Further Studies on Singular Value Method for Star Pattern Recognition and Attitude Determination
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rther Studies on Singular Value Method for Star Pattern Recognition and Attitude Determination Jer-Nan Juang,1 and Yu-Chi Wang2
Abstract The objective of this paper is to study the effectiveness of a star pattern recognition method using singular value decomposition of a measured unit column vector matrix in a measurement frame and the corresponding catalog vector matrix in a reference frame. The approach is to use sensitivity analysis to define an effectiveness measure for a pairing process for individual measured and cataloged stars. The sensitivity of singular values relative to separation angle of star vectors will be studied to establish their correlation. A new method is proposed to generate the mission catalog to improve the quality of pattern recognition in speed and accuracy.
Introduction Star recognition for attitude determination is based on the invariant properties from coordinate transformation. Many of the invariant properties, such as angular separation, brightness of star, shape of triangles with vertices of star, and constellations, have been used for star identification [1–9]. One challenge in star recognition arises during initialization and recovery from sudden failure of star trackers. It is commonly called the lost-in-space problem. One popular pattern recognition method uses triplet angular separation matching, which is discussed by Gottlieb [10]. Mortari [8] introduced a Search-Less algorithm, where angular separation is indexed as integer, including a procedure to directly access all possible star pairs that correspond to a given measured star pair. For the past three decades, Davenports q method [11–15] and the Singular Value Decomposition (SVD) method by Markley [14] are the most robust estimators in 1 Professor, Department of Engineering Science, National Cheng-Kung University, Tainan 70101, Taiwan; Adjunct Professor, Texas A&M University, USA; Fellow AAS, AIAA, ASME. 2 Graduate student, Department of Engineering Science, National Cheng Kung University, Tainan 70101, Taiwan.
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the attitude determination problem. The q method minimizes the Wahba’s loss function [11] to compute the optimal quaternion as the eigenvector of a symmetric 4 ⫻ 4 matrix associated with the largest eigenvalue. The SVD solution is equivalent to the original solution by Farrell and Stuelpnagel [18]. The difference is that computing the SVD is one of the most robust numerical algorithms. On the other hand, Juang, Kim, and Junkins [19] developed a simple and inexpensive attitude initialization method for solving the lost-in-space problem by introducing other unique and transformation invariant properties. These invariant properties are derived from the SVD of the reference star vectors and their corresponding vectors measured in the camera axes used for both star pattern recognition and attitude determination. The advantage of this method is that the pattern recognition is extremely fast, since only three singular values are compared, no matter how many vectors are considered. This is desired
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