Remaining useful lifetime (RUL) estimation is a key issue in prognosis and health management for industrial systems.Currently

the use of the observed degradation data of a system holds promise to estimate its RUL.Due to the effect of system's stochastic deterioration and uncertain measurements

the measured data are inevitably contaminated by the stochasticity of the degradation and measurement uncertainty.However

in current studies of the RUL estimation based on the measured data

there is no report considering the effect of the degradation stochasticity and measurement uncertainty on the estimated RUL distribution.In this paper

a new degradation modeling approach is proposed based on Wiener process

which considers system's stochastic deterioration and uncertain measurements simultaneously

and the Kalman filtering technique is utilized to estimate the underlying degradation state.On the basis of the estimated degradation state

the analytical RUL distribution is derived which accounts for the uncertainties in the estimated degradation state and measurements.Additionally

a parameter estimation method for the developed model is presented based on the maximum likelihood method.Finally

a case study for gyros verifies the proposed method and the results indicate that the proposed method is superior to the method without considering uncertain measurements and can improve the accuracy of the estimated RUL.