Optimal errors-in-variables filtering in the MIMO case

The Errors-in-Variables (EIV) stochastic environment constitutes a superset of most common stochasticenvironments considered, for instance, in Kalman filtering or in equation-error identification wherethe process input is assumed as noise-free. Errors-in-variables models assume, on the contrary, thepresence of unknown additive noise also on the inputs; the associated filtering procedures concern thusthe 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) makingreference to SISO models; this paper extends the efficient algorithm proposed in (Diversi et al., 2003),based on the Cholesky factorization, to the more general multivariable case.