An Accurate and Efficient Gaussian Fit Centroiding Algorithm for Star Trackers
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An Accurate and Efficient Gaussian Fit Centroiding Algorithm for Star Trackers Tjorven Delabie1 · Joris De Schutter1 · Bart Vandenbussche2
© American Astronautical Society 2015
Abstract This paper presents a novel centroiding algorithm for star trackers. The proposed algorithm, which is referred to as the Gaussian Grid algorithm, fits an elliptical Gaussian function to the measured pixel data and derives explicit expressions to determine the centroids of the stars. In tests, the algorithm proved to yield accuracy comparable to that of the most accurate existing algorithms, while being significantly less computationally intensive. Hence, the Gaussian Grid algorithm can deliver high centroiding accuracy to spacecraft with limited computational power. Furthermore, a hybrid algorithm is proposed in which the Gaussian Grid algorithm yields an accurate initial estimate for a least squares fitting method, resulting in a reduced number of iterations and hence reduced computational cost. The low computational cost allows to improve performance by acquiring the attitude estimates at a higher rate or use more stars in the estimation algorithms. It is also a valuable contribution to the expanding field of small satellites, where it could enable low-cost platforms to have highly accurate attitude estimation. Keywords Star tracker · Centroiding algorithm
Presented at the Space Flight Mechanics Meeting. Kauai, Hawaii. February 10-14, 2013. Tjorven Delabie
[email protected] 1
Department of Mechanical Engineering, KU Leuven, Celestijnenlaan 300B, Heverlee, Belgium
2
Department of Astronomy, KU Leuven, Celestijnenlaan 300B, Heverlee, Belgium
J of Astronaut Sci
Introduction Accurate attitude determination is a crucial aspect in many spacecraft missions. Several sensors to determine the attitude of a spacecraft have been developed, of which the star tracker is the most accurate [1]. This sensor estimates the attitude of the spacecraft by comparing star positions in an image taken on board of the spacecraft with a database of known star positions. The attitude determination error of a star tracker depends greatly on the accuracy of the algorithm that estimates the centroids of the stars in the focal plane, referred to as the centroiding algorithm [2]. To facilitate the determination of these centroids with subpixel accuracy, the optics of the star tracker are slightly defocused so that the star light is spread out over several pixels [3]. A variety of different algorithms to determine star centroids has been developed. An overview of the most common of these algorithms is given in [4] and [5]. The most accurate of these centroiding algorithms rely on fitting a point spread function (PSF) to the measured pixel data [6]. This point spread function is the impulse response of the imaging system [7] and can be very accurately modeled by a Gaussian profile [8]. While these algorithms determine the star centroid with great accuracy, they are computationally expensive because they use an iterative least squares funct
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