1. Getting AHD heights from GNSS: some “insider information”
Will Featherstone
Western Australian Centre for Geodesy, Curtin University

2. Outline The basics and not so basics of heights
North-south tilt and distortions in the AHD
Geoid comps 101 (without maths, I promise)
Vertical errors in GNSS, AHD and geoid
What’s new in AUSGeoid09?
Weaknesses of AUSGeoid09
Check, check and check again
Q&A

3. The basics: AHD from GNSS
Absolute (AUSPOS or PPP)
H (AHD) ~= h (from GNSS) – N (from AUSGeoid)
Suffers from biases [covered later]
Relative (GNSS baselines)
ΔH (AHD) ~= Δh (from GPS/GNSS) – ΔN (from AUSGeoid)
Constant biases cancel over shorter baselines
Remember that it’s algebraic
Important over most of WA as N can be negative
E.g., h=0m, N=-30m, thus H ~=+30m

4. The not-so basics Geoid vs quasigeoid - subtly different surfaces
AHD fixed to 32 TGs
MDT+IBR+v offsets AHD from geoid
AHD is normal orthometric H*
Need AHD- ellipsoid separation
HAHD
AHD

5. North-south tilt in the AHD
Slope of 48mm/deg explained near-fully by MDT+IBR+v
Distortions (>10cm)

6. Geoid comps 101
Because the AHD is normal-orthometric, we must model the quasigeoid
Long-wavelengths from an Earth gravity model
satellite orbit analyses, land, airborne and altimeter gravity (EGM2008)
Add gravity and terrain data via Stokes’s integral
Integral must be modified to filter out errors
Our modifier works OK

7. H errors: levelling/vertical datum
Datum point(s) offset from geoid (0-2m)
Type/realisation of height system (~5-20cm)
Temporal variations, e.g. GIA (~0-10cm)
Instrumentation & methodology (? 2-50cm)
Refraction, # setups, tedious method, etc.
Tidal system (1-2cm)
Distortion in the vertical datum (10-50cm)
Confusion over height system

8. h errors: GNSS ellipsoidal heights
Vintage of data (2-10cm)
e.g. pre-IGS, old equipment/methods/models, etc.
Datum (1-5cm)
e.g., variants of ITRF, observed vs transformed, etc.
Antenna height measurement (2mm-1.8m)
And… to which point: ARP, slope, true vertical, top, bottom, etc.
Intrinsic GNSS errors (? 2-20cm)
VDOP, orbits, atmospherics, multipath, RF interference, etc.
Algorithmic/theoretical errors
Occupation time (longer needed for h)

9. N errors: quasigeoid model
Earth gravity model (EGM) (~5-20cm)
Data treatment errors (? 10-20cm)
Local gravity and terrain data (? ~20cm)
Algorithmic/theoretical errors (? 1-20cm)
Zero- and first-degree terms (~1-10cm)
Temporal geoid variations (? ~2-10cm)
Tidal system (1-2cm)
Mountains and coasts – quasigeoid poorer

10. What’s new in AUSGeoid09? Lots of new data Improved processing
>0.5M extra gravity obs, new TCs, new EGM
Improved processing
Higher resolution (1’x1’)
Better interpolation
Perth has v steep gradient
LSC-fitted to AHD using ~6,000 GPS-levelling points
RMSE 3-5cm

11. Weaknesses of AUSGeoid09
Poorer in the coasts and hills
Lack of data
AHD not defined offshore, but LSC-fitting has extrapolated
Model of MSL (loosely)
LSC correlation length
Some large residuals & randomly scattered
Sources still unknown
Checks always needed mm

12. Check, check and check again
A blanket statement of the precision of AHD heights from GNSS is indefensible
AUSGeoid09 is a weak link, though errors in GNSS and AHD cannot be dismissed
e.g., GNSS and/or AHD used in fitting may be wrong
Just as the good surveyor validates his/her levelling, the same applies to GNSS-AHD
Do your own validation for each and every project
Always remain sceptical

13. Check, check and check again
Just because AUSGeoid09 may have performed well on previous projects does not mean that it will elsewhere!
GNSS heighting is spatially and temporally variable
[Bad] anecdote
“Oh, it’s been OK, so we don’t bother checking any more”

14. References (all in PDF on my website)
Featherstone WE (1998) Do we need a gravimetric geoid or a model of the base of the AHD to transform GPS heights? Australian Surveyor 43(4):
Featherstone WE, Kuhn M (2006) Height systems and vertical datums: a review in the Australian context, J Spatial Sci 51(1):21-42,
Featherstone WE, Kirby JF, Hirt C, Filmer MS, Claessens SJ, Brown NJ, Hu G, Johnston GM (2011) The AUSGeoid09 model of the AHD, J Geodesy 85(3):
Brown NJ, Featherstone WE, Hu G, Johnston GM (2011) AUSGeoid09: a more direct and more accurate model for converting ellipsoidal heights to AHD heights, J Spatial Sci 56(1):27-37
Featherstone WE, Filmer MS (2012) The north-south tilt in the AHD is explained by the ocean’s MDT, J Geophys Res 117, C08035, doi: /2012JC007974

15. Acknowledgements
Australian Research Council for endorsement and funding for nearly two decades
My numerous collaborators on geoid and height determination
The many providers of data, particularly Geoscience Australia
Q&A

16. Australian surveyors already well know that GPS-measured ellipsoidal heights have to be transformed to AHD heights by application of AUSGeoid; it’s a simple [algebraic] subtraction (i.e., AHD=GPSh--AUSGeoid).  However, knowing how reliable, precise and accurate this seemingly simple coordinate conversion is rather murky, and varies widely depending on location. 
As the chief investigator on the production of the AUSGeoid98 and AUSGeoid09 national standards, which are promulgated by Geoscience Australia, I will attempt to demystify really how well we might be able to measure reliable heights on the AHD with GPS and AUSGeoid.  
Some of the considerations to be covered are practical and simple (e.g., remembering to measure the antenna height and to which point); some are rather more esoteric (e.g., the effect of gravity on heights and the north-south slope in the AHD with respect to the geoid). 
In conclusion, the veracity of GPS-AUSGeoid-derived AHD heights has to be treated sceptically by the practicing surveyor before supplying so-derived AHD heights to clients.