By Bahr H., Heck B.
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Extra info for Variance Component Estimation for Combination of Terrestrial Reference Frames (2007)(en)(80s)
An overview of the sequence of steps can be found in appendix D. 1 Constitution of the Normal Equation Matrix Although the normal matrix N is of dimension u × u, its complete storage cannot be avoided. The inversion routine needs access to the whole matrix at a time. To minimise the amount of memory required beyond that, the normal matrix is constituted by computing its elements directly without storing intermediate results. Initially, neither the datum definition nor model extensions like local ties and velocity constraints will be considered.
30) illustrate that the elements of the u×u matrix N are derived from the matrices A = Asol and Pi (i = 1 . . k). As to A (n × u), the matrix is not stored at all, since more than 95 % of its elements are zeros; the required coefficients are computed on demand. The weight matrices Pi (ni × ni ) have to be stored, but only one at a time. More precisely, the elements of N are computed in the following way: k k ATi Pi Ai . 1) i=1 After N1 has been computed, P1 can be suspended from memory, and P2 is loaded.
60. This result is not expected from a time series of homogeneous data. Indeed, there are some outliers in the data that have a significant impact on the variance components. It has been verified that the homogeneity of the estimates is enhanced if the outlying stations are rejected from the respective solutions. 5: Time series stacking: Updates of coordinates and velocities in iteration step ν, given in units of the respective standard deviations. 6: Time series stacking: Iteration of three exemplarily chosen variance components (solutions 8 (ilrsa010224), 11 (ilrsa010317) and 33 (ilrsa010818)) by three different methods, given in terms of standard deviations and variances, respectively.
Variance Component Estimation for Combination of Terrestrial Reference Frames (2007)(en)(80s) by Bahr H., Heck B.