Comparison of Spherical Data Interpolation Methods for Spacecraft Radiation Pressure Characteristics Interpolation

Abstract

This paper presents a comparison of four interpolation techniques for interpolation of spacecraft solar radiation data characteristics. As radiative characteristics are functions of spacecraft orientation with respect to the incoming radiation vector they should be interpolated taking into account the periodicity of angular orientation. Interpolation is performed using four approaches: spherical harmonic functions, two-dimensional planar interpolation, Gaussian kernel, and direct spherical interpolation. In the spherical harmonics method, the interpolated function is approximated by a spherical harmonic function fitted onto the sample data representing radiative characteristic as a function of incoming radiation ray versor. In the two-dimensional planar interpolation method, the incoming ray direction is mapped to a set of two incidence angles, and the interpolation is performed in the 2D plane with appropriate boundary conditions to assure periodicity. In the direct spherical interpolation method, the data is interpolated directly on a unit sphere representing the coordinates of incoming ray versors. For two-dimensional planar interpolation and spherical interpolation methods both linear and natural neighbour interpolations are investigated. For spherical harmonics the impact of order/degree of harmonics expansion onto the interpolation error is investigated. The comparison is performed based on sample data representing the full set of solar radiation pressure coefficients of a generic satellite model for different numbers of sample points used for interpolation. The presented techniques can be applied to interpolate other orientation-dependent characteristics, such as aerodynamic characteristics.

Keywords

• Aerospace engineering
• aerospace simulation
• approximation methods
• interpolation
• numerical analysis
• numerical models