Optimal filtering for Gauss—Markov noise

Abstract

The optimal continuous-filtering problem for the caso of linear dynamics, linear measurements, and gaussian whito disturbance and measurement noise has been Solved by Kalman and Buey. In this study, their rosults are generalized for the caso where measurement noise is a Gauss—Markov process, but without the technique of state augmentation, as has already been done. Proof is presented that the optimal continuous-filtering problem can be solved by simply replacing the observation vector with a derived observation vector and an initial condition. When the derived observation vector is used, coloured noise is eliminated and only the standard Kalman filter problem, easily solvable, remains.