Least-Squares Collocation Error Estimates in a Test of Newton’s Gravitational Law

Abstract

Recently, the Air Force Geophysics Laboratory conducted an upward continuation experiment to test the validity of Newton’s law of gravitation. One technique that was used to upward-continue ground data was least-squares collocation (LSC). The predicted standard deviation at 600 m above ground in the LSC estimate was significantly smaller than the observed discrepancy between the upward continuation estimate and the measured value. This indicates either a possible violation of Newton’s law or a model error (bias). Although the LSC error estimates of gravity interpolation on the ground are shown to be quite reasonable, it is suggested that a terrain misrepresentation can invalidate the error estimates of upward continuation.