Software and Mathematic Alternative to Infrared Vertical Sensor During Orbital Motion of a Spacecraft

We consider a task of software and mathematic defining the angular position (in roll and pitch) of a spacecraft during its orbital motion under the influence of gravity torque. We suggest a new algorithm of roll and pitch angles estimation by data of only angular rate sensor. One may apply the algorithm as an alternative to measurements of the infrared vertical sensor in case of its absence or failure. The algorithm is obtained based on a solution of the two-point boundary value problem by means of analytic synthesis of modal observer for discrete identification model. A reasonable choice of parameters of the identification model and estimation algorithm is presented. Mathematic simulation and statistic tests confirm the algorithm efficiency. The limits of the algorithm applicability by the values of angles and angular rates are determined. The limits of applicability of the suggested algorithm as well as its operating speed allow applying the algorithm in real time on board an orbiting spacecraft.