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We present novel, tight, convex relaxations for rotation and pose estimationproblems that can guarantee global optimality via strong Lagrangian duality.Some such relaxations exist in the literature for specific problem setups thatassume the matrix von Mises-Fisher distribution (a.k.a., matrix Langevindistribution or chordal distance) for isotropic rotational uncertainty.However, another common way to represent uncertainty for rotations and poses isto define anisotropic noise in the associated Lie algebra. Starting from anoise model based on the Cayley map, we define our estimation problems, convertthem to Quadratically Constrained Quadratic Programs (QCQPs), then relax themto Semidefinite Programs (SDPs), which can be solved using standardinterior-point optimization methods. We first show how to carry out basicrotation and pose averaging. We then turn to the more complex problem oftrajectory estimation, which involves many pose variables with both individualand inter-pose measurements (or motion priors). Our contribution is toformulate SDP relaxations for all these problems, including the identificationof sufficient redundant constraints to make them tight. We hope our results canadd to the catalogue of useful estimation problems whose global optimality canbe guaranteed.

Certifiably Optimal Rotation and Pose Estimation Based on the Cayley Map