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© 2016 by the authors. The authors would like to thank the support of the Nanosat Program of INTA institution and the specific research fund (FEI16/67) at the Complutense University of Madrid., Most satellites use an on-board attitude estimation system, based on available sensors. In the case of low-cost satellites, which are of increasing interest, it is usual to use magnetometers and Sun sensors. A Kalman filter is commonly recommended for the estimation, to simultaneously exploit the information from sensors and from a mathematical model of the satellite motion. It would be also convenient to adhere to a quaternion representation. This article focuses on some problems linked to this context. The state of the system should be represented in observable form. Singularities due to alignment of measured vectors cause estimation problems. Accommodation of the Kalman filter originates convergence difficulties. The article includes a new proposal that solves these problems, not needing changes in the Kalman filter algorithm. In addition, the article includes assessment of different errors, initialization values for the Kalman filter; and considers the influence of the magnetic dipole moment perturbation, showing how to handle it as part of the Kalman filter framework., Unión Europea. FP7, Universidad Complutense de Madrid, Sección Deptal. de Arquitectura de Computadores y Automática (Físicas), Fac. de Ciencias Físicas, TRUE, pub