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Systems with a hidden degradation process are pervasive in the real world. Degrading critical components will undermine system performance and pose potential failures in the future. Prognostic aims at predicting potential failures before it evolves into faults. A prognostic procedure based on expectation maximization and unscented Kalman filter is proposed. System state, sensor measurement and hidden degradation process are viewed as data (incomplete or missing) in the expectation maximization method. System state and hidden degradation process are estimated by a unscented Kalman filter upon sensor measurements. Component-specific parameters in a degradation process are identified on the estimation of the degradation process. Residual life is measured by the median of estimated residual life distribution. The proposed procedure is verified by simulations on a first-order capacitor-resistance circuit with degrading resistance. Residual life estimation consists conservatively with the trend and is evaluated in terms of relative errors. Simulation results are reasonable. The proposed prognostic method expects applications in practice.