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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 nonvanishing 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.

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