Design of on-board calibration methods for a digital sun sensor based on Levenberg–Marquardt algorithm and Kalman filters

Digital sun sensor is one of the most important sensors used in the Attitude Determination System (ADS) of the satellite. Due to the harsh environmental conditions that exist in the space, various distortions may occur in the sun sensor optical system that lead to the reduced accuracy of this equipment. So, it is necessary to recalibrate the optical parameters of the aforementioned sensors. For this purpose, first a novel attitude independent error model is proposed for the SS-411 sun sensor that includes the central point of the CCD array, installation error, filter thickness and sensor misalignment. So, the mutual interfaces between the sensor parameters are considered in the developed model. In order to extract the sensor parameters, a nonlinear optimization technique called the Levenberg–Marquardt is applied to the developed model as a batch algorithm. In addition, the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF) have been utilized as sequential strategies. It will be shown that by considering a worst case of variation amount for sensor parameters, an accuracy improvement of about 17° is achieved by the developed calibration algorithms. Comparison between the developed algorithms represents that UKF has higher accuracy, shorter time convergence but higher computational load.