{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T22:14:18Z","timestamp":1782944058948,"version":"3.54.5"},"reference-count":23,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2011,7,25]],"date-time":"2011-07-25T00:00:00Z","timestamp":1311552000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The star centroid estimation is the most important operation, which directly affects the precision of attitude determination for star sensors. This paper presents a theoretical study of the systematic error introduced by the star centroid estimation algorithm. The systematic error is analyzed through a frequency domain approach and numerical simulations. It is shown that the systematic error consists of the approximation error and truncation error which resulted from the discretization approximation and sampling window limitations, respectively. A criterion for choosing the size of the sampling window to reduce the truncation error is given in this paper. The systematic error can be evaluated as a function of the actual star centroid positions under different Gaussian widths of star intensity distribution. In order to eliminate the systematic error, a novel compensation algorithm based on the least squares support vector regression (LSSVR) with Radial Basis Function (RBF) kernel is proposed. Simulation results show that when the compensation algorithm is applied to the 5-pixel star sampling window, the accuracy of star centroid estimation is improved from 0.06 to 6 \u00d7 10\u22125 pixels.<\/jats:p>","DOI":"10.3390\/s110807341","type":"journal-article","created":{"date-parts":[[2011,7,25]],"date-time":"2011-07-25T12:35:29Z","timestamp":1311597329000},"page":"7341-7363","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["A Novel Systematic Error Compensation Algorithm Based on Least Squares Support Vector Regression for Star Sensor Image Centroid Estimation"],"prefix":"10.3390","volume":"11","author":[{"given":"Jun","family":"Yang","sequence":"first","affiliation":[{"name":"Department of Automation, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7163-345X","authenticated-orcid":false,"given":"Bin","family":"Liang","sequence":"additional","affiliation":[{"name":"Department of Automation, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tao","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Automation, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jingyan","family":"Song","sequence":"additional","affiliation":[{"name":"Department of Automation, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2011,7,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1109\/TAES.2002.1008988","article-title":"Accuracy performance of star trackers\u2013A tutorial","volume":"38","author":"Liebe","year":"2002","journal-title":"IEEE Trans. Aero. Electron. Syst"},{"key":"ref_2","unstructured":"Katake, AB (2006). Modeling, Image Processing and Attitude Estimation of High Speed Star Sensors, Ph.D. Thesis, Texas A&M University, College Station, TX, USA."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Jahne, B (2004). Practical Handbook on Image Processing for Scientific Application, CRC Press. [2nd ed].","DOI":"10.1201\/9780849390302"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1117\/12.7973407","article-title":"Performance analysis and size optimization of focal planes for point-source tracking algorithm applications","volume":"23","author":"Grossman","year":"1984","journal-title":"Opt. Eng"},{"key":"ref_5","first-page":"101","article-title":"Shape measurement in industry with sub-pixel definition","volume":"150","author":"Hegedus","year":"1985","journal-title":"Acta Polytech. Scand. Appl"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"930","DOI":"10.1117\/12.7974173","article-title":"Optical tracking using charge-coupled devices","volume":"26","author":"Stanton","year":"1987","journal-title":"Opt. Eng"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1320","DOI":"10.1117\/12.55947","article-title":"Elimination of systematic error in subpixel accuracy centroid estimation","volume":"30","author":"Alexander","year":"1991","journal-title":"Opt. Eng"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2465","DOI":"10.1117\/12.59956","article-title":"Subpixel accuracy location estimation from digital signals","volume":"31","author":"Jean","year":"1992","journal-title":"Opt. Eng"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/S0094-5765(02)00199-6","article-title":"Enhancement of the centroiding algorithm for star tracker measure refinement","volume":"53","author":"Rufino","year":"2003","journal-title":"Acta Astronaut"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3145","DOI":"10.1007\/s11431-010-4129-7","article-title":"Systematic error analysis and compensation for high accuracy star centroid estimation of star tracker","volume":"53","author":"Jia","year":"2010","journal-title":"Sci. China Ser. E: Eng. Mater. Sci"},{"key":"ref_11","unstructured":"Eisenman, AR, and Liebe, CC (1998, January 1\u20134). The Advancing State-of-the Art in Second Generation Star Trackers. Aspen, CO, USA."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2676","DOI":"10.1109\/TIP.2006.877363","article-title":"CCD noise removal in digital images","volume":"15","author":"Faraji","year":"2006","journal-title":"IEEE T. Image. Proc"},{"key":"ref_13","first-page":"666","article-title":"Research of hyper accuracy subpixel subdivision location algorithm for star image","volume":"31","author":"Li","year":"2005","journal-title":"Opt. Technol"},{"key":"ref_14","unstructured":"Smith, WJ (1992). Modern Lens Design: A Resourse Manual, McGraw-Hill."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Vapnik, V (1995). The Nature of Statistical Learning Theory, Springer-Verlag.","DOI":"10.1007\/978-1-4757-2440-0"},{"key":"ref_16","first-page":"281","article-title":"Support vector method for function approximation, regression estimation and signal processing","volume":"9","author":"Vapnik","year":"1996","journal-title":"Adv. Neural Inf. Proc. Syst"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1023\/B:STCO.0000035301.49549.88","article-title":"A tutorial on support vector regression","volume":"14","author":"Scholkopf","year":"2004","journal-title":"Stat. Comput"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1023\/A:1018628609742","article-title":"Least squares support vector machine classifiers","volume":"9","author":"Suykens","year":"1999","journal-title":"Neuroendocrinol. Proc. Lett"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Suykens, JAK, Gestel, TV, Brabanter, JD, Moor, BD, and Vandewalle, J (2002). Least Squares Support Vector Machines, World Scientific.","DOI":"10.1142\/9789812776655"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/j.talanta.2006.10.022","article-title":"A consensus least squares support vector regression (LS-SVR) for analysis of near-infrared spectra of plant samples","volume":"72","author":"Li","year":"2007","journal-title":"Talanta"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/j.chemolab.2010.02.003","article-title":"pKa modeling and prediction of a series of pH indicators through genetic algorithm-least square support vector regression","volume":"101","author":"Goodarzi","year":"2010","journal-title":"Chemom. Intell. Lab"},{"key":"ref_22","first-page":"558","article-title":"Astronomical calibration method and observation analysis for high-accuracy star sensor","volume":"14","author":"Li","year":"2006","journal-title":"Opt. Precis. Eng"},{"key":"ref_23","unstructured":"IERS Technical Note No. 32. Available online: http:\/\/www.iers.org\/nn_11216\/SharedDocs\/Publikationen\/EN\/IERS\/Publications\/tn\/TechnNote32\/tn32,templateId=raw,property=publicationFile.pdf\/tn32.pdf (accessed on 25 April 2010)."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/11\/8\/7341\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:56:52Z","timestamp":1760219812000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/11\/8\/7341"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,7,25]]},"references-count":23,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2011,8]]}},"alternative-id":["s110807341"],"URL":"https:\/\/doi.org\/10.3390\/s110807341","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,7,25]]}}}