OBSERVER/KALMAN FILTER IDENTIFICATION BY A KALMAN FILTER OF A KALMAN FILTER (OKID2)

The original Observer/Kalman filter identification (OKID) algorithm identifies a state-space model and an associated steady-state Kalman filter gain from input-output data corrupted by process and measurement noises with unknown covariances. An extension of OKID uses the estimated Kalman filter residual to convert the stochastic system identification problem into a deterministic one, then identifies a state-space model and the steady-state Kalman filter gain directly. Since the estimation of the Kalman filter residual itself is not exact, a second Kalman filter of the first Kalman filter can be employed. This paper describes a new algorithm, OKID2 that identifies a system state-space model and the steady-state Kalman filter gains directly, optimally, and simultaneously.