Distributed Least-Squares Iterative Methods in Large-Scale Networks: A Survey

SHI Lei, ZHAO Liang, SONG Wenzhan, Goutham Kamath, WU Yuan, and LIU Xuefeng (1. Georgia State University, Atlanta, GA 30302, USA; 2. Georgia Gwinnett College, Lawrenceville, GA 30043, USA; 3. University of Georgia, Athens, GA 30602, USA; 4. Zhejiang University of Technology, Hangzhou 310023, China; 5. The Hong Kong Polytechnic University, Hong Kong, China) Many science and engineering applications involve solving a linear least ⁃ squares system formed from some field mea⁃ surements. In the distributed cyber ⁃ physical systems (CPS), each sensor node used for measurement often only knows partial independent rows of the least ⁃ squares system. To solve the least ⁃ squares all the measurements must be gath⁃ ered at a centralized location and then perform the computa⁃ tion. Such data collection and computation are inefficient be⁃ cause of bandwidth and time constraints and sometimes are infeasible because of data privacy concerns. Iterative meth⁃ ods are natural candidates for solving the aforementioned problem and there are many studies regarding this. However, most of the proposed solutions are related to centralized/par⁃ allel computations while only a few have the potential to be applied in distributed networks. Thus distributed computa⁃ tions are strongly preferred or demanded in many of the real world applications, e.g. smart⁃grid, target tracking, etc. This paper surveys the representative iterative methods for distrib⁃ uted least⁃squares in networks.