Feature Tracking and Motion Classification Using a Switchable Model Kalman Filter

In order to successfully track moving objects it is necessary to understand their motion. Such motion will inevitably change with time, thus attempting to fit the same model all of the time is inappropriate. An evaluation of the single model Kalman filter described in this paper demonstrates this. A maximum model coverage technique, however, would provide a intractable solution because of the exponentially increasing number of models required. We present a solution which uses a finite set of models all making predictions on the data. One model is selected from the set on the basis that it best accounts for the data. A Kalman filter is then used to refine this model whilst it is appropriate. The remaining models continue to make predictions and at any time the filtered model may be replaced by one that more accurately describes the data. Experimental results demonstrate the improvement the switchable model Kalman filter provides over the single model Kalman filter. Problems using the chi-squared metric for model selection are discussed and a more appropriate metric, the Bhattacharyya integral, introduced. The desired properties of this integral are exposed via its analytic solution. It is believed that the statistical methods underlying this work may also have applications in other system identification problems.