Asymptotic Property of Optimal Quantization for System Identification

In this paper, we analyse the asymptotic property of the optimal quantization of signals used for system identification in high resolution case. We show an optimal quantization scheme for minimizing estimation errors under a constraint on the number of subsections of the quantized signals or the expectation of the optimal code length. The optimal quantization schemes can be given by solving Eular–Lagrange’s equations and the solutions are functions of the distribution density of the regressor vector. We show examples of solutions for several cases of the regressor vectors and discuss their meanings with respect to the possibility of parameter estimations. In the case of the constraint of code length, the necessary information to attain the optimal identification errors is given as a function of the entropy of the regressor vector.