Abstract： A class of degradation modeling approach was proposed, in which the nonlinear stochastic deterioration and uncertain measurements of the system were considered simultaneously, and the Kalman filtering technique was utilized to estimate the underlying degradation state. Based on the estimated degradation state, the analytical RUL distribution was derived according to the concept of the first passage time which accounted for the uncertainties in the estimated degradation state and measurements, and the effect of the degradation nonlinearity. Additionally, a parameter estimation method for the developed model was presented based on the maximum likelihood method. Finally, a case study of the gyros verified that the proposed method could improve the accuracy of the predicted RUL.