A second order minimum-energy filter on the special orthogonal group

@article{Zamani2012ASO,
  title={A second order minimum-energy filter on the special orthogonal group},
  author={Mohammad Zamani and Jochen Trumpf and Robert E. Mahony},
  journal={2012 American Control Conference (ACC)},
  year={2012},
  pages={1895-1900}
}
This work documents a case study in the application of Mortensen's nonlinear filtering approach to invariant systems on general Lie groups. In this paper, we consider the special orthogonal group SO(3) of all rotation matrices. We identify the exact form of the kinematics of the minimum-energy (optimal) observer on SO(3) and note that it depends on the Hessian of the value function of the associated optimal control problem. We derive a second order approximation of the dynamics of the Hessian… CONTINUE READING

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