Robust State Estimations in Controlled ARMA Processes with the Non-Gaussian Noises: Applications to the Delayed Dynamics

IFAC-PapersOnLine. 2021. Vol. 50. No. 20. P. 334–339.

Azhmyakov V., Pereira Arango J., Bonilla M., Juarez del Torro R., Pickl S.

This paper deals with a novel theoretic approach to the robust state estimations
in discrete-time dynamic systems with the non-Gaussian correlated stochastic noises. The
methodology we develop is based on the so-called ”worst case” robust Kalman Filter (KF)
approach proposed in [2,3]. We are interested in the robust state estimation for the controlled
ARMA models under assumption of the colored noises. Since an ARMA model involves the
correlated noises in the equivalent Linear Model (LM) representation, the resulting dynamic
system also includes the correlated stochastic variables. These two crucial properties of the
ARMA models under consideration imply the impossibility of application of the classic KF-type
state estimations. We use the modified ”instrumental variable” method and derive an auxiliary
LM with the uncorrelated noises. Application of the robust KF to this auxiliary LM makes
it possible to derive a guaranteed state estimation in the initially given ARMA model. The
proposed non-standard KF based state estimations are finally applied to the linear stochastic
dynamic systems with the time delays. 

Keywords: applied mathematics, Systems and Control Engineering