Nonlinear Moving Horizon Estimation: Adaptive Arrival Cost with Prescribed Conditioning Number

In this paper, we propose a tuning mechanism for the arrival cost (AC) of nonlinear moving horizon estimators (NMHE) with quadratic stage cost (SC) that are robustly global asymptotically stable (RGAS). We consider general detectable nonlinear systems subject to bounded disturbances that are a priori unknown. Based on the robust stability results for NMHE, which state an optimal relation between the eigenvalues of the AC and SC weighting matrices in the sense of minimising the estimation error, we propose a mechanism that preserves the optimal conditioning number of the AC in every sampling time. The performance of the proposed mechanism is illustrated through simulation studies.