测日定位中病态问题的有偏估计及精度分析

doi:10.11947/j.AGCS.2016.20150525

测绘学报 ›› 2016, Vol. 45 ›› Issue (8): 911-918.doi: 10.11947/j.AGCS.2016.20150525

测日定位中病态问题的有偏估计及精度分析

詹银虎, 郑勇, 张超

信息工程大学导航与空天目标工程学院, 河南郑州 450001

收稿日期:2015-10-23 修回日期:2016-03-28 出版日期:2016-08-20 发布日期:2016-08-31
作者简介:詹银虎(1986-),男,博士生,研究方向为天文导航。E-mail:oscardad@163.com

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

ZHAN Yinhu, ZHENG Yong, ZHANG Chao

College of Navigation and Aerospace Engineering, Information Engineering University, Zhengzhou 450001, China

Received:2015-10-23 Revised:2016-03-28 Online:2016-08-20 Published:2016-08-31
Supported by:
lunar/mars rovers navigation;celestial positioning;least squares method;Ill-posed problem;bias estimation;root mean square error

摘要/Abstract

摘要： 目前月球/火星车上均搭载有太阳敏感器用于导航，但需要较长的跟踪观测时间才能实现绝对定位，影响了导航的实时性。本文研究如何在超短的跟踪观测时间（1～2 min）内，实现测日绝对定位。首先推导了高度法定位的最小二乘法求解模型，并首次从病态问题的角度看待测日定位问题，采用奇异值分解法对病态问题进行了诊断。通过仿真算例，将有偏估计的方法应用于测日定位，并对不同有偏估计方法进行了比较。仿真计算结果表明，有偏估计总是能够改善初值的精度，明显优于最小二乘法。但初值的选取对有偏估计的影响非常显著，有偏估计总是将初值沿着太阳的指向稳定收敛到一条与太阳指向垂直的直线上，且这条直线通过真值。

关键词: 月球/火星车导航, 天文定位, 最小二乘法, 病态问题, 有偏估计, 均方根误差

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

中图分类号:

P228

詹银虎, 郑勇, 张超. 测日定位中病态问题的有偏估计及精度分析[J]. 测绘学报, 2016, 45(8): 911-918.

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.

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测日定位中病态问题的有偏估计及精度分析

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

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