Adaptive estimation based on quantized measurements

In this paper, the tracking of a slowly varying scalar Wiener process based on quantized noisy measurements is studied. An adaptive algorithm using a quantizer with adjustable input gain and bias is presented as a low complexity solution. The mean and asymptotic mean squared error of the algorithm are derived. Simulations under Cauchy and Gaussian noise are presented to validate the results and a comparison with the optimal estimator in the Gaussian and real-valued measurement case shows that the loss of performance due to quantization is negligible using 4 or 5 bits of resolution.