Iterative and Algebraic Algorithms for the Computation of the Steady State Kalman Filter Gain

The Kalman filter gain arises in linear estimation and is associated with linear systems. The gain is a matrix through which the estimation and the prediction of the state as well as the corresponding estimation and prediction error covariance matrices are computed. For time invariant and asymptotically stable systems, there exists a steady state value of the Kalman filter gain. The steady state Kalman filter gain is usually derived via the steady state prediction error covariance by first solving the corresponding Riccati equation. In this paper, we present iterative per-step and doubling algorithms as well as an algebraic algorithm for the steady state Kalman filter gain computation. These algorithms hold under conditions concerning the system parameters. The advantage of these algorithms is the autonomous computation of the steady state Kalman filter gain.