Quantized system identification under a class of persistent excitations

Identification of quantized system with output noises is studied. The main theoretical difficulty exists is that the parameter estimation and the quantization are related, which is ignored in most literatures on identification and filtering of quantization systems. For right this difficulty, the control of quantization systems cannot be studied. By analyzing the condition expectation of quantization with prior parameter estimations, the identification algorithm is constructed under a class of persistently excited inputs. It is proved to converge to the real parameter in mean of almost sure and mean square and have a convergence speed of 1/k (the same order under classical systems with accurate values of system outputs). More importantly, the optimal convergence speed is achieved by choosing the best quantization value. A simulation example is used to support the algorithm developed in this paper. Finally, concluding remarks are addressed and related future work is discussed.