Moving Horizon Estimation for Nonlinear Systems with Time-Varying Parameters

We propose a moving horizon estimation scheme for estimating the states andtime-varying parameters of nonlinear systems. We consider the case whereobservability of the parameters depends on the excitation of the system and maybe absent during operation, with the parameter dynamics fulfilling a weakincremental bounded-energy bounded-state property to ensure boundedness of theestimation error (with respect to the disturbance energy). The proposedestimation scheme involves a standard quadratic cost function with an adaptiveregularization term depending on the current parameter observability. Wedevelop robustness guarantees for the overall estimation error that are validfor all times, and that improve the more often the parameters are detected tobe observable during operation. The theoretical results are illustrated by asimulation example.