Novel Gaussian State Estimator based on H2 Norm and Steady-State Variance

Abstract

This paper proposes a novel state estimator for discrete-time linear systems with Gaussian noise. The proposed algorithm is a fixed-gain filter, whose observer structure is more general than Kalman one for linear time-invariant systems. Therefore, the steady-state variance of the estimation error is minimized. For white noise stochastic processes, this performance criterion is reduced to the square H2 norm of a given linear time-invariant system. Then, the proposed algorithm is called observer H2 filter (OH2F). This is the standard Wiener-Hopf or Kalman-Bucy filtering problem. As the Kalman predictor and Kalman filter are well-known solutions for such a problem, they are revisited.