Dynamic modelling and fault detection play an important role in the condition monitoring of gas turbine engines (GTEs). Although system identification and Robust Fault Detection Observer (RFDO) have been studied intensively, on-board fault detection raises challenges. A fast identification and discrete observer design is required because of the limited computation ability. In this paper, an output error model is identified first and a discrete observer is designed to avoid the discrete-continuous conversion. With the aid of disturbance frequency estimation, an improved performance index and a fast left-eigenvector based robust observer design method are proposed. As illustrated in the application results, a better disturbance attenuation and fault detection performance have been achieved.