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Abstract-In the past decade, moving horizon estimation (MHE) has emerged as a powerful technique for estimating the state of a dynamical system in the presence of nonlinearities and disturbances. MHE is based on the idea of minimizing an estimation cost function defined on a sliding window composed of a finite number of time stages. The cost function usually comprises two contributions: a prediction error computed on a recent batch of inputs and outputs and an arrival cost that serves the purpose of summarizing the past data. The diffusion of such techniques has been hampered by the difficulty in choosing the arrival cost so as to ensure stability of the overall estimation scheme and by the need for an adequate computational time.In this paper, both problems are addressed and possible solutions are proposed. First, by means of a novel stability analysis, we show that in most situations a quadratic arrival cost is sufficient to ensure the stability of the estimation error provided that the weight matrix is adequately chosen. Second, we propose a novel approximate MHE algorithm based on nonlinear programming sensitivity calculations. This approximate algorithm has the same stability properties as those of the optimal counterpart and hence is suitable for on-line settings. Preliminary simulation results confirm the effectiveness of our proposed method.

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