Asymptotically efficient Quasi-Newton type identification with quantized observations under bounded persistent excitations

Abstract

This paper is concerned with the optimal identification problem of dynamical systems in which only quantized output observations are available under the assumption of fixed thresholds and bounded persistent excitations. Based on a time-varying projection, a weighted Quasi-Newton type projection (WQNP) algorithm is proposed. With some mild conditions on the weight coefficients, the algorithm is proved to be mean square and almost surely convergent, and the convergence rate can be the reciprocal of the number of observations, which is the same order as the optimal estimate under accurate measurements. Furthermore, inspired by the structure of the Cramér–Rao lower bound, an information-based identification (IBID) algorithm is constructed with an adaptive design about weight coefficients of the WQNP algorithm, where the weight coefficients are related to the parameter estimates which leads to the essential difficulty of algorithm analysis. Beyond the convergence properties, this paper demonstrates that the IBID algorithm tends asymptotically to the Cramér–Rao lower bound, and hence is asymptotically efficient. A numerical example is simulated to show the effectiveness of the proposed algorithms.