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

Alesi Augusto de Paula; Víctor Costa da Silva Campos; Guilherme Vianna Raffo; Bruno Otávio Soares Teixeira

doi:10.48011/asba.v2i1.1259

Alesi Augusto de Paula Universidade Federal de Minas Gerais
Víctor Costa da Silva Campos Universidade Federal de Minas Gerais
Guilherme Vianna Raffo Universidade Federal de Minas Gerais
Bruno Otávio Soares Teixeira Universidade Federal de Minas Gerais

DOI: https://doi.org/10.48011/asba.v2i1.1259

Keywords: Linear time-invariant systems, Gaussian random variables, H2 norm, Steady-state variance, Kalman filter

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.