Introduction

Abstract

One of the most significant ideas to emerge in the area of systems and control theory is the Kalman Filter. Given a signal model that consists of a linear dynamical system driven by stochastic white noise processes, the Kalman Filter provides a method for constructing an optimal estimate of the system state. Thus, the Kalman Filter provides an optimal way of extracting a signal from noise by exploiting a state space signal model. A key feature of the Kalman Filter is that it involves finite dimensional recursive computations, which are straightforward to implement on a digital computer. The Kalman Filter can be applied to state estimation problems defined over a finite or infinite time interval. It is applicable for the case in which the signal model is a linear but possibly time-varying linear system. Also, an approximate version of the Kalman Filter referred to as the “Extended Kalman Filter” can be applied in the case of a nonlinear signal model; e.g., see [2].