Disturbance estimator using sliding mode for discrete Kalman filter

Abstract

The optimality of Kalman filter is guaranteed only when the model is exactly valid. If there exist unmodeled dynamics or external disturbances the optimality is broken and the Kalman filter is no longer the best. In this thesis, we consider the stochastic filtering problem when disturbance or unknown external input exists. The complete solution to this problem can be divided up to 3 distinct actions. First, estimation action of Kalman filter, second the detection of disturbance within noisy measurements, finally the collection the error from external disturbances, or change its structure to compensate the errors. In this thesis, we proposed a novel detection algorithm for disturbance using the difference of calculated expectation error covariance and the process from measurements. The algorithm has a simple structure and doesn``t have complex calculations because it uses normal components of the Kalman filter update algorithm. The normalized designed test parameter make it possible to use the standard chi-square table with fewer numbers of samples than other testing algorithms such as auto-correlation test. The detection algorithm is valid even before the Kalman filter reaches steady state. Next, we suggest alternative method to solve disturbance estimation problem, which is to convertit to tracking one. Using the relation of time update and measurement update in Kalman filter, the disturbance estimation problem is solved such as calculating tracking input in conventional tracking problems. This idea gives simple and effective way to calculate external disturbance by using filter update parameters. In this thesis, the discrete sliding mode is used to realize this idea and we suggest improved discrete sliding mode algorithm by introducing the prediction parameter. The stability of the suggested algorithm is proved. Besides numerical simulations, the real experiments of filtering problem of Global Positioning System (GPS) are executed to verify proposed metho...