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The O (d) synchronization problem consists of estimating a set of n unknown orthogonal d d matrices O₁, , Oₙ from noisy measurements of a subset of the pairwise ratios OᵢOⱼ^-1. We formulate and prove a Cheeger-type inequality that relates a measure of how well it is possible to solve the O (d) synchronization problem with the spectra of an operator, the graph connection Laplacian. We also show how this inequality provides a worst-case performance guarantee for a spectral method to solve this problem.
Bandeira et al. (Tue,) studied this question.
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