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The solutions of navigation observation equations for CAPS

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Abstract

Chinese scientists invent the navigation and positioning system based on commercial communications satellites and develop them successfully into China Area Positioning System (CAPS). In principle, this system is different from the GPS broadcasting satellite navigation class, where the propagation epoch of original navigation signals for pseudo-range measurement is from a ground master control station rather than from satellite transponders. This paper addresses the establishment of the three observation equation models for the navigation and positioning system based on communications satellites, and expresses them identically to operator equations and optimized models. Furthermore, both algorithms of the linear solution for the observable characteristic equation and the least-squares solution for the condition number more than 4 are discussed, with several methods for the exact solution, such as improving the behavior of coefficient matrices, right estimation for the weighted right hand side and selection of iteration forms of solutions, and the influence of the condition number on improving navigation and positioning accuracy is also analyzed carefully. Hopefully, all the works would be contributive to further development of the navigation and positioning system based on communications satellites, and be potentially valuable to other satellite navigation and positioning systems.

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Authors and Affiliations

  1. National Astronomical Observatories, Chinese Academy of Sciences, Beijing, 100012, China

    HuLi Shi & Jun Pei

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  1. HuLi Shi
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  2. Jun Pei
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Correspondence to HuLi Shi.

Additional information

Supported by the National Basic Research and Development Program of China (Grant No. 2007CB815500)

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Shi, H., Pei, J. The solutions of navigation observation equations for CAPS. Sci. China Ser. G-Phys. Mech. Astron. 52, 434–444 (2009). https://doi.org/10.1007/s11433-009-0049-6

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  • DOI: https://doi.org/10.1007/s11433-009-0049-6

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