Installation Direction Analysis of Star Sensors by Hybrid Condition Number

With the development of space programs, autonomous navigation of spacecraft is required in case of emergencies. Celestial navigation is a kind of fully autonomous navigation method, which has widely been used in many space missions. Because of the measurement noise in the celestial navigation system, the geometric relations between the spacecraft and various celestial bodies have a great impact on navigation accuracy. The positions of the sun, Earth, and other planets are fixed at a certain time, but stars are distributed all over the sky. The position of the measured star is mainly determined by the pointing direction of the star sensor. To explicitly demonstrate the effect of different pointing directions, an improved observability analysis method based on the hybrid condition number of the observability matrix for a nonlinear system is presented. The impact of the pointing direction of the star sensor on the navigation accuracy is analyzed using this analysis method, with the star-Earth angle used as a measurement for a near-Earth satellite. Simulations show that the value of the hybrid condition number is in good agreement with the position estimation error. This analysis method and the corresponding analysis results are useful in the design, construction, and analysis of celestial navigation systems for spacecraft.