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. For the second part of the problem, we give computer simulations of filtering for given transitional probabilities of a target and discussion of results.