An improved constrained nonlinear state estimator for target tracking

In a series of earlier papers, the first author developed an estimator which generates an optimal sequential estimate of the state of a linear discrete-time dynamic system in which the state is subject to an instantaneous constraint. In the third paper of the series, an extended estimator, based on the optimal linear estimator, was developed for the constrained nonlinear estimation problem. In this paper, the extended nonlinear estimator is revised. One of the critical steps in the development of an extended estimator is the quasi-linearization step. In this step, the terms in the Taylor series expansion which have been evaluated at some nominal state trajectory are instead evaluated at the most recent 'best' available state estimate. In developing the estimator, the point in the development at which the quasi-linearization takes place is not fixed. In the earlier paper, the quasi-linearization is performed about midway through the overall development. In this paper, the quasi-linearization is taken at the last possible point in the development. The result is an improved version of the extended constrained nonlinear sequential estimator.