Residual life (RL) estimation is a key issue in the prognostics and health management (PHM). This paper proposes a heuristic algorithm for RL estimation based on the nonlinear Wiener process with measurement error (ME) and also proposes an unbiased parameters estimation method. First, we use the nonlinear Wiener process with ME to model the degradation process. Then, an analytical expression of parameters estimation results with restriction of the nonlinear coefficient and variance of ME is obtained and an unbiased parameters estimation method is also derived by analyzing the natures of parameters estimation. Moreover, an empirical unbiased parameters estimation method for the degradation data with different measurement times is also proposed. After that, we extend the heuristic algorithm to the nonlinear Wiener process with ME and some relevant conclusions are proved. Finally, some simulation examples and a case study of lithium-ion batteries are used for experimental verification. The results show that the unbiased parameters estimation method is superior to the traditional maximum likelihood estimation (MLE) method and the heuristic RL estimation method can overcome the influence of imperfect prior information for lithium-ion batteries based on the nonlinear Wiener process with ME.
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