Modified spectral method for optimal estimation in linear continuous-time stochastic systems

The spectral method to solve estimation problems for linear continuous-time stochastic systems with polynomial measurements is presented. It is based on both the spectral form of mathematical description (the representation of deterministic functions and random processes by orthogonal series) and the particle filter. The main goal of this work is to implement the continuous-time particle filter without a time discretization. The proposed spectral method provides the possibility to solve estimation problems such as filtering, smoothing and prediction. (paper)