Modeling errors in upward continuation for INS gravity compensation

Accurate upward continuation of gravity anomalies supports future precision, free-inertial navigation systems, since the latter cannot by themselves sense the gravitational field and thus require appropriate gravity compensation. This compensation is in the form of horizontal gravity components. An analysis of the model errors in upward continuation using derivatives of the standard Pizzetti integral solution (spherical approximation) shows that discretization of the data and truncation of the integral are the major sources of error in the predicted horizontal components of the gravity disturbance. The irregular shape of the data boundary, even the relatively rough topography of a simulated mountainous region, has only secondary effect, except when the data resolution is very high (small discretization error). Other errors due to spherical approximation are even less important. The analysis excluded all measurement errors in the gravity anomaly data in order to quantify just the model errors. Based on a consistent gravity field/topographic surface simulation, upward continuation errors in the derivatives of the Pizzetti integral to mean altitudes of about 3,000 and 1,500 m above the mean surface ranged from less than 1 mGal (standard deviation) to less than 2 mGal (standard deviation), respectively, in the case of 2 arcmin data resolution. Least-squares collocation performs better than this, but may require significantly greater computational resources.