The composite least-square method was proposed for establishing the state variable model.The method was also applied to develop high dimension state variable model with high accuracy.By taking health parameters as augmented state variables

a Kalman filter was then designed to predict the health parameters from the deviation of measurable parameters.To minimize the modeling errors between the self tuning model and real engine

a neural network was built to modify the steady-state modeling errors

thus improving the confidence level of fault diagnosis system.