OPTIMAL NONLINEAR ESTIMATION OF LINEAR STOCHASTIC-SYSTEMS

This paper presents a new nonlinear method of simultaneous parameter a nd state estimation called pseudo-linear identification (PLID), for st ochastic linear time-invariant discrete-time systems. No assumptions a re required about pole or zero locations; nor about relative degree, e xcept that the system transfer function must be strictly proper. Under standard gaussian assumptions, for completely controllable and observ able systems, it is proved that PLID is the minimum mean-square-error estimator of the states and model parameters, conditioned on the input and output measurements. It is also proved, given persistent excitati on, that the parameter estimates converge a.e. to the true parameter v alues. All results have been extended to the multiple-input, multiple- output case, but the single-input, single-output case is presented her e to simplify notation.