Aiming at the problems of the traditional adaptive filtering algorithm, such as poor noise reduction performance, slow convergence speed and insufficient ability to deal with mutation, this paper proposes an improved equation error algorithm and mirror image optimization algorithm. Among them, the improved equation error algorithm based on FURLMS algorithm carries out offline quadratic path modeling, which solves the problems of noise reduction performance and convergence speed. In order to improve the ability of the system to deal with mutation, the algorithm is optimized based on the FURLMS algorithm. The results show that when the system frequency is about 250 Hz, the mean square error of the proposed two algorithms can be stabilized at -20 db, and the improved equation error algorithm and the image modification algorithm have the noise attenuation effect of 28dBA and 30dBA respectively.