### A Space-Time Diffusion Scheme for Peer-to-Peer Least-Squares Estimation

- L. Xiao, S. Boyd and S. Lall.
- Proceedings of the International Conference on Information Processing in Sensor Networks (IPSN), p. 168--176, 2006.

We consider a sensor network where each sensor takes multiple measurements of some unknown parameters, corrupted by independent Gaussian noises. The number of measurements at each node can be nite or innite, each at a different time, occurring asynchronously in the network.We propose a space-time diffusion scheme that allows every node to asymptotically compute the global maximumlikelihood estimate of the parameters. This is a distributed iterative scheme that relies on only peer-to-peer communication. At each iteration, it diffuses information 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 time update and neighbors' data for spatial update. At each iteration, every node can compute a local weighted least-squares estimate, which converges to the global maximum-likelihood solution. With innite number of measurements, these estimates converge to the true parameters in mean square sense. We show that this scheme is robust to unreliable communication links and it works in a network with dynamically changing topology.