Development of Optimized Mathematical Model for Distortion Correction and Calibration for Sub-arc-sec Star Tracker

Star Trackers are an autonomous-absolute attitude sensors, deployed for space missions. These sensors consist of a camera with image processing algorithm. Sensor images the stars in the sky and determines the attitude in the form of quaternion’s (Qs) or direction cosine matrix (DCM). The accuracy of the measurement relies on the knowledge of correct position of stars in the detector frame. The exact position of the stars gets manipulated by factors like optical distortion, mounting tilts between the optical and detector planes, thermal expansion of opto-mechanical structure, gravitational effects, electronics noise in the system. leading to centroid computation inaccuracy. Conventionally in star sensors, these distortions are modelled by polynomial fitting. Such an approach calls for the usage of higher order polynomials to achieve better modelling accuracy having acceptable residual errors. For a high accuracy (<1 arc-sec) star tracker, the error budget for distortion residuals has to be as low as 0.5 arc-sec. Conventional methods [1] of implementing polynomials call for large number of coefficients, which also requires longer computation time. In this report, we are addressing the optical distortion and mounting tilts between the optical and detector plane viz., the systematic error created by the optics-detector assembly. Detailed studies on the development of optimized mathematical model for overall distortion correction in optics-detector assembly and its calibration aspects are also discussed.