Summary
Least squares collocation has been applied to global problems using a covariance function which is based on assumptions about the stochastic nature of the functions related to the earth' anomalous potential. The validity of the stochastic approach has been debated by different authors although its great practical advantages seem to be generally acknowledged. This paper discusses the possibility of using least squares collocation without assumptions on the stochastic nature of the functions involved. Different types of nonhomogeneous weight functions are derived and their characteristical features are pointed out. The suitability of this approach is demonstrated by computing harmonic coefficients from near resonant satellite orbits. A comparison of the homogeneous and a nonhomogeneous solution is given.
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Rummel, R., Schwarz, K.P. On the nonhomogeneity of the global covariance function. Bull. Geodesique 51, 93–103 (1977). https://doi.org/10.1007/BF02522279
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DOI: https://doi.org/10.1007/BF02522279