Nonlinear full information and moving horizon estimation: Robust global asymptotic stability

In this paper, we propose time-discounted schemes for full information estimation (FIE) and moving horizon estimation (MHE) that are robustly globally asymptotically stable (RGAS). We consider general nonlinear system dynamics with nonlinear process and output disturbances that are a priori unknown. For FIE being RGAS, our only assumptions are that the system is time-discounted incrementally input–output-to-state-stable (i-IOSS) and that the time-discounted FIE cost function is compatible with the i-IOSS estimate. Since for i-IOSS systems such a compatible cost function can always be designed, we show that i-IOSS is sufficient for the existence of RGAS observers. Based on the stability result for FIE, we provide sufficient conditions such that the induced MHE scheme is RGAS as well for sufficiently large horizons. For both schemes, we can guarantee convergence of the estimation error in case the disturbances converge to zero without incorporating a priori knowledge. Finally, we present explicit converge rates and show how to verify that the MHE results approach the FIE results for increasing horizons.