On-line Support Vector Regression of the transition model for the Kalman filter

Recursive Bayesian Estimation (RBE) is a widespread solution for visual tracking as well as for applications in other domains where a hidden state is estimated recursively from noisy measurements. From a practical point of view, deployment of RBE filters is limited by the assumption of complete knowledge on the process and measurement statistics. These missing tokens of information lead to an approximate or even uninformed assignment of filter parameters. Unfortunately, the use of the wrong transition or measurement model may lead to large estimation errors or to divergence, even when the otherwise optimal filter is deployed. In this paper on-line learning of the transition model via Support Vector Regression is proposed. The specialization of this general framework for linear/Gaussian filters, which we dub Support Vector Kalman (SVK), is then introduced and shown to outperform a standard, non adaptive Kalman filter as well as a widespread solution to cope with unknown transition models such as the Interacting Multiple Models (IMM) filter.

Graphical abstractFigure optionsDownload full-size imageDownload high-quality image (123 K)Download as PowerPoint slideHighlights► Recursive Bayesian Estimation is suboptimal when using wrong transition models. ► Yet, in a practical deployment the model is selected among a set of standard ones. ► Instead, we apply Support Vector Regression to learn it on-line from system evolution. ► We obtain a general adaptive Kalman filter, that we dub Support Vector Kalman. ► Our filter outperforms standard approaches (i.e. Kalman and IMM filters).