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As saturated output observations are ubiquitous in practice, identifyingstochastic systems with such nonlinear observations is a fundamental problemacross various fields. This paper investigates the asymptotically efficientidentification problem for stochastic dynamical systems with saturated outputobservations. In contrast to most of the existing results, our results do notneed the commonly used but stringent conditions such as periodic or independentassumptions on the system signals, and thus do not exclude applications tostochastic feedback systems. To be specific, we introduce a new adaptiveNewton-type algorithm on the negative log-likelihood of the partially observedsamples using a two-step design technique. Under some general excitation dataconditions, we show that the parameter estimate is strongly consistent andasymptotically normal by employing the stochastic Lyapunov function method andlimit theories for martingales. Furthermore, we show that the mean square errorof the estimates can achieve the Cramer-Rao bound asymptotically withoutresorting to i.i.d data assumptions. This indicates that the performance of theproposed algorithm is the best possible that one can expect in general. Anumerical example is provided to illustrate the superiority of our new adaptivealgorithm over the existing related ones in the literature.

Asymptotically efficient adaptive identification under saturated output observation