Abstract: The H ∞ estimation and optimization methodology ave applied to the fault detection of linear discrete-time uncertain system in order to reduce false alarm rate and improve fault detection accuracy. The key to fault detection based on estimation is to generate residual that are robust against system uncertainties and external disturbance inputs, and that are simultaneously sensitive to fault if occurrs. The robustness requirement of residual generation can be satisfied by application of H ∞ -estimator. The sensitivity requirement can be satisfied by the usage of optimization design that aims to maximize the effect of fault to residuals. Calculation and selection of threshold value are presented. The results are applying to detect fault occurred in sensor and actuator of aircraft in the existence of uncertainties and disturbance inputs. It is shown that the fault detection method based on robust H ∞ estimation and optimization proposed in this paper can reduce false alarm rate by comparing with Kalman filtering.