Data-driven models are widely used in process industries for monitoring and control purposes. No matter what kind of models one chooses, model-plant mismatch always exists; it is, therefore, important to implement model update strategies using the latest observation information of the investigated process. In practice, multiple observation sources such as frequent but inaccurate or accurate but infrequent measurements coexist for a same quality variable. In this article, we show how the flexibility of the Bayesian approach can be exploited to account for multiple-source observations with different degrees of belief. A practical Bayesian fusion formulation with time-varying variances is proposed to deal with possible abnormal observations. A sequential Monte Carlo sampling based particle filter is used for simultaneously handling systematic and nonsystematic errors (i.e., bias and noise) in the presence of process constraints. The proposed method is illustrated through a simulation example and a data-driven soft sensor application in an oil sands froth treatment process. (C) 2010 American Institute of Chemical Engineers AIChE J, 57: 1514-1526, 2011