Nonlinear Estimation and Condition Monitoring: State-Space Approach

Abstract

This second chapter on nonlinear filteringNonlinear filteringinvolves systems that use state-space models to represent the linear subsystems. The main estimation problem considered is the nonlinear minimum variance filtering problem. However, there is also an introduction to other linear and nonlinear estimation problems. The Kalman filter was used in many of the control solutions considered earlier and this is described in more detail. The algorithm for the computation of the Kalman gains is presented. The extended Kalman filterExtended Kalman Filter (EKF)for systems represented by nonlinear state-equation-based models is also described. A brief introduction to alternative nonlinear estimators is included beginning with particle filters and covering the unscented transformation and Unscented Kalman Filter. The nonlinear minimum variance filtering problem is unusual because it includes a possible nonlinear communications channel. To illustrate applications of this filter for state models the automotive air--fuel ratio estimation problem is again considered. A final example illustrates its use in condition monitoring, fault monitoring and detection problems. The main learning point is the natural structure the problem has for such applications, where the signal to be estimated lies deep within a system that includes uncertainties and nonlinearities before the measurements are obtained.