Distributed Diffusion-based Non-negative Least-Mean-Square
Algorithm Over Adaptive Networks
Xiaolong Deng
ABSTRACT
In wireless sensor networks, distributed estimation over networks has received a lot of attention due to its broad applicability. We formulate and study distributed estimation algorithm based on diffusion protocols to implement cooperation among individual adaptive nodes. In the networks, every node is equipped with local leaning abilities, and they can share their local estimation and information with their neighbors. When the nodes communicate with each other, they keep to peer-to-peer protocols. And due to the inherent physical characteristics of systems under investigation, non-negativity is one of the most interesting constraints that can usually be imposed on the parameters to estimate. In distributed diffusion-based least-mean-square (LMS) algorithm, we add non-negative characteristics of parameters to the algorithm so that we can get a distributed diffusion-base non-negative least-mean-square algorithm over adaptive networks.
Index Terms—Adaptive networks, diffusion algorithm, distributed estimation. least mean square algorithms, nonnegative constraints.
INTRODUCTION
Consider a network of nodes observing temporal data arising from different spatial sources with possibly different statistical profiles. Each node in the network could function as an individual adaptive filter whose aim is to estimate the parameter of interest through local observations [1]–[3]. An adaptive network structure is obtained where the structure as a whole is able to respond in real-time to the temporal and spatial variations in the statistical profile of the data [4]–[6]. Different adaptation or learning rules at the nodes, allied with different cooperation protocols, give rise to adaptive networks of various complexities and potential. Our formulation is useful in several problems involving estimation and event detection from multiple nodes collecting space–time data [7]–[12].
In many real-life phenomena including biological and physiological ones, due to the inherent physical characteristics of systems under investigation, non-negativity is a desired constraint that can be imposed on the parameters to estimate in order to avoid physically absurd and uninterpretable results. Over the last 15 years, a variety of methods have been developed to tackle nonnegative least-square problems (NNLS)[13]. Active set techniques for NNLS use the fact that if the set of variables which activate constraints is known, then the solution of the constrained least-square problem can be obtained by solving an unconstrained one that only includes inactive variables. The active set algorithm of Lawson and Hanson [14] is a batch resolution technique for NNLS problems. It has become a standard among the most frequently used methods. In [15], Bro and De Jong introduced a modification of the latter, called fast NNLS, which takes advantage of the special characteristics of iterative algorithms involving repeated use of non-negativity constraints. Another class of tools is the class of projected gradient
