An information-theoretic approach to the correspondence-free AX=XB sensor calibration problem

For the case of an exact set of compatible A's and B's with known correspondence, the AX=XB problem was solved decades ago. However, in many applications, data streams containing the A's and B's will often have different sampling rates or will be asynchronous. For these reasons and the fact that each stream may contain gaps in information, methods that require minimal a priori knowledge of the correspondence between A's and B's would be superior to the existing algorithms that require exact correspondence. We present an information-theoretic algorithm for recovering X from a set of A's and a set of B's that does not require a priori knowledge of correspondences. The algorithm views the problem in terms of distributions on the group SE(3), and minimizing the Kullback-Leibler divergence of these distributions with respect to the unknown X. This minimization is performed by an efficient numerical procedure that reliably recovers an unknown X.