Moving horizon numerical observers of nonlinear control systems

In this note, we develop moving horizon numerical observers and analyze the error. In the error estimation, we take into consideration both the integration error and the optimization error. The design facilitates the use of a variety of numerical algorithms to form different observers. As a special case, an Euler-Newton observer is introduced. The numerical observer is independent of any optimization software or toolbox. Furthermore, the observer is formulated in a way that is especially efficient for systems with sampled measurement.