# Robust stability of moving horizon estimation for nonlinear systems with bounded disturbances using adaptive arrival cost

## TL;DR

This paper proves the robust stability and convergence of a moving horizon estimator with adaptive arrival cost for nonlinear systems under bounded disturbances, supported by simulations comparing it to existing methods.

## Contribution

It introduces a novel adaptive arrival cost approach that ensures robust stability and convergence in nonlinear moving horizon estimation.

## Key findings

- Proves global asymptotic stability with bounded disturbances
- Demonstrates convergence to true state with vanishing disturbances
- Shows improved estimator performance through simulations

## Abstract

In this paper, the robust stability and convergence to the true state of moving horizon estimator based on an adaptive arrival cost are established for nonlinear detectable systems. Robust global asymptotic stability is shown for the case of non-vanishing bounded disturbances whereas the convergence to the true state is proved for the case of vanishing disturbances. Several simulations were made in order to show the estimator behaviour under different operational conditions and to compare it with the state of the art estimation methods.