Optimal quantisation for random parameter estimation

In this study, the optimal quantiser design for random parameter estimation is investigated. The objective is to find a quantiser to minimise the variance of the estimation error by the minimum mean-square estimation. The main results are presented for the cases of high and low resolutions, respectively. For high resolution, multi-dimensional quantisation is considered and a quantitative relationship between the quantisation density and the probability density function is presented. For low-resolution case, an indirect method is developed for one-dimensional optimal quantisation by exploiting the results of high resolution case. The measurement space is first evenly divided into a number of small intervals, then the quantisation is approximately represented by the grouping of the small intervals. At last, a dynamic programming-based method is presented for the optimal grouping.