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In this paper, we show that for a minimal pose-graph problem, even in theideal case of perfect measurements and spherical covariance, using theso-called "wrap function" when comparing angles results in multiple suboptimallocal minima. We numerically estimate regions of attraction to these localminima for some numerical examples, and give evidence to show that they are ofnonzero measure. In contrast, under the same assumptions, we show that the\textit{chordal distance} representation of angle error has a unique minimum upto periodicity. For chordal cost, we also search for initial conditions thatfail to converge to the global minimum, and find that this occurs with farfewer points than with geodesic cost.

Analysis of minima for geodesic and chordal cost for a minimal 2D pose-graph SLAM problem