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We show how to recover the 6-DOF transform between two sensors mounted rigidly on a moving body, a form of extrinsic calibration useful for data fusion. Our algorithm takes noisy, per-sensor incremental egomotion observations (i.e., incremental poses) as input and produces as output an estimate of the maximum-likelihood 6-DOF calibration relating the sensors and accompanying uncertainty. The 6-DOF transformation sought can be represented effectively as a unit dual quaternion with 8 parameters subject to two constraints. Noise is explicitly modeled (via the Lie algebra), yielding a constrained Fisher Information Matrix and Cramer-Rao Lower Bound. The result is an analysis of motion degeneracy and a singularity-free optimization procedure. The method requires only that the sensors travel together along a motion path that is non-degenerate. It does not require that the sensors be synchronized, have overlapping fields of view, or observe common features. It does not require construction of a global reference frame or solving SLAM. In practice, from hand-held motion of RGB-D cameras, the method recovered inter-camera calibrations accurate to within ~0.014 meter and ~0.022 radians (about 1 cm and 1 degree). |
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