Algoritms of object three-dimensional orientation determination based on global satellite navigation systems

In recent years, global satellite navigation systems intended for high-precision observation of coordinates, velocity and time have received wide acceptance. Of great interest is to investigate ways for expansion of functional capabilities in user equipment of such systems, in particular, important is to investigate possibilities to carry out, based on global satellite navigation systems, angular coordinate observations for objects in space with a high degree of accuracy, e.g., spacecrafts, for which of vital importance is their basic angular position, with respect to which both antenna precision guidance to Earth and an orientation of solar batteries and star sensors take place. In general, angular coordinates of an object in space are described by Eulerian angles. To determine object angular coordinates, most widely used are an azimutal angle la, an angle of elevation yyy and angle of elevation yK, descriptive of an angular position of an object having made in TCCS (Topocentric Coordinate System) successively a rotation about the axis OX, by the angle of heel yK, about the axis OZ, by the angle of elevation y,, and about the axis OY, by the azimutal angle ya out of the original position y,, = yyy = yK = 0. The angular position of an object can be also determined through direction cosines of its two axes, e.g., longitudinal and lateral ones. To determine these angles by phase methods, it is necessary to mount on an antenna platform three antennas Ao, AI, and A*, which form two baselines. Antenna baselines are strongly fixed to object axes, e.g., baseline B1 is aligned with the longitudinal axis of the object, baseline Bz is tumed relative to baseline B, in the horizontal plane by an 90’ angle clockwise. The angular coordinates are determined from phase shifts of navigation spacecraft (NSC) signals received by the antennas, i.e., by the interferometric method. The phase shift of a NSC signal, receive4 onto twca antennas, and a cosine afthe angle between vector-baseline and vector-direction to NSC are related by the expression: hQ 2 d ’ cosa = (1)