Sparse distributed learning based on diffusion minimum generalised rank norm

The traditional least-squares based diffusion least mean squares is not robust against outliers present in either desired data or input data. The diffusion minimum generalised rank (GR) norm algorithm proposed in the earlier works of the authors was able to effectively estimate the parameter of interest in presence of outliers in both desired and input data. However, this manuscript deals with the robust distributed estimation over distributed networks exploiting sparsity underlying in the system model. The proposed algorithm is based on both GR norm and compressive sensing, where GR norm ensures robustness against outliers in input as well as desired data. The techniques from compressive sensing endow the network with adaptive learning of the sparse structure form the incoming data in real-time and it also enables tracking of the sparsity variations of the system model. The mean and mean square convergence of the proposed algorithm are analysed and the conditions under which the proposed algorithm outperforms the unregularised diffusion GR norm algorithm are also investigated. The proposed algorithms are validated for three different applications namely distributed parameter estimation, tracking and distributed power spectrum estimation.