This M.Sc. thesis intends to evaluate various algorithms based on Bayesian statistical
theory and validates with both synthetic data as well as experimental
data. The focus is given in comparing the performance of new kind of sequential
Monte Carlo filter, called cost reference particle filter, with other Kalman based
filters as well as the standard particle filter.
Different filtering algorithms based on Kalman filters and those based on sequential
Monte Carlo technique are implemented in Matlab. For all linear Gaussian
system models, Kalman filter gives the optimal solution. Hence only the
cases which do not have linear-Gaussian probabilistic model are analyzed in this
thesis. The results of various simulations show that, for those non-linear system
models whose probability model can fairly be assumed Gaussian, either Kalman
like filters or the sequential Monte Carlo based particle filters can be used. The
choice among these filters depends upon various factors such as degree of nonlinearity,
order of system state, required accuracy, etc. There is always a tradeoff
between the required accuracy and the computational cost. It is found that whenever
the probabilistic model of the system cannot be approximated as Gaussian,
which is the case in many real world applications like Econometrics, Genetics,
etc., the above discussed statistical reference filters degrade in performance.
To tackle with this problem, the recently proposed cost reference particle filter
is implemented and tested in scenarios where the system model is not Gaussian.
The new filter shows good robustness in such scenarios as it does not make any
assumption of probabilistic model.
The thesis work also includes implementation of the above discussed prediction
algorithms into a real world application, where location of a moving robot
is tracked using measurements from wireless sensor networks. The flexibility of
the cost reference particle filter to adapt to specific applications is explored and
is found to perform better than the other filters in tracking of the robot.
The results obtained from various experiments show that cost reference particle
filter is the best choice whenever there is high uncertainty of the probabilistic
model 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
references can actually be more efficient than those based on the usual statistical
reference.
