A Kalman Filtering Approach for Systems Subject to Parametric Modeling Uncertainties

摘要

The paper presents a Kalman type filtering problem for linear systems with parametric uncertainties. A stochastic model with state dependent noise both in the state and in the output equations is used to represent the system with uncertain parameters. The solution of the filtering problem is a Kalman type filter whose gain is determined by solving the H_2 optimization problem resulting from the coupling between the filter and the stochastic system with multiplicative noise. It is proved that this optimal gain results by solving a trace minimization problem with constraints expressed in terms of a system of matrix inequalities. The theoretical developments are illustrated by a case study aiming to estimate the states of the pitch dynamics of a space launch vehicle.