A Fuzzy-Kalman filtering strategy for state estimation

Abstract

This thesis considers the combination of Fuzzy logic and Kalman Filtering that have traditionally been considered to be radically different. The former is considered heuristic and the latter statistical. In this thesis a philosophical justification for their combination is presented. Kalman Filtering is revised to enable the incorporation of fuzzy logic in its formulation. This formulation is subsequently referred to as the Revised-Kalman Filter. Heuristic membership functions are then used in the Revised-Kalman Filter to substitute for the system and measurement covariance matrices to form a fuzzy rendition of the Kalman Filter. The Fuzzy Kalman Filter formulation is further revised according to a concept referred to as the “Parallel Distributed Compensation” to allow for further heuristic adjustment of the corrective gain. This formulation is referred to as the Parallel Distributed Compensated-Fuzzy Kalman Filter. Simulated implementations of the above filters reveal that a tuned Kalman Filter provides the best performance. However, if conditions change, the Kalman filter’s performance degrades and a better performance is obtained from the two versions of the Fuzzy Kalman Filters.