A proximity moving horizon estimator for a class of nonlinear systems

In this article, we present a proximity-based formulation for moving horizon estimation (MHE) of a class of constrained discrete-time nonlinear systems. The cost function of the proposed estimator includes a convex stage cost as well as a Bregman distance for the a priori estimate. This rather general formulation of the cost function allows for a flexible design of the estimator depending on the setting of the problem at hand. We derive sufficient conditions for the global exponential stability of the underlying estimation error. We also investigate the robustness properties of the proposed MHE scheme applied for linear systems subject to unknown process and measurement disturbances in terms of an input-to-state stability analysis. The estimator performance is illustrated by means of simulation examples.