Estimation of uncertain ARX models with ellipsoidal parameter variability

Traditional parameter estimation techniques deliver estimates for a given set of parameters, but do not in general provide an estimate of the parameter variability for systems with time-varying parameters. Accurate knowledge of the parameter variability becomes crucial in many contexts, e.g. robust control techniques. This paper proposes a method for joint parameter and variability estimation (PVE) which is based on optimizing a convex cost function subject to a linear matrix inequality (LMI) constraint. The method is described and compared to the Least Squares (LSQ) method for a linear AutoRegressive eXogenous (ARX) model with ellipsoidal parameter variability. The two techniques have been tested numerically in a simulation scenario. Simulation results indicate that PVE is more precise at characterizing the variability of estimated parameters.