I'm investigating applying Kalman filters (KF) to build a state space model right now.
For my model, the process equation is linear, and thus fits nicely in a KF approach. However, my observation equation cannot be described in linear terms, but it can be described with a differential function, which calls for an extended Kalman filter (EKF), if I'm understanding the two approaches correctly.
I'm relatively new to state space models and Kalman filters... but looking at the wikipedia pages for the KF and EKF, it seems the EKF --- in addition to formualting the models as differential equations --- essentially substitutes the observation and state transition matrices of the KF with the respective jacobians of the differential equations used in the EKF.
Perhaps its wishful thinking, but can I apply the state process as a KF and the observation process as an EKF, then expect it to work if I put it together? Or is there some deeper difference between the KF and EKF approaches?
When faced with such a model, I was wondering if its common practice to throw it all into a extended Kalman filter, or if there exists some flavor of Kalman filter which is specifically suited for my situation (linear process model, non-linear observation model).