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We examine the problem of estimating vector-valued variables from noisy measurements of the difference between certain pairs of them. This problem, which is naturally posed in terms of a measurement graph, arises in applications such as sensor network localization, time synchronization, and motion consensus. We obtain a characterization on the minimum possible covariance of the estimation error when...
We introduce the concept of matrix-valued effective resistance for undirected matrix-weighted graphs. Effective resistances are defined to be the square blocks that appear in the diagonal of the inverse of the matrix-weighted Dirichlet graph Laplacian matrix. However, they can also be obtained from a "generalized" electrical network that is constructed from the graph, and for which currents,...
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