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For an earth observing satellite, a line rate is the number of lines which the CCD of push broom type camera scans in a second. It can be easily calculated by ground velocity divided by ground sample distance. Accurate calculation of line rate is necessary to obtain high quality image using TDI CCD. The earth observing satellite has four types of imaging missions which are strip imaging, stereo imaging, multi-point imaging, and arbitrary directional imaging. For the first three types of imaging, ground scanning direction is aligned with satellite velocity direction. Therefore, if the orbit propagation and spacecraft attitude information are available, the ground velocity and ground sample distance could be easily calculated. However, the calculation method might not be applicable to the arbitrary directional imaging. In the arbitrary directional imaging mode, the ground velocity is not fixed value which could be directly derived by orbit information. Furthermore, the ground sample distance might not be easily calculated by simple trigonometry which is possible for the other types of imaging. In this paper, we proposed a line rate calculation method for the arbitrary directional imaging. We applied spherical geometry to derive the equation of ground point which is the intersection between the line of sight vector of the camera and earth surface. The derivative of this equation for time is the ground velocity except the factor of earth rotation. By adding this equation and earth rotation factor, the true ground velocity vector could be derived. For the ground sample distance, we applied the equation of circle and ellipse for yaw angle difference. The equation of circle is used for the yaw angle representation on the plane which is orthogonal to the line of sight vector. The equation of ellipse is used for the yaw angle representation on the ground surface. We applied the proposed method to the KOMPSAT-3A (Korea Multi-Purpose Satellite 3A) mission which is the first Korean satellite with optical and infrared sensor. The satellite was launched by a Dnepr on 26 March 2015 and started normal operation on September 2015. The payload of the satellite is AEISS-A(Advanced Earth Imaging Sensor System-A) which has 0.55m GSD for panchromatic image, 2.2m GSD for multi-spectral image, and day-and-night infrared image. The main mission objective of the satellite is providing high resolution electro-optical images and infrared images for GIS application. By applying the proposed method, the line rate error was reduced to about 0.2% from 0.5% of previous method. The arbitrary directional imaging mode became a major operation mode and various application modes including due north directional imaging, pitch steering imaging, pitch step imaging are now developing. These application modes are based on technical achievement of the proposed method. In this paper, the details of line rate calculation method are described. The experimental results show the accuracy of the proposed method is less than 0.2% in average. For the application results, the mission operation of KOMPSAT-3A and arbitrary directional imaging results are described.
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