INTERPOLATION ON THE UNIT SPHERE IN LAPLACE'S METHOD

This paper proposes an alternative interpolation approach for the line-of-sight measurements in Laplace's method for angles-only initial orbit determination (IOD). The classical implementation of the method uses Lagrange polynomials to interpolate three or more unit line-of-sight (LOS) vectors from a ground based or orbiting site to an orbiting target. However, such an approach does not guarantee unit magnitude of the interpolated line-of-sight path except at the three measurement points. The violation of this constraint leads to unphysical behavior in the derivatives of the interpolated line-of-sight history, which can lead to poor IOD performance. By adapting a spherical interpolation method used in the field of computer graphics, we can obtain an interpolated line-of sight history that is always unit norm. The first and second time derivatives of this interpolation yield the estimated line-of-sight rate and acceleration used in Laplace's method. This new spherical interpolation method often leads to significant performance improvements in Laplace's IOD method, which will be demonstrated through careful study of simulation results.