18. Robust Kalman Filtering

Peter Ruckdeschel
18 November 2003

As already pointed out in Härdle, Klinke, and Müller (2000, Chapter 10), state-space models are very useful and flexible in the sense that various recursive methods for time-dependent situations can be formulated as general solutions of filtering, smoothing and prediction problems in state-space models.

The classically optimal solutions to these problems, the Kalman-type filters, smoothers and predictors are all based on second moments of the underlying distributions, however. This is clearly a robustness problem, i.e. small deviations from the model assumptions will cause large effects on the quality of the filter/smoother/predictor. As a way out for the filtering problem--at least for one type of ``danger''--we suggest instead using robust Kalman filtering methods such as described in this tutorial.

All routines for robust Kalman filtering, which will be explained in the following, are part of the kalman quantlib. Notice that the quantlets for Kalman filtering explained in Härdle, Klinke, and Müller (2000, Chapter 10) are part of quantlib times .