以拉格朗日反演理论为基础，导出空间直角坐标向大地坐标转换的一种新的直接解法：该方法将归化纬度的正弦函数sin μ表达为以空间直角坐标（X, Y, Z）为基础的相关变量的多项式

展开。为验证公式的精度水平和实用性，以WGS-84椭球参数代入验算，结果表明：新解法在－2×10⁶≤H≤＋10¹⁰范围内，展开至b₄项纬度反解误差不超过9.71×10^-6″，展开至b₅项的误差

不超过9.67×10^-8″，有效范围比Bowring公式广，在H≥＋10⁵的区域精度明显优于Bowring公式；与迭代算法相比，新方法在H≥－2×10⁶的区域精度与迭代算法精度相当，但计算效率明显

优于迭代算法，展开至b1/2、1/10。兼顾精度和效率，本文算法优于Bowring公式和迭代算法。₄项、b₅项的CPU执行时间分别约为迭代4次、5次的

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.