Multitask diffusion affine projection sign algorithm and its sparse variant for distributed estimation

Distributed adaptation over multitask networks has attracted particular attention due to its enhanced modeling capacity compared to that over conventional single-task networks. Most of the existing works derive their multitask adaptive algorithms using mean-square error (MSE) or least squares (LS) criterion, leading to multitask LMS- or LS-type algorithms. These algorithms, however, may suffer from deteriorated convergence rate or even divergence in impulsive noise environments. In order to address this problem, we propose a robust diffusion affine projection sign algorithm for multitask parameter estimation. The algorithm is derived by using the method of data reusing and minimizing the weighted sum of the l₁-norms of some intermediate error vectors plus a similarity term subject to constraints on intermediate weight vectors at each agent. The multitask similarity relationship is characterized by the distance regularization among weight vectors. Furthermore, a variant of this algorithm, which is obtained by further regularizing the cost function by the l₀-norm of the intermediate weight vector at each agent, is presented to promote convergence rate for jointly sparse parameter vectors estimation.