We consider the problem of signal parameter estimation using a collection of distributed sensors. Each sensor quantizes its data to one-bit information and sends it to a fusion processor for the estimation of the parameter. Estimation of a constant signal in additive noise is considered. Since the emphasis is for the case of a moderately large number of sensors, we consider in this study two cases of estimation with 8 sensors and 20 sensors. We formulate several estimators based on one-bit sensor data and evaluate their mean squared error performances through simulation studies. Two parametric noise densities are simulated to ascertain the efficacies of various estimators. Results from this study show that robust estimation of parameter is possible by using a moderately large number of one-bit quantized sensor data.