Nonlinear Kalman Filters in RKHS

University Of Florida, Gainesville FL

Investigators

Abstract

Recently, there has been an increased interest within the machine learning and signal processing communities in kernel methods because they offer an attractive alternative to design nonlinear systems for the demanding current applications of information processing. Recursive state estimation and in particular the Kalman filter, would benefit from such an effort because there are many important applications in aerospace, automotive, surveillance, and medical fields that are intrinsically nonlinear, and the current nonlinear models have drawbacks. This proposal will study the feasibility of a (nonlinear) mapping to a linear functional space (a Reproducing Kernel Hilbert Space) to implement there the Kalman filter equations and achieve performance commensurate with nonlinear models. One of the difficulties of this approach that will be investigated is the growing memory requirements that will be dealt with novel sparsification criteria and algorithms based on information theory. The approach will be tested in the design of brain machine interfaces to help quadraplegics and also in automotive engine control for which there are data available and benchmarks. Two graduate students will be working on this important topic.