Tracking and Detection for the Target State Model
Aleksandar Zatezalo
Master of Science, March 1997
ABSTRACT
The following research is devoted to investigation and possible construction
of trackers, target identifiers and detectors in noisy environment, i.e. environment
in which it is hard to spot the object of interest and then follow its movement.
We divide the problems into two parts. First part is to calculate transitional
probabilities of target movement represented by Ito stochastic differential
equation. Second part is to simulate observations and calculate conditional
densities. For the first part of the problem, we consider simple one-dimensional
target state model.
Several numerical schemes are tried out on the Fokker-Planck equation which
corresponds to the model: multigrid method adapted to parabolic PDE, explicit
Euler scheme, the splitting-up and the alternating direction implicit method
(ADI) with several modifications and variations on their implementation. The
alternating direction implicit method shows the best performance, in particular
its CPU-time is much smaller than the CPU-time of other schemes. For the second
part of the problem, we give computer simulations of filtering for given transitional
probabilities of a target and discussion of results.
Research supported by the Minnesota Center for Industrial
Mathematics (MCIM)
