Variance–Covariance Matrix of Transformed GPS Positions: Case Study for the NAD 83 Geodetic Datum

Abstract

This investigation introduces a rigorous mathematical transformation of variance–covariance matrices between a global geocentric frame and a plate-fixed geodetic frame. A practical example between the geocentric frame of International GNSS Service 2008 (IGS08) epoch 2005.00 and the geodetic frame North American Datum of 1983 (NAD 83) (2011) epoch 2010.00 was implemented. Although the theory is general, the transformation used here is controlled by the assumptions implicit in the definition of NAD 83. However, the same approach could be extended to future definitions of fixed-plate datums used by geodetic organizations for charting and mapping applications. Consequently, because the transformation between these two specific frames is assumed by definition to be a one-to-one errorless transformation, the uncertainties for the 14 Helmert transformation parameters between the two frames are assumed to be zero. Nevertheless, the formulation is complete and applicable to other specific datum-transformation situations.