The Multi-Epoch Least-Squares Adjustment Problem: Models Relating Estimable Parameters at a Single Epoch to Geodetic Observations, Stochastic Constraints and Fixed Constraints at Multiple Epochs Volume I: The Projection Method

This is Volume I of a three-volume report. In the modernized National Spatial Reference System (NSRS) the National Geodetic Survey (NGS) will have new tools for external users of the NSRS (such as a revised version of the Online Positioning User Service, OPUS) as well as for internal computations of new NSRS coordinates called reference epoch coordinates (RECs) and survey epoch coordinates (SECs). Each of these three applications (OPUS, REC, and SEC) will use a least-squares adjustment (LSA) to estimate coordinates (and their associated variances). But each LSA will be faced with the same basic problem — observations are made at a variety of epochs (dates and times) while estimated coordinates are required at one specific epoch. This is further complicated by the possibility that both stochastic constraints and fixed constraints are imposed on the parameters, and that they may be imposed at a variety of additional epochs.