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.