Adaptive-gain Extended Kalman Filter: Extension to the Continuous-discrete Case

In the present article we propose a nonlinear observer that merges the behaviors 1) of an extended Kalman filter, mainly designed to smooth off noise , and 2) of high-gain observers devoted to handle large perturbations in the state estimation. We specifically aim at continuous-discrete systems.
The strategy consists in letting the high-gain self adapt according to the innovation.
We define innovation computed over a time window and justify its usage via an important lemma. We prove the general convergence of the resulting observer.