Bearings have been widely used with the broad application of rotating machines. Hence, in order to increase the efficiency, reliability and safety of rotating machinery, condition monitoring of bearings is significant during the operation. However, due to the influence of high background noise and components slippage, incipient faults are difficult to detect. With the continuous research on the bearing system, the modulation effects have been well known and the demodulation based on optimal frequency bands is approved as a promising method in condition monitoring. For the purpose of enhancing the performance of demodulation analysis, a robust method, ensemble average autocorrelation based stochastic subspace identification (SSI), is introduced to determine the optimal frequency bands. Furthermore, considering that both the average and autocorrelation functions can reduce noise, auto-correlated envelope ensemble average (AEEA) is proposed to suppress noise and highlight the localised fault signature. In order to examine the performance of this method, the slippage of bearing signals is modelled as a Markov process in the simulation study. Based on the analysis results of simulated bearing fault signals with white noise and slippage and an experimental signal from a planetary gearbox test bench, the proposed method is robust to determine the optimal frequency bands, suppress noise and extract the fault characteristics.