Numerical-analytical method for analyzing the behavior of a dynamical system using incorrect observations without state space extension

Various continuous linear functionals of integral curves of a dynamical system are optimally estimated using incorrect additive observations of this system. A numerical-analytical method for analyzing the behavior of the system is developed in the case when observations contain not only counts of an integral curve and fluctuation noise, but also counts of singular disturbance. The method yields optimal unbiased and invariant (with respect to the given noise) estimates without using conventional state space extension. The random and systematic errors are analyzed, and illustrative examples are given.