  A statistical framework is introduced for a broad class of problems involving
synchronization or registration of data across a sensor network in the presence
of noise. This framework enables an estimation-theoretic approach to the design
and characterization of synchronization algorithms. The Fisher information is
expressed in terms of the distribution of the measurement noise and standard
mathematical descriptors of the network's graph structure for several important
cases. This leads to maximum likelihood and approximate maximum-likelihood
registration algorithms and also to distributed iterative algorithms that, when
they converge, attain statistically optimal solutions. The relationship between
optimal estimation in this setting and Kirchhoff's laws is also elucidated.
