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

Considering defects of current single celestial-body positioning methods such as discontinuity and long period, a new sun positioning algorithm is herein put forward. Instead of traditional 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 algorithm 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 presented 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 fixing 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 navigation systems