This project studied the feasibility of a (nonlinear) mapping to a linear functional space (a Reproducing Kernel Hilbert Space) to implement the Kalman filter equations and achieve performance commensurate with nonlinear models. One of the difficulties of this approach investigated is the growing memory requirements that will be dealt with novel sparsification criteria and algorithms based on information theory. The developed approaches are applied in automotive engine control, and state estimation in non-linear and non-Gaussian systems.