The presence of measurement bias and random noise significantly deteriorates the information quality of plant data. Data reconciliation techniques for steady-state processes have been widely applied to processing industries to improve the accuracy and precision of the raw measurements. This paper develops an algorithm for simultaneous bias correction and data reconciliation for dynamic processes. The algorithm considers process model error as an important contributing factor in the estimation of the measurement bias and process state variables. It employs black-box models for the process as would be done when phenomenological models are difficult or impractical to obtain. Simulation results of a distillation column demonstrated that this algorithm effectively compensates constant and non-constant measurement biases yielding much improved reconciled values of process variables. It has computational advantages over previously proposed algorithms based on non-linear dynamic data reconciliation because an analytical solution is available when using linear process models to approximate the process.