A Variance component estimation method for sparse matrix applications

Methods for estimating variance components from the observation data used in a least squares adjustment are becoming important in geodesy because of the variety of data that need to be combined into a single adjustment. Unbiased estimators of the MINQUE <Minimum Norm Quadratic Unbiased Estimation> type have received the most attention, but these estimators have some short-comings that make them unattractive in certain applications. In particular, they require the full inverse of the least squares normal equation matrix, thus limiting the use of sparse matrix methods so common to geodesy. This report proposes an iterative estimation method, which may not be unbiased, but produces reliable estimates in controlled numerical tests and is compatible with sparse matrix adjustments.