Adjustable quantizers for joint estimation of location and scale parameters

An adaptive algorithm to estimate jointly unknown location and scale parameters of a sequence of symmetrically distributed independent and identically distributed random variables using quantized measurements from a quantizer with adjustable input gain and input offset is presented. The asymptotic variance of estimation is obtained, simulations under Cauchy and Gaussian distributions are presented to validate the asymptotic results and they are compared to the continuous optimal estimator performance.