A new bi-quintic latitude/longitude spline is developed and applied to the problem of Lunar surface modeling. The new spline provides a singularity-free parameterized function over an oblate spheroid. The bi-quintic spline uses 9 parameters at each of its regular latitude/longitude nodes. At the two poles there are only 6 parameters. The resulting function is continuous and has continuous first and second partial derivatives. Latitude and longitude partial derivatives go to zero at the poles in ways that guarantee continuous first and second partial derivatives of the function when evaluated with respect to Cartesian coordinates as its underlying inputs. The new spline model has been applied to the problem of navigating a Lunar lander. The lander measures slant-ranges to points on the Lunar surface. Its navigation filter uses a model of how the slant-ranges vary with its location and orientation. This model is based on a bi-quintic spline of the Lunar surface, and it returns slant-ranges and their first partial derivatives with respect to spacecraft position and sensor line-of-sight direction. The new sensor model works well in truth-model simulation tests of the navigation filter.

中文翻译：

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航天器导航的双五次纬度/经度样条和月球表面建模

开发了一种新的双五次经纬度样条，并将其应用于月球表面建模问题。新的样条曲线在扁球体上提供了无奇点的参数化功能。双五阶样条曲线在其每个常规纬度/经度节点处使用9个参数。在两个极点处只有6个参数。所得函数是连续的，并且具有连续的一阶和二阶偏导数。纬度和经度偏导数在极点处为零，以确保在相对于笛卡尔坐标作为其基础输入进行评估时函数连续的一阶和二阶偏导数。新的样条曲线模型已应用于导航月球着陆器的问题。着陆器测量倾斜范围到月球表面上的点。它的导航过滤器使用一个模型，说明倾斜范围如何随其位置和方向变化。该模型基于月球表面的双五次样条，并返回相对于航天器位置和传感器视线方向的倾斜范围及其一阶偏导数。新的传感器模型在导航滤波器的真实模型仿真测试中运行良好。