Polynomial Filtering With Uncertain Observations in Stochastic Linear Systems
R. Caballero‐Águila, A. Hermoso‐Carazo, J. Linares‐Pérez · International Journal of Modelling and Simulation · 2003
In this article we consider the least mean-squared error polynomial estimation problem in systems with uncertain observations. For this purpose we define an augmented system such that the optimal linear estimator of the augmented state based on the augmented observations provides the optimal polynomial estimator for the state of the original system. This augmented system satisfies the necessary conditions to apply the Nahi algorithm, which provides the desired optimal linear filter. Stationary systems are also treated, and we show that the augmented system is asymptotically stationary provided that the original system is asymptotically stable. So, by applying the steady-state form of the Nahi algorithm, we obtain the steady-state polynomial filter of the original state.