Estimation & Identification Of Bilinear Systems

In this paper, the state estimation and parameter identification problems for a class of continuous bilinear systems is studied. It is shown that the optimal filter, even for the scalar case, is of infinite dimension and an approximate solution is proposed. The solution method involves the use of a conditional best estimate of the state in the multi plicative term rather than the actual state. The Parameter identification scheme is based on the use of the proposed filter and a maximum likelihood approach. The filter provides the mean and variance information for the likelihood functional which in turn is maximized with respect to the para meters for a given set of observations. In order to simulate the proposed filter on a digital computer a discrete version of the original continuous model is developed, employing the closed form solution to the original Ito differential equation. This closed form solution is not available in all cases and we center our discussion around the scalar case. Computations with simulated data are presented and the effect of sampling time, multiplicative noise, observation noise, and the control are discussed.