The value of minimum norm estimation of geopotential fields

SUMMARY For the determination of gravity field parameters using satellite observations, regularization (with, e.g. Kaula's rule) is widely used, because the derived normal equations are ill-conditioned. The procedure is interpreted as a kind of collocation. Alternatively, it can be viewed as biased estimation. Thus several questions arise concerning the bias problem of the estimated geopotential fields, the uncertainty about the proper Kaula's constant column, and the unrealistic accuracy measure of the estimate. These factors may affect its application, depending on the magnitudes of the bias values and the accuracy difference between least-squares (LS) collocation and biased estimation. Two tests are carried out based on the GEM-T1 model. Test A uses the actual GEM-T1 coefficients and because test A is influenced by the biased underestimated values, a second test B assumes that Kaula's rule reflects the magnitudes of the geopotential coefficients. The results show that the coefficients of lower degrees are well determined if Kaula's rule is applied to degree and order 6 and above. In test A, the bias of each coefficient reaches 20 per cent of the estimated value at degree 19, and more than 30 per cent after degree 25. The computation of the mean squared errors of biased estimation indicates that the accuracy measure of LS collocation is very conservative globally. The reason for this is the underestimation of the coefficients. Test B shows that the bias of each coefficient increases to 20 per cent of the estimated value at degree 15 and 30 per cent at degree 19. More than 100 per cent is reached at degree 25. About 4/5 of the total number of the coefficients are too optimistic in accuracy, if the variance-covariance matrix of LS collocation is used.