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.

在本文中，我们提出了用于全局渐近稳定 (RGAS) 的全信息估计 (FIE) 和移动水平估计 (MHE) 的时间折扣方案。我们考虑具有先验未知的非线性过程和输出扰动的一般非线性系统动力学。对于 RGAS 的 FIE，我们唯一的假设是系统是时间折扣增量输入输出到状态稳定 (i-IOSS) 并且时间折扣的 FIE 成本函数与 i-IOSS 估计兼容。由于对于 i-IOSS 系统，始终可以设计这样一个兼容的成本函数，我们表明 i-IOSS 足以满足 RGAS 观察者的存在。基于 FIE 的稳定性结果，我们提供了充分的条件，使得诱导的 MHE 方案对于足够大的视野也是 RGAS。对于这两种方案，我们可以保证估计误差收敛，以防扰动收敛到零而不包含先验知识。最后，我们提出明确的收敛率并展示如何验证 MHE 结果接近 FIE 结果以增加视野。