This paper aims to deal with the problem of fault detection in a closed-loop mode for a three-axis gyro-stabilized camera mount under the consideration of unknown disturbances. First, the influences of potential actuator and sensor faults are analysed and, based on this, the faults model as well as an equivalent additive fault input are introduced. For the purpose of fault detection, an observer-based fault detection filter is considered to generate the residual. The sensitivity of the residual to fault is evaluated by the non-zero singular values of the transfer function from fault to residual, whereas the robustness to disturbance is represented by the H-norm of the transfer function from disturbance to residual. To obtain a maximum sensitivity/robustness ratio criterion, the design of fault detection filter is formulated as an H_i/H optimization problem and the unified solutions for the optimization criterion are given. For residual evaluation, a window evaluation function is developed and an analysis of threshold selection is given to reduce the conservativeness of fault detection. Finally, experimental results are presented to demonstrate the effectiveness of the proposed method. It is demonstrated that the proposed method can effectively detect the provided fault as soon as possible.