There are both linear and non-linear forms of the Kalman filter, with the non-linear forms being the Extended Kalman Filter (EKF), the invariant Extended Kalman Filter, and the Unscented Kalman Filter (UKF). The non-linear versions of this algorithm represent the current "gold standard" in many application areas, including GPS and navigation.Before jumping in the deep end of the pool, I decided to implement a simple example that shows the ideas and implementation of Kalman filtering, using a recursive Bayesian approach.
I need to understand this better and see if this could be used in climate simulations.