Pseudo-Linear Identification: Optimal Joint Parameter and State Estimation of Linear Stochastic MIMO Systems

This paper presents a new method of joint parameter and state estimation called pseudo-linear identification (PLID), extending a method given by Salut et.al. (1) to the more general case where the system inputs and output measurements are corrupted by noise. PLID can be applied to linear, strictly proper, completely observable, completely controllable, discrete-time MIMO systems with known structure and unknown parameters, without assumptions about pole and zero locations. It is proved, under standard gaussian assumptions, that for time-invariant systems PLID is the optimal estimator (in the mean-square error sense) of the states and parameters conditioned on the input and output measurements; and, under a reasonable criterion for persistency of excitation, that the PLID parameter estimates converge a.e. to the true parameter values.