Parallel optimal Kalman filtering for stochastic systems in multimodeling form

In this paper we show how to completely and exactly decompose the optimal Kalman filter of stochastic systems in multimodeling form in terms of one pure-slow and two pure-fast, reduced-order, independent, Kalman filters. The reduced-order Kalman filters are all driven by the system measurements. This leads to a parallel Kalman filtering scheme and removes ill-conditioning of the original full-order singularly perturbed Kalman filter. The results obtained are valid for steady state. In that direction, the corresponding algebraic filter Riccati equation is completely decoupled and solved in terms of one pure-slow and two pure fast, reduced-order, independent, algebraic Riccati equations. A nonsingular stare transformation that exactly relates the state variables in the original and new coordinates tilt which the required decomposition is achieved) is also established The eighth order model of a passenger cur under road disturbances is used to demonstrate efficiency of the proposed filtering technique.