Adaptive arrival cost update for improving Moving Horizon Estimation performance

Moving horizon estimation is an efficient technique to estimate states and parameters of constrained dynamical systems. It relies on the solution of a finite horizon optimization problem to compute the estimates, providing a natural framework to handle bounds and constraints on estimates, noises and parameters. However, the approximation of the arrival cost and its updating mechanism are an active research topic. The arrival cost is very important because it provides a mean to incorporate information from previous measurements to the current estimates and it is difficult to estimate its true value. In this work, we exploit the features of adaptive estimation methods to update the parameters of the arrival cost. We show that, having a better approximation of the arrival cost, the size of the optimization problem can be significantly reduced guaranteeing the stability and convergence of the estimates. These properties are illustrated through simulation studies.