  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.
