  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.
