In this paper, we consider the problem of estimating the parameters in mathematical models of complex systems from experimental observations; the methods and procedures that we develop are general, but in this work we make specific reference to the problem of parameter estimation for multibody-based rotorcraft vehicle models from flight test data. We consider methods that are applicable to unstable systems, since rotorcraft vehicles are typically unstable at least in certain flight regimes. Unstable vehicles must be operated in closed-loop, and this must be explicitly accounted for when formulating parameter estimation methods. We describe two alternative classes of methods in the time domain, namely, the recursive filtering and the batch optimization methods. In the recursive approach, we formulate a novel version of the extended Kalman filter that accounts for the presence of unobservable states in the model. In the case of the batch optimization methods, we present a formulation based on a new single-multiple shooting approach, specifically designed for models with slow and fast solution components. We perform some initial steps toward the validation of the proposed procedures with the help of applications regarding manned and unmanned rotorcraft vehicles.

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