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Partial Extended Observability Certification and Optimal Design of Moving Horizon Estimators Under Uncertainties

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Document pages: 16 pages

Abstract: This paper addresses the observability analysis and the optimal design ofobservation parameters in the presence of noisy measurements and parametricuncertainties. The main underlying frameworks are the nonlinear constrainedmoving horizon estimator design and the probabilistic certification viarandomized optimization. As the perfect observability concept is not relevantunder the considered uncertain and noisy context, the notion of almost$ epsilon$-observability is introduced and a systematic procedure to assess itssatisfaction for a given system with a priori known measurement noisestatistics and parameter discrepancy is sketched. A nice feature in theproposed framework is that the observability is not necessarily defined as theability to reconstruct the whole state, rather, the more general concept ofobservation-target quantities is used so that one can analyze the precisionwith which specific chosen expressions of the state and the parameters can bereconstructed. The overall framework is exposed and validated through anillustrative example.

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