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Uniform Star Catalogue using GWKM Clustering for Application in Star Sensors

Published online by Cambridge University Press:  21 January 2019

Farshad Somayehee ,
Amir Ali Nikkhah  and
Jafar Roshanian
Farshad Somayehee
Affiliation:
(K. N. Toosi University of Technology, P.O.B. 16569-83911, Tehran, Iran)
Amir Ali Nikkhah*
Affiliation:
(K. N. Toosi University of Technology, P.O.B. 16569-83911, Tehran, Iran)
Jafar Roshanian
Affiliation:
(K. N. Toosi University of Technology, P.O.B. 16569-83911, Tehran, Iran)
*
(E-mail: nikkhah@kntu.ac.ir)
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Abstract

In this paper, a novel algorithm of weighted k-means clustering with geodesic criteria is presented to generate a uniform database for a star sensor. For this purpose, selecting the appropriate star catalogue and desirable minimum magnitude and eliminating double stars are among the steps of the uniformity process. Further, Delaunay triangulation and determining the scattered data density by using a Voronoi diagram were used to solve the problems of the proposed clustering method. Thus, by running a Monte Carlo simulation to count the number of stars observed in different fields of view, it was found that the uniformity leads to a significant reduction of the probability of observing a large number of stars in all fields of view. In contrast, the uniformity slightly increased the field of view needed to observe the minimum number of required stars for an identification algorithm.

Keywords

Optimized star catalogueGeodesic k-means clusteringDelaunay triangulationScattered data density
Type
Research Article
Information
The Journal of Navigation , Volume 72 , Issue 4 , July 2019 , pp. 948 - 964
Copyright
Copyright © The Royal Institute of Navigation 2019 

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References

REFERENCES

Bagirov, A. M. (2008). Modified global k-means algorithm for minimum sum-of-squares clustering problems. Pattern Recognition, 41(10), 3192–3199.10.1016/j.patcog.2008.04.004Google Scholar
Bauer, R. (2000). Distribution of points on a sphere with application to star catalogs. Journal of Guidance, Control, and Dynamics, 23(1), 130–137.10.2514/2.4497Google Scholar
Buchta, C., Kober, M., Feinerer, I. and Hornik, K. (2012). Spherical k-means clustering. Journal of Statistical Software, 50(10), 1–22.Google Scholar
De Berg, M., Van Kreveld, M., Overmars, M. and Schwarzkopf, O. C. (2000). Computational Geometry. Springer, 1–17.10.1007/978-3-662-04245-8Google Scholar
De Loera, J. A., Rambau, J. and Santos, F. (2010). Triangulations Structures for algorithms and applications. Springer-Verlag Berlin Heidelberg.Google Scholar
Delaunay, B. (1934). On the null sphere, In memory of Georges Voronoi. Bulletin de l'Académie des Sciences de l'URSS, Classe des Sciences Mathématiques et Naturelles, 6 (793–800).Google Scholar
Dhillon, I. S. and Modha, D. S. (2001). Concept decompositions for large sparse text data using clustering. Machine learning, 42 (1–2), 143–175.10.1023/A:1007612920971Google Scholar
Ebrahimi, M., Roshanian, J., Yazdani, S. and BekranBehesht, S. (2017). Develop mission catalog and robust pattern recognition algorithm to enhance the performance of the star tracker throughout the day. Tabriz Mechanical Engineering, 50(2), 20–26.Google Scholar
Estivill-Castro, V. (2002). Why so many clustering algorithms: a position paper. ACM SIGKDD Explorations Newsletter, 4(1), 65–75.10.1145/568574.568575Google Scholar
Gärtner, B. and Hoffmann, M. (2013). Computational Geometry Lecture Notes 1 HS 2012. Citeseer.Google Scholar
Hartigan, J. A. and Wong, M. A. (1979). Algorithm AS 136: A k-means clustering algorithm. Journal of the Royal Statistical Society Series C (Applied Statistics), 28(1), 100–108.Google Scholar
Hirvonen, R. A. (1961). The reformation of geodesy. Journal of Geophysical Research, 66(5), 1471–1478.10.1029/JZ066i005p01471Google Scholar
Hopcroft, J. and Kannan, R. (2014). Foundations of data science. Available at: https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/book-No-Solutions-Aug-21-2014.pdf.Google Scholar
Jain, A. K. (2010). Data clustering: 50 years beyond K-means. Pattern Recognition Letters, 31(8), 651–666.10.1016/j.patrec.2009.09.011Google Scholar
Kim, H.-Y. and Junkins, J. L. (2002). Self-organizing guide star selection algorithm for star trackers: thinning method. Aerospace Conference Proceedings, IEEE, 5.Google Scholar
Kohout, J., Kolingerová, I. and Žára, J. (2005). Parallel Delaunay triangulation in E2 and E3 for computers with shared memory. Parallel Computing, 31(5), 491–522.10.1016/j.parco.2005.02.010Google Scholar
Li, J., Wang, G. and Wei, X. (2018). Generation of Guide Star catalog for Star Trackers. IEEE Sensors Journal, 11(5), 543–548.Google Scholar
Li, X., Yang, J., Zhang, L., Li, S. and Jin, G. (2014). A new simplified selection algorithm of the guide star catalog for a star sensor. The Journal of Navigation, 67(6), 984–994.10.1017/S0373463314000411Google Scholar
Liu, F. C., Liu, Z. H., Liu, W., Liang, D. S., Cui, K. (2013). A research on navigation star catalog selection algorithm based on SVM. Advanced Materials Research, 706, 613–617.Google Scholar
Martín-Fleitas, J., Mora, A., Sahlmann, J., Kohley, R., Massart, B., L'hermitte, J. and Roy, M. L., Paulet, P. (2014). Enabling Gaia observations of naked-eye stars. In pace Telescopes and Instrumentation 2014: Optical, Infrared, and Millimeter Wave. International Society for Optics and Photonics. SPIE 9143.10.1117/12.2056325Google Scholar
Murphy, K. P. (2012). Machine learning: a probabilistic perspective. Adaptive computation and machine learning, MIT Press, Cambridge.Google Scholar
O'Neill, B. (1966). Elementary differential geometry. Orlando, Florida: Academic press.Google Scholar
Pisacane, V. L. (2005). Fundamentals of space systems. Johns Hopkins University/Appli.Google Scholar
Plaue, M., Bärwolff, G. and Schwandt, H. (2014). On measuring pedestrian density and flow fields in dense as well as sparse crowds. In Pedestrian and Evacuation Dynamics 2012. Springer, 411–424.10.1007/978-3-319-02447-9_34Google Scholar
Prakash, A., Wu, A., Liu, J. and Li, R. K. (2002). Performance based evaluation of star catalog generation methods. In AIAA Guidance, Navigation, and Control Conference and Exhibition, 4669.10.2514/6.2002-4669Google Scholar
Renka, R. J. (1997). Algorithm 772: STRIPACK: Delaunay triangulation and Voronoi diagram on the surface of a sphere. ACM Transactions on Mathematical Software (TOMS), 23(3), 416–434.10.1145/275323.275329Google Scholar
Roshanian, J., Yazdani, S., Ebrahimi, M. and Kabutarkhani, M. J. H. (2015a). Uniform Star catalog Generation and Comparison Criterion Introduction for a Typical Star Tracker. Modares Mechanical Engineering, 15(3), 344–352.Google Scholar
Roshanian, J., Hasani, S. M. M., Yazdani, S. and Ebrahimi, M. (2015b). Star catalog Criteria Selection and Mission catalog Update for a Typical Star Tracker, Journal of Space Science & Technology, 5(4), 8.Google Scholar
Roshanian, J., Yazdani, S., BekranBehesht, S. and Ebrahimi, M. (2015c). 2MASS infrared star catalog data mining for use onboard a daytime star tracker. In Recent Advances in Space Technologies (RAST), 2015 7th International Conference on. IEEE, 75–79. doi:10.1109/RAST.2015.7208319.Google Scholar
Saifudin, M.A. Silalahi, B. P. and Sitanggang, I. S. (2015). Star catalog Generation for Satellite Attitude Navigation Using Density Based Clustering. Journal of Computer Science, 11(12), 1082–1089.10.3844/jcssp.2015.1082.1089Google Scholar
Samaan, M. A., Bruccoleri, C., Mortari, D. and Junkins, J. L. (2004). Novel techniques for creating nearly uniform star catalog. Advances in the Astronautical Sciences, 116(979), 1–13.Google Scholar
Somayehee, F., Nikkhah, A. A. and Roshanian, J. (2018). Uniform star catalog using triangulation for application in star sensor. Modares Mechanical Engineering, 18(04), 725–734.Google Scholar
Sonagara, D. and Badheka, S. (2014). Comparison of basic clustering algorithms. International Journal of Computer Science and Mobile Computing, 3(10), 58–61.Google Scholar
Spratling, B. B. and Mortari, D. (2009). A survey on star identification algorithms. Algorithms, 2(1), 93–107. doi:10.3390/a2010093.Google Scholar
Steffen, B. and Seyfried, A. (2010). Methods for measuring pedestrian density, flow, speed and direction with minimal scatter. Physica A: Statistical Mechanics and its Applications, 389(9), 1902–1910.10.1016/j.physa.2009.12.015Google Scholar
Zhang, C., Chen, C. and Shen, X. (2004). A new guide star selection algorithm for star tracker. In Intelligent Control and Automation, 2004. WCICA 2004. Fifth World Congress on. IEEE, 5445–5449.Google Scholar
Zhang, G. (2017). Star Identification: Methods, Techniques and Algorithms. Springer.10.1007/978-3-662-53783-1Google Scholar
Zhong, S. (2005). Efficient online spherical k-means clustering. In Neural Networks, Proceedings. 2005 IEEE International Joint Conference on. IEEE, 3180–3185.Google Scholar