Calibration of Extrinsic Transformation Using Manifold Optimization

Data fusion with multiple heterogeneous sensors has shown great importance for motion control and navigation filter design of autonomous vehicles. However, data fusion often
requires the prior knowledge of the extrinsic transformations between sensors. This paper focuses on the usage of manifold optimization to calibrate the extrinsic transformation for a pair of sensors from a batch of measurements. Instead of reparameterization the transformation matrix in other forms, we formulate an objective function directly with the special Euclidean group.
Then this manifold optimization problem is solved iteratively in a Gauss-Newton fashion. The usage of manifold optimization guarantees the obtained result being strictly within the special
Euclidean group without the need of further operations like normalization and orthogonalization. The experimental results on both synthetic and real data show the superiority and robustness of the proposed method. Considering the performance and time consumption, the proposed approach is a good option for real applications.