Research On Diffusion Estimation Based On Sparse Signal

Distributed data collect and analysis are ubiquitous over networks,especially,over wireless sensor network?WSN?.Distributed estimation over networks is to collaboratively estimate some parameters of interest based on noisy measurements collected at nodes distributed over a geographic region.Based on the local estimate at each node and the communication among one-hop neighboring nodes,distributed estimation obtains good estimation performance whilst saves energy.Due to its good characteristics,distributed estimation is widely used in many applications,including military surveillance,industrial automation,and precision agriculture.As we know,there are three different strategies in distributed estimation algorithms:incremental,consensus,and diffusion.Since distributed algorithms based on incremental strategy have many shortcomings,such as inability to adapt and learn in real time,the consensus strategy requires the network to have strict symmetry,otherwise it will lead to unstable growth of the entire network state.The diffusion strategy can avoid the above disadvantages well and is robust to node and link failures.Therefore,we mainly studies the distributed estimation algorithm based on diffusion strategy in this paper.It is interesting to notice that many signals in the nature present high level of sparsity,which contain only a few large coefficients among many negligible ones.Such as,speech signals,image signals,and solar waves.Recent studies have revealed that exploiting the prior sparsity of a signal can improve the performance of estimation.Therefore,sparse estimation has aroused considerable interest,and has been extended to the context of distributed estimation.We mainly studies the diffusion algorithms based on sparse signals in wireless sensor networks in this paper.Firstly,we propose the diffusion sparse sign algorithm with variable step-size for distributed estimation in sparse and impulsive interference environments.We address the problem of in-network distributed estimation for sparse vectors under the impulsive noise environment.In order to exploit the sparsity of the vector of interest,we incorporate the sparse norms?₁l-norm andRWl₁-norm?into the cost function of the standard diffusion sign algorithm,which accelerates the convergence speed of zero or near-zero components.In addition,we propose the adaptive variable step-size to further improve the convergence rate of the proposed algorithm.The variable step-size is derived by the correlation entropy,which contains a modified Gaussian kernel function and is robust to impulsive noise.In this paper,every node combines its correlation entropy function with the information of its neighborhood to drive the variable step-size at each iteration.Simulation results show that the proposed algorithm outperforms the standard diffusion SA in the sparse and impulsive system and the convergence rate of the proposed algorithm is faster than constant step-size algorithms.We also propose a distributed adaptive algorithm to solve a node-specific sparse parameter estimation problem where the nodes are interested in estimating parameters that can be of local interest,common interest to a subset of nodes and global interest to the whole network.In most of the distributed estimation problems,it is considered that the nodes have the same interests.This scenario can be viewed as a special case of a more general problem where the nodes of the network have overlapping but different estimation interests.In order to solve the node-specific sparse parameter estimation problem,we add l_p-norm into the cost function of LMS algorithm based on node-specific parameter estimation,so as to effectively utilize the sparsity of different types of parameters and improve the estimation performance of the algorithm The study of convergence in the mean sense reveals that the proposed algorithm is asymptotically unbiased.We also give the simulation results of the algorithm to confirm its excellent performance.