Filters with quaternions for localization

Rangaprasad Arun Srivatsan, Mengyun Xu, Nicolas Zevallos, and Howie Choset, Probabilistic pose estimation using a Bingham distribution-based linear filter, The International Journal of Robotics Research DOI: 10.1177/0278364918778353.

Pose estimation is central to several robotics applications such as registration, hand–eye calibration, and simultaneous localization and mapping (SLAM). Online pose estimation methods typically use Gaussian distributions to describe the uncertainty in the pose parameters. Such a description can be inadequate when using parameters such as unit quaternions that are not unimodally distributed. A Bingham distribution can effectively model the uncertainty in unit quaternions, as it has antipodal symmetry, and is defined on a unit hypersphere. A combination of Gaussian and Bingham distributions is used to develop a truly linear filter that accurately estimates the distribution of the pose parameters. The linear filter, however, comes at the cost of state-dependent measurement uncertainty. Using results from stochastic theory, we show that the state-dependent measurement uncertainty can be evaluated exactly. To show the broad applicability of this approach, we derive linear measurement models for applications that use position, surface-normal, and pose measurements. Experiments assert that this approach is robust to initial estimation errors as well as sensor noise. Compared with state-of-the-art methods, our approach takes fewer iterations to converge onto the correct pose estimate. The efficacy of the formulation is illustrated with a number of examples on standard datasets as well as real-world experiments.

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