The Stability of the Kalman Filter for Systems with Colored Observation Noises

The stability of the Kalman filter for the stochastic time varying linear systems with colored observation noises has been treated. In this paper, we first introduce a suitable stochastic observability (or excitation) condition to guarantee both the L
_r
- and exponential stability of random Riccati equations. Then we give a sufficient condition to ensure the stability of Kalman filter.