A discrete-time Kalman filtering method for launch vehicle under parametric modelling uncertainty

The paper presents a Kalman filtering problem for discrete–time linear systems with parametric uncertainties. A stochastic model with multiplicative 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 which gain is determined by solving the H2 optimization problem for the resulting system obtained by coupling the filter with the stochastic system. It is proved that the optimal gain of the filter may be computed by solving a trace minimization problem with constraints expressed in terms of a system of matrix inequalities. The proposed filtering approach is illustrated by a case study aiming to estimate the states of the pitch dynamics of a space launch vehicle in its center of mass.