State estimation and detection of measurement systematic errors are critical components of plant monitoring and control procedures. Reliable estimations of the process variables are attained by Classic Dynamic Data Reconciliation procedures when measurements follow exactly a known distribution. However, if this assumption happens approximately due to the presence of systematic errors, as outliers, classic dynamic data reconciliation provides biased results. In this work, a two-step methodology of Robust Dynamic Data Reconciliation and Systematic Error Detection is proposed. It takes advantages of a moving measurement window of fixed dimension and the features of the M-estimators. Furthermore, the presence of outliers is detected using a Robust Measurement Test. Two case studies are proposed, which work with the Huber and Biweigth M-estimators. A nonlinear benchmark extracted from the literature is considered, and performance measures are reported. The results obtained demonstrate the effectiveness of the proposed methodology.