Robust Compressive-Sensing-Based Diffusion Bayesian Strategies Over Networks

The traditional diffusion algorithms usually suffer from high communication load in distributed networks. Regarding this issue, the distributed compressed estimation (DCE) scheme reduce the communication load by compressing the weight vector which needs to be estimated. However, the performance between convergence rate and steady-state error need to be balanced, and under impulsive noise interferences, the DCE performance will significantly decrease. To tackle these issues, we propose a compressive-sensing-based diffusion Bayesian (CSB-DB) algorithm with low communication burden and high estimation accuracy. To improve its robustness against impulsive noise, we design a robust CSB-DB (RCSB-DB) algorithm, leading to a selective weight function in the step-size. The selective weight function prevents the update of step-size and weight vector when outliers occur. Additionally, we design an algorithm to optimize the measurement matrix under the gradient descent to enhance the convergence rate and steady-state performance of the proposed algorithms. The mean and mean-square analyses are also conducted. Numerical experiments verify that the simulation results corroborate with the theoretical development, and reveal the excellent performance of the proposed algorithms.