- Modern geospatial data are frequently represented in some type of three-dimensional (3D) coordinate system, for example geodetic latitude, longitude, and ellipsoid height (φ, λ, h) derived from Global Navigation Satellite Systems (GNSS). But for engineering and surveying work, φ, λ, h coordinates are usually converted to a topocentric system consisting of a horizontal coordinate pair—for example northing and easting (N, E)—combined with an “elevation” (often orthometric height, H). The N, E, H components are treated as mutually orthogonal, even though in physical reality the horizontal plane represented by N, E is generally not perfectly perpendicular to the H plumbline. However, it is a reasonable and practical approximation, and one that is enforced mathematically by determining horizontal separately from height. The components can then be combined into a coordinate triplet, which, by convention, is often ordered so as to represent a left-handed N, E, H system.
For GNSS-derived positions, a commonly used approach is to compute N, E, from φ, λ using a map projection, and to compute H from h using a geoid model. That approach will continue in the future, when the National Geodetic Survey (NGS) transitions to new Terrestrial Reference Frames and the associated State Plane Coordinate System of 2022 (SPCS2022), along with the North American-Pacific Geopotential Datum of 2022 (NAPGD2022). These systems will replace the existing U.S. “horizontal” (geometric) and vertical datums. This research investigates methods that could be applied to either or both the horizontal and vertical components of the 2022 systems.
For the horizontal component, two approaches are presented for developing conformal projected coordinate systems that could be incorporated into SPCS2022. Both are concerned with reduction of linear distortion, which is the difference in distance between a pair of projected (grid) coordinates and the actual horizontal distance at the topographic surface (ground). One is design of low distortion projections (LDPs) that minimize linear distortion for specific areas of interest such that the difference between grid and ground distances is negligible, typically within ±20 parts per million (ppm). The other is design of SPCS2022 zones for entire states and to replace existing SPCS zones. These areas are so large that they have too much distortion to serve as LDPs. Thus, population distribution is also considered in the design process, so that distortion can be minimized more effectively where the majority of people are located.
For the vertical component, a method was developed for integrating GNSS and leveling observations into a single 3D network for simultaneous least-squares adjustment. The purpose was to determine the role of spirit leveling in NAPGD2022, which will be primarily accessed using GNSS and a gravimetric geoid model. This is important, because leveling is more accurate vertically than GNSS over distances of less than a few kilometers. A key element was developing a geoid slope error model, to correctly weight the transformed leveling observations. The high redundancy of GNSS and its accuracy over long distances compensated for the low redundancy of leveling and its rapid error growth with distance. Conversely, the high relative accuracy of leveling offset the lower vertical accuracy of GNSS over short distances. The combined network yielded residuals and error estimates that were smaller than those of the separate networks.