Previous studies by the authors have shown that nodal demands in a water distribution system (WDS) can be estimated in real-time using pipe flow data collected by supervisory control and data acquisition (SCADA) system. Estimated demands can be used for optimal operation of system to support pressure and water quality. It is not unusual the data from SCADA systems contain gross errors due to system failure and/or meter malfunctions. The estimator is sensitive to these erroneous measurements and the estimates based on the bad measurements are not reliable for system operation; therefore bad data should be filtered prior to demand estimation. However, system failure and meter malfunctions are random phenomena and hard to identify. This study presents a series of statistical methods to detect bad data, identify their locations, and correct the data values. The proposed methods are based on a linear measurement model that linearly relates state variables (nodal demands) to the field measurements (pipe flow rates). The scheme is applied prior to a demand estimation to eliminate the effects of erroneous data on the demand estimates. The proposed method is applied to a hypothetical simple network using synthetically generated data sets, such as error-free data, Gaussian-noisy data, fire flow data, and noisy data containing one or more contaminated measurements. Application to a simple hypothetical network using synthetically generated data shows that the method can be successfully used as a pre-processing for single and multiple non-interacting bad data for reliable demand estimation.