Sparse Robust Distributed Estimation by Diffusion Adaptation

The least squares based cost functions are sensitive to outliers in the measured data. The presence of outliers is considered as impulsive noise. In practical scenarios, the co channel interference, saturation effects, non linearity of the measuring instruments, atmospheric conditions and malfunction of sensors will result in outliers or impulsive noise. The robust function obtained by considering the error as the linear combination of sign preserving basis functions is found to be robust against outliers in the desired data. In many practical applications, the parameter to be estimated can be sparse in nature, i.e. only a few elements are large values and the rest are insignificantly small. In such sparse systems, if the prior information about the sparsity is known, then the known information can be incorporated in the cost function as a regularization function. A robust sparse diffusion algorithm is proposed in this work, which is robust against outliers in the desired data and performs better than the existing algorithms in sparsity underlying systems. Simulations performed for different cases of outliers conditions and sparsity conditions validate that the proposed method outperforms the state of the art methods.