Quaternion normalization in spacecraft attitude determination
Methods are presented to normalize the attitude quaternion in two extended Kalman filters (EKF), namely, the multiplicative EKF (MEKF) and the additive EKF (AEKF). It is concluded that all the normalization methods work well and yield comparable results. In the AEKF, normalization is not essential, since the data chosen for the test do not have a rapidly varying attitude. In the MEKF, normalization is necessary to avoid divergence of the attitude estimate. All of the methods of the methods behave similarly when the spacecraft experiences low angular rates.
Quantum Mechanics at Planck scale is considered as a deformation of the conventional Quantum Mechanics. Similar to the earlier works of the author, the main object of deformation is the density matrix. On this basis a notion of the entropy density is introduced that is a matrix value used for a detail study of the Information Problem at the Universe, and in particular, for the Information Paradox Problem.