Stochastic filtering of Hidden diffusion processes

Abstract

The problem of determining the state of a system from noisy measurements is called estimation, or filtering. It is of central importance in engineering, since state estimates are required in the monitoring, and for the control of systems. In this thesis we consider the filtering problem that the signal process $x_t$ is a 1-dimensional Markov diffusion process and the observation process is of the form $Y_t=x_t$$I_{R\setminus\Gamma}(x_t)$. That is, the signal process is unobservable when it moves behind an obstacle. The filtering equation is derived by using reverse-time diffusion process. Numerical simulations are also presented for the justification of the results.