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Kalman filtering for non-Euclidean setting

Kalman filter

SPD matrices

  • Tyagi, A. and Davis, J. W. (2008). “A Recursive Filter For Linear Systems on Rieman- nian Manifolds.” In IEEE Conference on Computer Vision and Pattern Recognition.

Grassmannians

  • Srivastava, A. and Klassen, E. (2004). “Bayesian and Geometric Subspace Tracking.” Advances in Applied Probability, 36(1): 43–56.

Stiefel manifold

  • Tompkins, F. and Wolfe, P. J. (2007). “Bayesian Filtering on the Stiefel Manifold.” In Computational Advances in Multi-Sensor Adaptive Processing, 261 – 264.

SE(n) group

  • Choi, C. and Christensen, H. I. (2011). “Robust 3D Visual Tracking Using Particle Filters on the SE(3) Group.” In IEEE International Conference on Robotics and Automation, 4384–4390.
  • Berger, J., Lenzen, F., Becker, F., Neufeld, A., & Schnörr, C. (2017). Second-Order Recursive Filtering on the Rigid-Motion Lie Group $ ${\text {SE}} _ {3} $ $ SE 3 Based on Nonlinear Observations. Journal of Mathematical Imaging and Vision, 58(1), 102-129.
  • Estimating SE(3) elements using a dual quaternion based linear Kalman filter
  • Articulated motion estimation from a monocular image sequence using spherical tangent bundles

Unscented Kalman filter

SPD matrices

  • Hauberg, S., Lauze, F., and Pedersen, K. S. (2013). “Unscented Kalman Filtering on Riemannian Manifolds.” Journal of Mathematical Imaging and Vision, 46: 103–120.

Lie groups

  • M. Brossard, S. Bonnabel and J. P. Condomines, "Unscented Kalman filtering on Lie groups," 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Vancouver, BC, 2017, pp. 2485-2491. doi: 10.1109/IROS.2017.8206066
  • Martin Brossard, Silvère Bonnabel, Axel Barrau. Unscented Kalman Filtering on Lie Groups for Fusion of IMU and Monocular Vision. submitted to the International Conference on Robotics and Automation (ICRA) 2018. 2017.
  • Barrau, A., & Bonnabel, S. (2018). Invariant Kalman Filtering. Annual Review of Control, Robotics, and Autonomous Systems, (0).
  • Unscented Kalman Filtering on Lie Groups for Fusion of IMU and Monocular Vision
  • Moving object tracking employing rigid body motion on matrix Lie groups

Kalman filter on parallel architectures

  • Cerati, G., Elmer, P., Lantz, S., McDermott, K., Riley, D., Tadel, M., ... & Yagil, A. (2015). Kalman filter tracking on parallel architectures. In Journal of Physics: Conference Series (Vol. 664, No. 7, p. 072008). IOP Publishing.
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