An analysis on the Earth geoid surface variation effect for use of the tilt sensor in celestial navigation system

The celestial navigation is one of alternatives to GPS system and can be used as a backup of GPS. In the celestial navigation system using more than two star trackers, the vehicle's ground position can be solved based on the star trackers' attitude information if the vehicle's local vertical or horizontal angle is given. In order to determine accurate ground position of flight vehicle, the high accurate local vertical angle measurement is one of the most important factors for navigation performance. In this paper, the Earth geophysical deflection was analyzed in the assumption of using the modern electrolyte tilt sensor as a local vertical sensor for celestial navigation system. According to the tilt sensor principle, the sensor measures the tilt angle from gravity direction which depends on the Earth geoid surface at a given position. In order to determine the local vertical angle from tilt sensor measurement, the relationship between the direction of gravity and the direction of the Earth center should be analyzed. Using a precision orbit determination software which includes the JGM-3 Earth geoid model, the direction of the Earth center and the direction of gravity are extracted and analyzed. Appling vector inner product and cross product to the both extracted vectors, the magnitude and phase of deflection angle between the direction of gravity and the direction of the Earth center are achieved successfully. And the result shows that the angle differences vary as a function of latitude and altitude. The maximum 0.094$^{circ}$angle difference occurs at 45$^{circ}$latitude in case of 1000 Km altitude condition.