Finite sliding window maximum correntropy criterion conjugate gradient adaptive filtering algorithm

The maximum correntropy criterion (MCC) adaptive filtering algorithm is widely used in impulsive noise environments due to its good robustness. However, the stochastic gradient (SG) method can lead to a slow convergence of MCC. As an alternative to SG, the conjugate gradient (CG) method provides a solution to accelerate MCC convergence. Unfortunately, the CG based robust adaptive filtering algorithms usually cannot simultaneously achieve good tracking performance with high convergence accuracy due to the long memory property of the exponentially decaying data window scheme. To address such problem, we propose a finite sliding window MCC conjugate gradient (FSWMCCCG) algorithm and a variable window length FSWMCCCG (VWL-FSWMCCCG) algorithm in this paper. The proposed FSWMCCCG algorithm can get excellent tracking performance through a short memory data window scheme, while VWL-FSWMCCCG can further improve the convergence performance of FSWMCCCG by indirectly adjusting the window length using the error signal. Then, we analyze the convergence behavior, steady-state mean square deviation (MSD) and computational complexity of FSWMCCCG. Finally, simulations demonstrate the correctness of the theoretical steady-state MSD under Gaussian noise and the superiority of the proposed algorithms in impulsive noise environments.