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Failure prognosis is the key point of prognostic and health management or condition-based maintenance, the multiple uncertainty sources in real world will lead to inaccurate prediction. In this paper, an advanced failure prognosis method with Kalman filter is presented to address the real-world uncertainties. The multiple uncertainty sources are analyzed and classified first and then theoretical methods are derived, respectively, for the different uncertainty sources. Afterward, the failure prognosis algorithm is developed by taking into consideration. In the end, an aircraft fuel feeding system health monitoring case simulation is presented to demonstrate the effectiveness of the proposed method.