Nonlinear moving horizon estimation in the presence of bounded disturbances

In this paper, we propose a new moving horizon estimator for nonlinear detectable systems. Similar to a recently proposed full information estimator, the corresponding cost function contains an additional max-term compared to more standard least-squares type approaches. We show that robust global asymptotic stability in case of bounded disturbances and convergence of the estimation error in case of vanishing disturbances can be established. Second, we show that the same results hold for a standard least-squares type moving horizon estimator, which so far has not been proven even in the full information estimation case. An additional advantage of the proposed estimators is that a suitable prior weighting appearing in the cost function can explicitly be determined offline, which is not the case in various existing approaches.