Optimal Errors–in–variables Filtering in the Mimo Case

Abstract

The Errors-in-Variables (EIV) stochastic environment constitutes a superset of most common stochastic environments considered, for instance, in Kalman filtering or in equation-error identification where the process input is assumed as noise-free. Errorsin-variables models assume, on the contrary, the presence of unknown additive noise also on the inputs; the associated filtering procedures concern thus the optimal (minimal variance) estimation not only of the system state and output but also of the input. Optimal EIV filtering has been formulated and solved only recently (Guidorzi et al., 2003) making reference to SISO models; this paper extends the efficient algorithm proposed in (Diversi et al., 2003a), based on the Cholesky factorization, to the more general multivariable case.