I suggest a method for converting geodetic height and latitude from one oblate ellipsoid of revolution to another having the same center and symmetry axis. Unlike other approaches, the method here does not obtain height and latitude from Earth-centered, Earth-fixed (ECEF) Cartesian coordinates; this feature allows height conversion with high accuracy even in cases where the data format limits the precision of the latitude data. Height and latitude conversions can be expressed as a Fourier series in even multiples of latitude, with height changes having only cosines and latitude changes having only sines. The absolute difference of the flattenings of the two ellipsoids furnishes a simple upper bound on the maximum absolute latitude change. Conversions between the TOPEX and WGS84 ellipsoids, a practical necessity for the inter-mission comparison of satellite laser and radar altimeter data, illustrate the findings. Because the differences in the flattenings and semi-major axes of these ellipsoids are small, truncating the Fourier series after the term in twice the latitude gives an approximate conversion with an error less than 9 \(\times \) 10^–12 radians of latitude and about 6 \(\times \) 10^–6 m of height.

我建议一种将大地高度和纬度从一个旋转椭圆体转换为另一个具有相同中心和对称轴的方法。与其他方法不同，这里的方法不是从地心地球固定（ECEF）笛卡尔坐标中获取高度和纬度；即使在数据格式限制了纬度数据精度的情况下，此功能也可以实现高精度的高度转换。高度和纬度转换可以表示为纬度偶数倍的傅里叶级数，高度变化只有余弦，纬度变化只有正弦。两个椭球的平坦度的绝对差为最大绝对纬度变化提供了一个简单的上限。TOPEX 和 WGS84 椭球之间的转换，卫星激光和雷达高度计数据的任务间比较的实际必要性，说明了调查结果。由于这些椭球的展平度和半长轴的差异很小，因此将傅里叶级数在纬度的两倍处截断后得到近似转换，误差小于 9\(\times \) 10 ^–12弧度的纬度和大约 6 \(\times \) 10 ^–6  m 的高度。