A new method of single celestial-body sun positioning based on theory of mechanisms

• Published in: Chinese journal of aeronautics 2016-02, Vol.29 (1), p.248-256
• Main Authors: Zhang, Wei, Xu, Xiaofeng, Wu, Yuanzhe
• Format: Article
• Language: English
• Subjects: Algorithms; Celestial navigation; Discontinuity; Inverse kinematics; Latitude; Longitude; Longitude and latitude coordinates; Mathematical analysis; Mechanisms; Navigation systems; Position measurement; Positioning devices (machinery); Single celestial-body positioning; Sun; Vectors (mathematics); 坐标系统; 天体定位; 天文导航系统; 太阳; 定位算法; 惯性导航系统; 智能手机; 机构
• ISSN: 1000-9361
• DOI: 10.1016/j.cja.2015.12.009

Considering defects of current single celestial-body positioning methods such as discon- tinuity and long period, a new sun positioning algorithm is herein put forward. Instead of tradi- tional astronomical spherical trigonometry and celestial coordinate system, the proposed new positioning algorithm is built by theory of mechanisms. Based on previously derived solar vector equations （from a C1R2p2 series mechanism）, a further global positioning method is developed by inverse kinematics. The longitude and latitude coordinates expressed by Greenwich mean time （GMT） and solar vector in local coordinate system are formulated. Meanwhile, elimination method of multiple solutions, errors of longitude and latitude calculation are given. In addition, this algo- rithm has been integrated successfully into a mobile phone application to visualize sun positioning process. Results of theoretical verification and smart phone＇s test demonstrate the validity of pre- sented coordinate＇s expressions. Precision is shown as equivalent to current works and is acceptable to civil aviation requirement. This new method solves long-period problem in sun sight running fix- ing and improves applicability of sun positioning. Its methodology can inspire development of new sun positioning device. It would be more applicable to be combined with inertial navigation systems for overcoming discontinuity of celestial navigation systems and accumulative errors of inertial nav- igation systems.