  The estimation of signal parameters using quantized data is a recurrent
problem in electrical engineering. As an example, this includes the estimation
of a noisy constant value and of the parameters of a sinewave, that is, its
amplitude, initial record phase, and offset. Conventional algorithms, such as
the arithmetic mean, in the case of the estimation of a constant, are known not
to be optimal in the presence of quantization errors. They provide biased
estimates if particular conditions regarding the quantization process are not
met, as it usually happens in practice. In this paper, a quantile-based
estimator is presented, which is based on the Gauss-Markov theorem. The general
theory is first described and the estimator is then applied to both direct
current and alternate current input signals with unknown characteristics. Using
simulations and experimental results, it is shown that the new estimator
outperforms conventional estimators in both problems, by removing the
estimation bias.
