Robust Multitask Diffusion Normalized M-estimate Subband Adaptive Filtering Algorithm Over Adaptive Networks

In recent years, the multitask diffusion least mean square (MD-LMS) algorithm has been extensively applied in the distributed parameter estimation and target tracking of multitask network. However, its performance is mainly limited by two aspects, i.e, the correlated input signal and impulsive noise interference. To overcome these two limitations simultaneously, this paper firstly introduces the subband adaptive filter (SAF) into the multitask network. Then, a robust multitask diffusion normalized M-estimate subband adaptive filtering (MD-NMSAF) algorithm is proposed by solving the modified Huber function based global network optimization problem in a distributed manner, which endows the multitask network strong decorrelation ability for correlated inputs and robustness to impulsive noise interference, and accelerates the convergence of the algorithm significantly. Compared with the robust multitask diffusion affine projection M-estimate (MD-APM) algorithm, the computational complexity of the proposed MD-NMSAF is greatly reduced. In addition, the stability condition, the analytical expressions of the theoretical transient and steady-state network mean square deviation (MSD) of the MD-NMSAF are also provided and verified through computer simulations. Simulation results under different input signals and impulsive noise environment fully demonstrate the performance advantages of the MD-NMSAF algorithm over some other competitors in terms of steady-state accuracy and tracking speed.