Bayesian Filtering for Dynamic Systems with Applications to Tracking

摘要

This M.Sc. thesis intends to evaluate various algorithms based on Bayesian statistical\ntheory and validates with both synthetic data as well as experimental\ndata. The focus is given in comparing the performance of new kind of sequential\nMonte Carlo filter, called cost reference particle filter, with other Kalman based\nfilters as well as the standard particle filter.\nDifferent filtering algorithms based on Kalman filters and those based on sequential\nMonte Carlo technique are implemented in Matlab. For all linear Gaussian\nsystem models, Kalman filter gives the optimal solution. Hence only the\ncases which do not have linear-Gaussian probabilistic model are analyzed in this\nthesis. The results of various simulations show that, for those non-linear system\nmodels whose probability model can fairly be assumed Gaussian, either Kalman\nlike filters or the sequential Monte Carlo based particle filters can be used. The\nchoice among these filters depends upon various factors such as degree of nonlinearity,\norder of system state, required accuracy, etc. There is always a tradeoff\nbetween the required accuracy and the computational cost. It is found that whenever\nthe probabilistic model of the system cannot be approximated as Gaussian,\nwhich is the case in many real world applications like Econometrics, Genetics,\netc., the above discussed statistical reference filters degrade in performance.\nTo tackle with this problem, the recently proposed cost reference particle filter\nis implemented and tested in scenarios where the system model is not Gaussian.\nThe new filter shows good robustness in such scenarios as it does not make any\nassumption of probabilistic model.\nThe thesis work also includes implementation of the above discussed prediction\nalgorithms into a real world application, where location of a moving robot\nis tracked using measurements from wireless sensor networks. The flexibility of\nthe cost reference particle filter to adapt to specific applications is explored and\nis found to perform better than the other filters in tracking of the robot.\nThe results obtained from various experiments show that cost reference particle\nfilter is the best choice whenever there is high uncertainty of the probabilistic\nmodel and when these models are not Gaussian. It can also be concluded that,contrary to the general perception, the estimation techniques based on ad-hoc\nreferences can actually be more efficient than those based on the usual statistical\nreference.