18-Geom-A3 Geodesy and Positioning · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, May 2015 — 3 hours, closed book (approved Casio/Sharp calculators only). EIGHT numbered questions; six constitute a complete paper and each is of equal value. Most answers are required in essay format — clarity and organization are marked. All eight questions are solved below for completeness.
Reference texts: Vaníček & Krakiwsky, Geodesy: The Concepts (2nd ed., North-Holland); Torge & Müller, Geodesy (4th ed., de Gruyter); Hofmann-Wellenhof, Lichtenegger & Wasle, GNSS — Global Navigation Satellite Systems (Springer, 2008); Snyder, Map Projections — A Working Manual (USGS PP 1395); Heiskanen & Moritz, Physical Geodesy (Freeman, 1967); Natural Resources Canada / Canadian Geodetic Survey references for NAD83(CSRS), CGVD2013 and CGG2013. Canadian datums and regulators throughout (NRCan; Ontario CORS network).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Given. Satellite-positioning reference frames (WGS84, NAD83(CSRS), ITRF) and two precise GNSS techniques — Precise Point Positioning (PPP) and network Real-Time Kinematic (RTK).
Find. (a) WGS84 vs NAD83(CSRS) compatibility and its precision; (b) WGS84 vs ITRF compatibility; (c) the PPP concept, field procedure and accuracy; (d) the definition, principle, accuracy, an Ontario network and its access for network RTK.
(a) WGS84 vs NAD83(CSRS+epoch). They are not the same datum, but they are compatible only at the metre level. When NAD83 was created (1980s) it was intentionally aligned with the original WGS84 to about a metre, and both were intended to be geocentric. However, WGS84 has since been refined (G730, G873, G1150, G1674, G1762…) to agree with successive ITRFs at the centimetre level, while NAD83(CSRS) stays fixed to the North American plate. As a result NAD83(CSRS) and modern WGS84 differ by roughly 1–2 m. So: compatible for navigation/GIS at the metre level, but not interchangeable for centimetre survey work — a datum transformation (with epoch) is required.
(b) WGS84 vs ITRF. Yes — the current realizations of WGS84 are compatible with the ITRF at the centimetre level. Since the WGS84(G730) realization the U.S. has aligned WGS84 to the contemporaneous ITRF using a globally distributed station set, so for all practical (even geodetic) purposes GPS broadcast positions in modern WGS84 and ITRF coincide to a few centimetres. The caveat is epoch: because both are kinematical, one must use consistent epochs when combining precise results. (The original 1987 WGS84 differed from early ITRF by 1–2 m, so historical data must be treated carefully.)
(c) GPS-PPP. Precise Point Positioning determines the absolute coordinates of a single receiver — no local base station — by using precise satellite orbit and clock products (from the IGS) instead of the broadcast ephemeris, together with dual-frequency carrier-phase and code observations and careful modelling of all systematic effects (ionosphere removed by the L1/L2 combination, tropospheric delay estimated, plus solid-earth tides, antenna phase-centre and relativity). Field procedure: occupy the point with a geodetic dual-frequency receiver, log carrier-phase data for a suitable period, then post-process (or stream, for real-time PPP) through a PPP engine such as NRCan’s CSRS-PPP online service, which returns coordinates directly in NAD83(CSRS) or ITRF at a chosen epoch. Accuracy: static PPP reaches a few centimetres to ~2–10 cm after 30 min–2 h of convergence (sub-cm with 24 h and ambiguity resolution); kinematic PPP is at the decimetre level.
(d) GPS-RTK network. A network RTK system is a set of permanently installed continuously operating reference stations (a CORS network) whose data are combined at a central server to model the spatially correlated errors (ionosphere, troposphere, orbits) across the whole region, so a single roving receiver can obtain centimetre positions in real time anywhere inside the network without its own nearby base. Principle: the server interpolates the network corrections to the rover’s location — commonly as a Virtual Reference Station (VRS) synthesized a few metres from the rover — and streams RTCM corrections to the rover (via cellular/NTRIP internet); the rover fixes its carrier-phase ambiguities against that correction and outputs coordinates immediately. Accuracy: ~2–3 cm horizontal (a few cm vertical) in real time. Ontario network: for example the provincial GNSS/CORS network operated in Ontario (e.g. Can-Net, Leica SmartNet or Trimble VRS Now, commercial CORS networks covering southern Ontario); a user accesses it by subscribing to the service, then connecting a cellular-enabled RTK rover to the network’s NTRIP caster (IP address, mountpoint, and login) to receive the VRS/network-RTK correction stream.
