Abstract

Systems containing uncertainty are traditionally analyzed with probabilistic methods. However, for non-linear, non-Gaussian systems solutions can sometimes be very difficult to obtain. The focus of this work is to determine if in such cases fuzzy dynamic system models may provide an alternative approach that more easily leads us to a good solution. In this paper, we present a fuzzy estimator whose system model is a fuzzy dynamic system. We show that for the linear, Gaussian case the fuzzy estimator produces the same result as the Kalman filter. More importantly, we show that the fuzzy estimator can succeed for some non-Gaussian, nonlinear systems. Finally, we illustrate the application of the fuzzy estimator on a non-linear, non-Gaussian, time-varying rocket launch problem where we show that it performs better than the extended Kalman filter. From a broad perspective this paper essentially shows how to build on Zadeh's seminal ideas in fuzzy sets, logic, and systems and use Kalman's seminal ideas on optimal estimators to construct a novel fuzzy estimator for non-linear estimation problems. While this seems to reconcile some of the fundamental ideas of Zadeh and Kalman it is unfortunate that the fuzzy estimator can be very computationally complex to implement for practical applications.

Author Keywords: Fuzzy dynamic systems; State estimation; Probability theory and statistics; Engineering