Asymptotically Efficient Recursive Identification Method for FIR System with Quantized Observations

In this paper, a new recursive identification method is proposed for the FIR linear system with quantized measurements, and without full the information of noise. In this problem, we will try to identify the coefficients of FIR system, the variance of output noise and the threshold of quantized sensor. The maximum likelihood estimate approach is used to deduce the efficient way to identify all unknown parameters of the system. The existence and uniqueness of the estimation is proved, and the Cramer-Rao lower bound of the identification problem is calculated. Then based on some general results on stochastic approximation, we proposed a recursive algorithm, and proved the convergency and asymptotic efficiency of this algorithm.