Abstract: The implementation of autonomous navigation using line-of-sight measurements is receiving considerable attention in research. In this paper, a twice-rotation multiplicative measurement model for observed unit vectors is introduced which attempts to deal with the non-norm of the additive measurement model and the impractical error distribution of the multiplicative measurement model. The error is modeled as twice rigid rotations of the true direction about axes orthogonal to it. Though the ultimate form of the model is identical to that of the multiplicative measurement model, the rotation angle obeys the Rayleigh random distribution. The statistical characteristics of the estimation error are obtained and the speciality of couple vectors is developed, followed by geometrical explanation. Results of numerical tests show that the twice-rotation multiplicative measurement model well makes up for the error caused by the linearized additive measurement model, consequently more accurate. Potential areas to apply the model are hereby given.

Key words: navigation, autonomous navigation, unit vector, multiplicative measurement model, twice rigid rotation, Rayleigh distribution, earth observing