Bias Estimations for Ill-posed Problem of Celestial Positioning Using the Sun and Precision Analysis

doi:10.11947/j.AGCS.2016.20150525

Abstract

Abstract: Lunar/Mars rovers own sun sensors for navigation, however, long-time tracking for the sun impacts on the real-time activity of navigation. Absolute positioning method by observing the sun with a super short tracking period such as 1 or 2 minutes is researched in this paper. Linear least squares model of altitude positioning method is deduced, and the ill-posed problem of celestial positioning using the sun is brought out for the first time. Singular value decomposition method is used to diagnose the ill-posed problem, and different bias estimations are employed and compared by simulative calculations. Results of the calculations indicate the superiority of bias estimations which can effectively improve initial values. However, bias estimations are greatly impacted by initial values, because the initial values converge at a line which passes by the real value and is vertical relative to the orientation of the sun. The research of this paper is of some value to application.

Key words: lunar/mars rovers navigation, celestial positioning, least squares method, Ill-posed problem, bias estimation, root mean square error

CLC Number:

P228

ZHAN Yinhu, ZHENG Yong, ZHANG Chao. Bias Estimations for Ill-posed Problem of Celestial Positioning Using the Sun and Precision Analysis[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(8): 911-918.

References

[1] GONG Weishu.Discussions on Localization Capabilities of MSL and MER Rovers[J].Annals of GIS,2015,21(1):69-79.
[2] TREBI-OLLENNU A,HUNTSBERGER T,CHENG Yang,et al.Design and Analysis of a Sun Sensor for Planetary Rover Absolute Heading Detection[J].IEEE Transactions on Robotics and Automation,2001,17(6):939-947.
[3] EISENMAN A R,LIEBE C C,PEREZ R.Sun Sensing on the Mars Exploration Rovers[C]//Aerospace Conference Proceedings.Big Sky,MT:IEEE,2002,5:2249-2262.
[4] KURODA Y,KUROSAWA T,TSUCHIYA A,et al.Accurate Localization in Combination with Planet Observation and Dead Reckoning for Lunar Rover[C]//Proceedings of IEEE International Conference on Robotics and Automation.New Orleans,LA:IEEE,2004,2:2092-2097.
[5] DEANS M C,WETTERGREEN D,VILLA D.A Sun Tracker for Planetary Analog Rovers[C]//Proceedings of the 8th International Symposium on Artificial Intelligence,Robotics and Automation in Space.Munich:[s.n.],2005:1-7.
[6] D'AMARIO L A.Mars Exploration Rovers Navigation Results[J].The Journal of the Astronautical Sciences,2006,54(2):129-173.
[7] FURGALE P,ENRIGHT J,BARFOOT T.Sun Sensor Navigation for Planetary Rovers:Theory and Field Testing[J].IEEE Transactions on Aerospace and Electronic Systems,2011,47(3):1631-1647.
[8] 邸凯昌.勇气号和机遇号火星车定位方法评述[J].航天器工程,2009,18(5):1-5.DI Kaichang.A Review of Spirit and Opportunity Rover Localization Methods[J].Spacecraft Engineering,2009,18(5):1-5.
[9] COZMAN F,KROTKOV E.Robot Localization Using a Computer Vision Sextant[C]//Proceedings of IEEE International Conference on Robotics and Automation.Nagoya,Aichi:IEEE,1995,1:106-111.
[10] ENRIGHT J,FURGALE P,BARFOOT T.Sun Sensing for Planetary Rover Navigation[C]//Proceedings of Aerospace Conference.Big Sky,MT:IEEE,2009:1-12.
[11] 杨鹏.基于太阳观测图像的月球车天文导航[D].杭州:浙江大学,2011.YANG Peng.Sun Observation Image Based Celestial Navigation for Lunar Rover[D].Hangzhou:Zhejiang University,2011.
[12] 李崇辉,郑勇,张超,等.一种无需精密整平的抗差天文定位方法[J].测绘学报,2013,42(6):810-816.LI Chonghui,ZHENG Yong,ZHANG Chao,et al.A Robust Celestial Positioning Method without Precise Leveling[J].Acta Geodaetica et Cartographica Sinica,2013,42(6):810-816.
[13] 王斌会.复共线性诊断方法的比较[J].统计与决策,2003(8):7-8.WANG Binhui.Comparison of Multiple Linear Diagnostic Methods[J].Statistics and Decision,2003(8):7-8.
[14] KUSCHE J,KLEES R.Regularization of Gravity Field Estimation from Satellite Gravity Gradients[J].Journal of Geodesy,2002,76(6-7):359-368.
[15] HANSEN P C,O'LEARY D P.The Use of the L-curve in the Regularization of Discrete Ill-posed Problems[J].SIAM Journal on Scientific Computing,1993,14(6):1487-1503.
[16] GOLUB G H,HEATH M,WAHBA G.Generalized Cross-validation as a Method for Choosing a Good Ridge Parameter[J].Technometrics,1979,21(2):215-223.
[17] 詹银虎,郑勇,张超,等.超大视场太阳敏感器图像质心提取算法[J].测绘学报,2015,44(10):1078-1084.DOI:10.11947/j.AGCS.2015.20150118.ZHAN Yinhu,ZHENG Yong,ZHANG Chao,et al.Image Centroid Algorithms for Sun Sensors with Super Wide Field of View[J].Acta Geodaetica et Cartographica Sinica,2015,44(10):1078-1084.DOI:10.11947/j.AGCS.2015.20150118.
[18] SHEN Yunzhong,XU Peiliang,LI Bofeng.Bias-corrected Regularized Solution to Inverse Ill-posed Models[J].Journal of Geodesy,2012,86(8):597-608.
[19] 李崇辉,李铸洋,郑勇,等.利用多星矢量观测信息进行天文导航定位技术的研究[J].导航定位学报,2013,1(3):62-65.LI Chonghui,LI Zhuyang,ZHENG Yong,et al.Celestial Positioning Analysis Based on Multi-star Vector Observation Information[J].Journal of Navigation and Positioning,2013,1(3):62-65.
[20] 张新帅,周召发.航天器姿态算法在地面天文定位中的应用研究[J].测绘科学,2015,40(5):139-143.ZHANG Xinshuai,ZHOU Zhaofa.Application of Attitude Determination Algorithms of Spacecraft in Celestial Positioning on Earth[J].Science of Surveying and Mapping,2015,40(5):139-143.