Abstract

The online estimation utilizing the group sparse property is developed in the presence of the impulsive noise. The traditional algorithm, for example, least mean squares (LMS), cannot perform accurate estimation because its cost function is not well defined under the impulsive noise environment. Close inspecting the impulsive noise reveals that the noise is not only sparse because of its impulsive nature, but also has the group sparse property in the time domain since non-zero values occur in cluster. By utilizing this feature, the cost function of LMS is reformulated, and a joint group sparse online estimation approach is developed. The proposed approach explores advantage of this noise structure to better suppress the impulsive noise. Numerical simulations demonstrate that the proposed methods perform well in terms of the estimation accuracy, convergence rate and steady state error than traditional estimation approaches.

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