisfactory results in a dense clutter environment. In this dissertation, the sequential PHD filter using passive sensors in two different manners for localization of multiple emitters is introduced. Simulation results show that the sequential PHD filter can achieve better performance and smaller computational complexity than the method based on S-D assignment programming in a dense clutter environment.2. The Cardinaized PHD (CPHD) filter differs from the PHD filter in that, in addition to the PHD, it propagates the entire probability distribution on target number. It provides more accurate estimate of target number than the PHD filter, and hence also of the states of the targets. This additional capability comes at the price of greater computational complexity. The computational cost of CPHD can be reduced by means of reducing the cardinality of measurement set. In this dissertation, a new method of reducing the computational cost of the Gaussian Mixture CPHD (GM-CPHD) filter is proposed by incorporating the elliptical gating. Computer simulation results show that the computational cost of the proposed method is reduced and that the tracking performance loss incurred is not significant.3. The intensity of birth RFS is assumed known beforehand when the PHD filter and CPHD filter are used to demonstrate their behavior in many literatures. In fact, the intensity of birth RFS is not known beforehand in many practical applications. Simulations show that new birth targets can not be detected by the GM-PHD filter without using the intensity of birth RFS. In this dissertation, a matrix reformulation of the GM-PHD filter is introduced, and a revised Gaussian component pruning method based on the matrix reformulation of the GM-PHD filter is proposed. Simulation results show that those new birth targets can be detected, if the revised Gaussian component method is employed by the GM-PHD filter without using the intensity of birth RFS. Furthermore, the performance loss incurred is not significant.4. The PHD filter is a more tractable alternative to the optimal multitarget Bayes recursion. However, the generalization of the PHD filter to multisensor case is too complicated to be of practical use. A sequential PHD filter proposed by Mahler can only be used when all those targets lie in the intersection part of the surveillance regions of those sensors. In this dissertation, a new multisensor GM-PHD filter is constructed based on the matrix reformulation. Simulation results show it can be used in some applications when the sequential GM-PHD filter fails. In addition, it outperforms the sequential GM-PHD filter when those sensors have poor detection probabilities, even though the surveillance regions of those sensors are same.