本文基于δ算子构造了Ｈｉｌｂｅｒｔ空间中的信号向量，推导了系统的输入输出关系，得出了前向和后向预测误差向量的表达式．借助格形滤波器理论导出了故障残差序列的递归算法，从而设计出故障检测滤波器．将该滤波器与自适应噪声抵消技术相结合，实现了对被噪声污染信号的故障实时在线检测．最后，仿真实验验证了这种故障检测方法的有效性． In this paper, the signal vector in Hilbert space is constructed based on δ operator, and the relationship between input and output of the system is deduced. The expression of forward and backward prediction error vector is obtained. With the help of the lattice filter theory, the recursive algorithm of fault residual sequence is derived, and the fault detection filter is designed. The filter and adaptive noise cancellation technology combined to achieve a real-time on-line noise fault signal detection. Finally, simulation experiments verify the effectiveness of this fault detection method.