A space-time diffusion scheme for peer-to-peer least-squares estimation

  • Authors:

  • Lin Xiao;Stephen Boyd;Sanjay Lall

  • Affiliations:

  • Caltech, Pasadena, CA;Stanford University, Stanford, CA;Stanford University, Stanford, CA

  • Venue:
  • Proceedings of the 5th international conference on Information processing in sensor networks
  • Year:
  • 2006

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Abstract

We consider a sensor network in which each sensor takes measurements, at various times, of some unknown parameters, corrupted by independent Gaussian noises. Each node can take a finite or infinite number of measurements, at arbitrary times (ie, asynchronously). We propose a space-time diffusion scheme, that relies only on peer-to-peer communication, and allows every node to asymptotically compute the global maximum-likelihood estimate of the unknown parameters. At each iteration, information is diffused across the network by a temporal update step and a spatial update step. Both steps update each node's state by a weighted average of its current value and locally available data: new measurements for the time update, and neighbors' data for the spatial update. At any time, any node can compute a local weighted least-squares estimate of the unknown parameters, which converges to the global maximum-likelihood solution. With an infinite number of measurements, these estimates converge to the true parameter values in the sense of mean-square convergence. We show that this scheme is robust to unreliable communication links, and works in a network with dynamically changing topology.