  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 Cramer-Rao lower bound, an
information-based identification (IBID) algorithm is constructed with 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
Cramer-Rao lower bound, and hence is asymptotically efficient. Numerical
examples are simulated to show the effectiveness of the information-based
identification algorithm.
