Application of singular value decomposition to gravity field model development using satellite data

Models of the Earth's gravity fields are necessary for satellite orbit determination. Obtaining a gravity field model involves solving a set of linear equations, where the unknowns are coefficients in a spherical harmonics approximation of the gravity field. Standard solution techniques require the linear system of equations to be full rank. In order to obtain more accurate gravity field models, more terms are added to the spherical harmonic series. These higher order terms can introduce observability problems and make the system of linear equations to be rank deficient. To prevent rank deficiency, a priori information based on Kaula's rule can be used, or surface gravity anomaly data can be added.;An alternative method to overcome the rank deficiency problem is to use the singular value decomposition (SVD). In this study, SVD was applied to solutions of various gravity fields of degree and order 70. The SVD routine from EISPACK was modified to accommodate the orthogonalized observation matrix, 27 Mw in size, in the available memory of a Cray YMP-864.;Three cases are studied. The first case uses only satellite tracking data, which results in a highly singular system of equations. The second case is satellite tracking and altimeter data, which is full rank but has problem caused by uneven data distribution. The third case is full rank system of the equations. The SVD solutions, which were obtained by zeroing 30 to 40 small singular values, fit the observation better than the gravity fields obtained by full rank solutions.;The orbits obtained by processing actual satellite observation data were compared with the orbits obtained using the SVD gravity fields. Using the SVD, a few gravity fields having the comparable total RMS fit to that of JGM-3 were produced. Some of these gravity fields showed better orbit fit in total RMS than JGM-3.;The SVD gravity fields were also evaluated by their degree variances and covariances. The geoid undulation differences of the SVD gravity fields and the JGM-3 were investigated. The geographically correlated orbit differences were generated to check the orbit difference due to gravity field difference of the SVD gravity fields and the JGM-3.;This study demonstrated that the SVD can be used to solve large gravity field problems regardless of the singularity of the system and the SVD solution provides an opportunity for better gravity fields when compared to the full rank solution.