### 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

Belgrade

Yugoslavia

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.
*