Question 5 of 7: Space Geodetic Positioning — WGS84, ITRF and VLBI

Question 5: Space Geodetic Positioning — WGS84, ITRF and VLBI (20 marks — a 6, b 6, c 8)

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. GPS positioning referenced to WGS84, the relationships of WGS84 to NAD83(CSRS+epoch) and to the ITRF, and VLBI as the technique that underpins the long-term stability of the terrestrial and celestial frames.

Find. (a) WGS84↔NAD83(CSRS+epoch) compatibility and level; (b) WGS84↔ITRF compatibility with justification; (c) how VLBI works and why it is stable relative to GNSS.

(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 coordinates of the same point 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 GPS positions (nominally WGS84) can be used interchangeably with ITRF at the accuracy of most field surveys.

(c) How VLBI works and why it is stable. Very Long Baseline Interferometry observes extragalactic radio sources (quasars) — objects so distant they are effectively fixed points of light defining an inertial (non-rotating) direction set. Two or more radio telescopes, separated by up to intercontinental baselines, record the same quasar’s noise signal simultaneously, each time-tagging its data with a hydrogen-maser atomic clock. Because the plane wavefront reaches the two antennas at slightly different times, there is a geometric delay \(\tau\); cross-correlating the two recorded data streams recovers \(\tau\) very precisely, and since \(c\,\tau = \mathbf{B}\cdot\hat{\mathbf{s}}=B\cos\theta\) (baseline \(\mathbf{B}\), source direction \(\hat{\mathbf{s}}\)), a set of such delays to many quasars solves for the baseline vectors between stations and for Earth’s orientation. Why it is stable: VLBI is referenced to the quasars, which realize the inertial celestial reference frame (ICRF) — a frame that does not rotate, has no satellites and no orbit dynamics, and effectively no proper motion, so it provides an absolute, time-independent orientation and scale. GNSS, by contrast, depends on orbiting satellites whose orbits must themselves be determined and continually modelled (gravity field, radiation pressure, clock drift), so a GNSS-only frame slowly drifts and cannot by itself fix the long-term orientation or the connection between the terrestrial (ITRF) and celestial (ICRF) frames. VLBI supplies exactly that tie — the Earth-orientation parameters and the frame scale — anchoring the space-based systems to an inertial reference and keeping them stable over decades.