Optimal state estimation of singular stochastic systems

This paper deals with optimal state estimation problem of both singular and especially non-singular stochastic causal systems solution of which is based on recently submitted new approach to system theory. The solution to so important a task is well known as the Kalman filtering. However, some surprisingly serious problems arise in case of stochastic system with singular uncertainty in the continuous-time domain. The presented solution transforms, according to the new approach to system theory, the original problem into the discrete-time domain whereupon the optimal discrete-time Kalman filter can be designed. In regard of the given continuous-time problem, the obtained estimator is to be transformed from the discrete-time to the continuous-time domain. Such a transformation procedure is called the continualisation process. The solution leads to utilization of backward derivatives.