Filtering for linear stochastic systems with small measurement noise

In this paper we present a method which produces complete decomposition of the optimal global Kalman filter for linear stochastic systems with small measurement noise into exact pure-slow and pure-fast reduced-order optimal filters both driven by the system measurements. The method is based on the exact decomposition of the global small measurement noise algebraic Riccati equation into exact pure-slow and pure-fast algebraic Riccati equations. An example is included in order to demonstrate the proposed method.