Focal Length Deviation of Star Sensor Coupled with Optical Distortion:Modeling and Analysis

Accurate calibration of focal length deviation is the key to ensure that the star sensors outputs high-precision attitude information,and optical distortion is the primary source of focal length deviation.According to the geometric model of star sensor imaging and the optical distortion model,the mathematical model describing the coupling relationship between optical distortion and focal length deviation is established,and the expression describing the relationship between the optical distortion and the equivalent focal length deviation is derived.The reference distortion threshold δr_max of navigation star point is proposed for focal length deviation calibration.The simulation results show that the calibration accuracy of focal length deviation when selecting the star points that are all within the distortion threshold is 5 to 10 times higher than selecting those that are partly or all outside the distortion threshold,which reduces the influence of optical distortion on calibration accuracy of focal length deviation to a great extent.

This article focuses on the traditional focal length error calibration method that does not consider optical distortion, and its calibration results may not meet the requirements of high-precision attitude measurement. After analyzing the equivalent focal length error caused by optical distortion in star sensors, a mathematical model for coupling optical distortion and focal length error is established; From the analysis of the model, it was found that optical distortion affects the calibration results in focal length error calibration; By designing appropriate simulation comparative experiments, the relationship between the calibration of star sensor focal length error and optical distortion is verified, and the feasibility of controlling the distortion caused by optical distortion to minimize the impact of optical distortion on focal length error calibration is verified. This provides theoretical support for improving the accuracy of star sensor attitude determination and has certain reference value. For further research content, it is necessary to consider when the threshold of abnormal variables is exceeded δ R_ What measures should be taken to eliminate the serious impact of optical distortion during max.