U. A. Khan, S. Kar and J. M. F. Moura, "Higher dimensional consensus algorithms
in sensor networks," in 34th IEEE International
Conference on Acoustics, Speech, and Signal Processing,
Taipei, Taiwan, Apr. 2009, pp. 2857-2860.
This paper introduces higher dimensional consensus, a framework to capture a number of different, but, related distributed, iterative, linear algorithms of interest in sensor networks. We show that, by suitably choosing the iteration matrix of the higher dimensional consensus, we can capture, besides the standard average-consensus, a broad range of applications, including sensor localization, leader-follower, and distributed Jacobi algorithm. We work with the concept of anchors and explicitly derive the consensus subspace and provide the dimension of the limiting state of the sensors.