Acta Geodaetica et Cartographica Sinica >

2014 , Vol. 43 >Issue 10: 998 - 1004

DOI: https://doi.org/10.13485/j.cnki.11-2089.2014.0152

Transformation from Cartesian to Geodetic Coordinates Using Lagrange Inversion Theorem

  • GUO Jiachun ZHAO Xiuxia
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  • 1. School of Resources and Environmental Engineering, Anhui University
    2. School of Science, Anhui Agricultural University
    3. Fishery Institute of Anhui Academy of Agricultural Sciences
    4.

Received date: 2014-01-05

  Revised date: 2014-06-23

  Online published: 2014-10-24

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Abstract

According?to?Lagrange?Inversion?Theorem,?a?Taylor-series?expansion?method?for?transforming?Cartesian?to?Geodetic?Coordinates?is?obtained,?which?express?the?sine?function?of?reduce?latitude?sin?μ?as?a?convergent?polynomial?

of?geodetic?coordinates?（X,?Y,?Z）.?Comparative?computation?of?the?new?method?and?Bowring’s?formula?shows?that?the?new?method?is?sufficiently?precise?in?the?sense?that?

the?maximum?error?of?the?latitude?is?less?than?9.71×10-6″,?9.67×10-8″for?the?range?of?－2×106≤H≤＋1010,?truncating?at?b4?and?b5?respectively,?while?Bowring’s?formula?only?works?well?for?the?range?of?－105≤H≤＋105.?Meanwhile,?new?algorithm?is?around?50%~90%?faster?than?the?iterative?algorithm?with?the?approximate?accuracy. 

Key words： Cartesian coordinates; geodetic coordinate; coordinate transformation; Lagrange inversion theorem

Cite this article

GUO Jiachun ZHAO Xiuxia . Transformation from Cartesian to Geodetic Coordinates Using Lagrange Inversion Theorem[J]. Acta Geodaetica et Cartographica Sinica, 2014 , 43(10) : 998 -1004 . DOI: 10.13485/j.cnki.11-2089.2014.0152

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