A Star Sensor On-Orbit Calibration Method Based on Singular Value Decomposition

Abstract

The navigation accuracy of a star sensor depends on the estimation accuracy of its optical parameters, and so, the parameters should be updated in real time to obtain the best performance. Current on-orbit calibration methods for star sensors mainly rely on the angular distance between stars, and few studies have been devoted to seeking new calibration references. In this paper, an on-orbit calibration method using singular values as the calibration reference is introduced and studied. Firstly, the camera model of the star sensor is presented. Then, on the basis of the invariance of the singular values under coordinate transformation, an on-orbit calibration method based on the singular-value decomposition (SVD) method is proposed. By means of observability analysis, an optimal model of the star combinations for calibration is explored. According to the physical interpretation of the singular-value decomposition of the star vector matrix, the singular-value selection for calibration is discussed. Finally, to demonstrate the performance of the SVD method, simulation calibrations are conducted by both the SVD method and the conventional angular distance-based method. The results show that the accuracy and convergence speed of both methods are similar; however, the computational cost of the SVD method is heavily reduced. Furthermore, a field experiment is conducted to verify the feasibility of the SVD method. Therefore, the SVD method performs well in the calibration of star sensors, and in particular, it is suitable for star sensors with limited computing resources.

An On-Orbit Calibration Method of Star Sensor Based on Angular Distance Subtraction

“…On the basis of Test 2, we compare the IADS2 method with the AD method and the previously proposed singular value decomposition(SVD) method [22]. The average number of stars per frame was 7.7 stars, and three sets of experiments were conducted.…”

Coresets for the Average Case Error for Finite Query Sets

“…In addition, our algorithms extend also to SVD, PCA, and LMS where these methods are known for their usages and efficiencies in discovering a low dimensional representation of high dimensional data. From a practical point of view, SVD showed promising results when dealing with on calibration of a star sensor on-orbit calibration [ 52 ], denoising a 4-dimensional computed tomography of the brain in stroke patients [ 53 ], removal of cardiac interference from trunk electromyogram [ 54 ], among many other applications.…”

Detection of Degraded Star Observation Using Singular Values for Improved Attitude Determination

“…The primary contribution lies in the computation of individual star observation quality by utilizing the singular values among stars. Singular values have also been adopted in star identification techniques [ 23 , 24 ] and calibration [ 25 ] due to their insensitivity to attitude changes, making them suitable as reference values for determining the degree of error in star observations. To quantify this, we introduce p-value hypothesis testing to derive a quantized error level.…”