Singular Kalman filtering: New aspects based on an alternative system theory
R. Arnošt, Pavel Žampa · WSEAS TRANSACTIONS on SYSTEMS archive · 2004
This paper is based on an alternative approach to system theory and deals with optimal filters for continuous linear dynamic systems with measurements disturbed by a ”colored” noise or a ”white” noise vector with a singular covariance matrix. It is shown that the optimal filter proposed in this paper is a slight modification of the Kalman-Bucy filter which can generally contain integrators as well as (backward) differentiators. The classical formulation was, however, reformulated in order to obtain a tractable mathematical interpretation of stochastic differential equations describing given processes and random errors.