Numerical Results from the Combination of Gravimetric and Satellite Data Using the Principles of Least Squares Collocation,
Abstract
The report develops working equations for carrying out the combination of gravimetric and satellite data starting from the equations of Moritz, and using the principles of the usual least squares adjustment and the least squares collocation. Of the two methods of combining data considered, one could not be carried out because of the need to invert a 1654 x 1654 full matrix. Numerical tests were conducted through the estimation of ten sets of potential coefficients complete to degree 20 plus certain resonance coefficients which have been derived starting from the GEM 3 potential coefficients and a 5 degree equal area block anomaly field. The solutions differ in two ways: first, the weighting applied to the a priori known potential coefficients, and second whether the usual least squares or collocation adjustment scheme is used for the estimation of the potential coefficients. To determine a best overall set of potential coefficients, comparisons have been made with astro-geodetic undulations (4196 values in Australia and the United States); with 5 degree anomalies; with anomaly degree variances, and by use of the coefficient sets in orbit fitting and prediction. Such comparisons indicate that collocation derived potential coefficients yield better values than those found using the usual least squares approach. A recommended set of potential coefficients and a consistent 5 degree equal area block anomaly field are given. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1973
- Accession Number
- AD0767313
Entities
People
- Richard H. Rapp
Organizations
- Ohio State University