18-Geom-A3 Geodesy and Positioning · December 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, December 2017 — 3 hours, closed book (approved Casio/Sharp calculators only). SEVEN numbered questions; six constitute a complete paper and each is of equal value (20 marks); the per-part marking scheme printed on page 4 of the paper is reproduced in each answer. Most answers are required in essay format. All seven questions are solved below for completeness.
Reference texts: Vaníček & Krakiwsky, Geodesy: The Concepts (2nd ed., North-Holland); Hofmann-Wellenhof, Lichtenegger & Wasle, GNSS — Global Navigation Satellite Systems (Springer, 2008); Torge & Müller, Geodesy (4th ed., de Gruyter); Heiskanen & Moritz, Physical Geodesy (Freeman); Snyder, Map Projections — A Working Manual (USGS PP 1395); Natural Resources Canada geodetic references for NAD83(CSRS), CGVD2013 and the CGG2013 geoid model. Canadian datums/regulators throughout (NRCan, Canadian Geodetic Survey).
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. GNSS positioning referenced to WGS84, and the relationships of WGS84 to NAD83(CSRS+epoch) and to the ITRF, plus the Precise Point Positioning technique.
Find. (a) WGS84↔NAD83(CSRS+epoch) compatibility and level; (b) WGS84↔ITRF compatibility with justification; (c) the PPP concept, field procedure and achievable accuracy.
(a) WGS84 vs NAD83(CSRS+epoch). They are not the same datum, but both are geocentric and closely aligned to the ITRF, so they are “compatible” only at the metre level (about 1–2 m). Modern WGS84 is aligned to the ITRF at the centimetre–decimetre level, whereas NAD83 carries its historic ~1–2 m non-geocentric offset and is fixed to the North American plate; consequently the coordinates of the same point in the two systems differ by 1–2 m and drift apart over time at the plate-motion rate. For any survey requiring better than a metre they must be related by a proper 14-parameter transformation (with epoch), not treated as equal.
(b) WGS84 vs ITRF. Yes — they are compatible at the centimetre to few-decimetre level. The justification is definitional: since 1994 the successive realizations of WGS84 (G730, G873, G1150, G1674, G1762…) have each been deliberately aligned by the U.S. NGA to the contemporaneous ITRF, so for practical positioning WGS84 and ITRF coordinates of a point agree to a few centimetres and any residual difference is at the noise level of ordinary GNSS work. That is why broadcast-orbit GNSS positions (nominally WGS84) can be used interchangeably with ITRF at the accuracy of most field surveys.
(c) GPS-PPP. Precise Point Positioning determines absolute coordinates with a single dual-frequency GNSS receiver — no local base station — by applying precise satellite orbit and clock products (from the IGS or NRCan) and rigorously modelling the ionosphere (via the ionosphere-free combination), troposphere, solid-Earth tides, antenna phase-centre variations and relativistic effects. Field procedure: occupy the point with a geodetic dual-frequency receiver and log carrier-phase and code data (typically tens of minutes up to a few hours), then submit the RINEX file to a PPP service such as NRCan’s CSRS-PPP, which returns coordinates directly in NAD83(CSRS) or ITRF at a chosen epoch. Accuracy: after the solution converges, a few centimetres in static mode (down to ~1–2 cm horizontally with long occupations); kinematic PPP gives decimetre-level results. The trade-off is a convergence period of typically 20–40 minutes before centimetre accuracy is reached.
