Abstract
The problem of spacecraft orientation through observations of space objects having zero as well as nonzero daily parallax is solved by means of quaternion algebra. It is assumed that there are unit vectors, which are known directions of several space objects in the inertial reference system, and the same unit vectors are measured in the body-fixed reference system. A new quaternion algorithm is suggested for the case when measurements of nearbody objects are used. The solution of the problem is formulated as a quaternion conditional extremum problem, and both the position vector and three-axis attitude of the spacecraft are determined by the Lagrange multipliers method. The application of quaternions avoids numerous trigonometric calculations and gives a solution suitable for both theoretical analysis and computations. The method can also be useful in space photogrammetry and astronomy.
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