  We estimate $n$ phases (angles) from noisy pairwise relative phase
measurements. The task is modeled as a nonconvex least-squares optimization
problem. It was recently shown that this problem can be solved in polynomial
time via convex relaxation, under some conditions on the noise. In this paper,
under similar but more restrictive conditions, we show that a modified version
of the power method converges to the global optimum. This is simpler and
(empirically) faster than convex approaches. Empirically, they both succeed in
the same regime. Further analysis shows that, in the same noise regime as
previously studied, second-order necessary optimality conditions for this
quadratically constrained quadratic program are also sufficient, despite
nonconvexity.
