Extended Kalman Filter and System Identification

Abstract

The Kalman filtering process has been designed to estimate the state vector in a linear model. If the model turns out to be nonlinear, a linearization procedure is usually performed in deriving the filtering equations. We will consider a real-time linear Taylor approximation of the system function at the previous state estimate and that of the observation function at the corresponding predicted position. The Kalman filter so obtained will be called the extended Kalman filter. This idea to handle a nonlinear model is quite natural, and the filtering procedure is fairly simple and efficient. Furthermore, it has found many important real-time applications. One such application is adaptive system identification which we will also discuss briefly in this chapter. Finally, by improving the linearization procedure of the extended Kalman filtering algorithm, we will introduce a modified extended Kalman filtering scheme which has a parallel computational structure. We then give two numerical examples to demonstrate the advantage of the modified Kalman filter over the standard one in both state estimation and system parameter identification.