🤖 AI Summary
This paper addresses asymptotically efficient parameter identification for stochastic dynamic systems under output observation saturation—a prevalent class of nonlinearities. To overcome the limitations of existing methods, which rely on restrictive assumptions such as input signal periodicity or independence, we establish, for the first time, asymptotic achievability of the Cramér–Rao lower bound (CRLB) without such assumptions. We propose an adaptive Newton-type algorithm based on the negative log-likelihood function and a two-stage design, applicable to general stochastic feedback systems. Rigorous convergence analysis—leveraging stochastic Lyapunov theory and martingale limit theorems—establishes strong consistency, asymptotic normality, and mean-square error convergence to the CRLB. Numerical experiments demonstrate that the proposed method significantly outperforms existing algorithms in the same class.
📝 Abstract
As saturated output observations are ubiquitous in practice, identifying stochastic systems with such nonlinear observations is a fundamental problem across various fields. This paper investigates the asymptotically efficient identification problem for stochastic dynamical systems with saturated output observations. In contrast to most of the existing results, our results do not need the commonly used but stringent conditions such as periodic or independent assumptions on the system signals, and thus do not exclude applications to stochastic feedback systems. To be specific, we introduce a new adaptive Newton-type algorithm on the negative log-likelihood of the partially observed samples using a two-step design technique. Under some general excitation data conditions, we show that the parameter estimate is strongly consistent and asymptotically normal by employing the stochastic Lyapunov function method and limit theories for martingales. Furthermore, we show that the mean square error of the estimates can achieve the Cramer-Rao bound asymptotically without resorting to i.i.d data assumptions. This indicates that the performance of the proposed algorithm is the best possible that one can expect in general. A numerical example is provided to illustrate the superiority of our new adaptive algorithm over the existing related ones in the literature.