Optimization and Systems Theory Seminar
Friday, Sept. 24, 1999, 13.00-14.00, Room 3721, Lindstedtsv. 25

Dr. Zeljko Djurovic
School of Electrical Engineering
University of Belgrade
E-mail: djurovic@kiklop.etf.bg.ac.yu

Robust Kalman filtering

The distribution of noise arising in application deviates frequently from assumed Gaussian model, often being characterized by heavier tails generating the outliers. Since in the presence of outliers, the performances of Kalman filter can be very poor, there appears to be considerable motivation for considering filters which are robustified to perform fairly well in non-Gaussian environment, especially in the presence of outliers. A particular approach based on a QQ-plot will be considered. In available literature, QQ-plot has only been used in order to verify the assumption about the measurement noise distribution. It will be shown that much more information is contained in this plot and it can be used to recognize bad data, so called outliers, and suppress their influence. Kalman filter based on this approach possesses the property of robustness, and considering the possibility of measurement noise statistics estimation, the filter also becomes adaptive. This result can be used not only in estimation theory but also in the applications where uncertain measurements with possible gross errors occur (systems identification, closed loop systems control, telecommunications and so on). Another approach to the problem of making the Kalman filter more robust is based on the neural networks. Implementing recurrent feed-forward neural networks with properly chosen structure and activating functions in the hidden layer, it is possible to obtain the estimations of the system states which are insensitive to the bad data points in the observation sequence. A special attention will be paid to the problem of desired output design that is responsible for the overall performance of estimation procedure.
Calendar of seminars
Last update: September 21, 1999 by Anders Forsgren, anders.forsgren@math.kth.se.