Mitigating low-frequency noise in various industrial applications often involves the use of the filter-x least mean squares (FxLMS) algorithm, which relies on the mean square error criterion. This algorithm has demonstrated effectiveness in reducing noise induced by Gaussian noise within noise control systems. However, the performance of this algorithm experiences significant degradation and does not converge properly in the presence of impulsive noise. Consequently, to uphold the stability of the ANC system, several robust adaptive algorithms tailored to handle shock noise interference have been introduced. This paper systematically organizes and classifies robust adaptive algorithms designed for impulse noise based on algorithmic criteria, offering valuable insights for the research and application of pertinent active impact noise control methods.