11.2.6 GPS Network Transformations

TRANSFORMATION OPTIONS IN AUSTRALIA

The transformation options for converting coordinates from one well defined datum or coordinate system to another are summarised in Figure below (STEED, 1990). There are a variety of transformation models; some are mathematically defined, others have been determined empirically (from an analysis of common points); some are global transformation models, others have only national or even local relevance (for example, interpolation of difference contours); some relate satellite datums, others different coordinate sets of the Australian Geodetic Datum. The transformation of particular relevance to GPS surveying is that relating AGD84 (the latest coordinate set of the AGD) and the GPS datum WGS84. Note there are two options:

• Using Higgin's formula: AGD84 <--> WGS84, or
• Using the path: AGD84 <--> NSWC9Z2 <--> WGS72 <--> WGS84.

   

In fact, the parameters of HIGGINS (1984) are derived empirically from a combination of the three other transformation models in Table below (DMA, 1987; SEPPELIN, 1974; ALLMAN & VEENSTRA, 1984), and were not computed from observed WGS84 positions. Because GPS is a relative surveying technique, it is in fact very difficult to obtain a national set of GPS coordinates that are on the WGS84 datum (in an absolute sense). Until this is done a set of transformation parameters cannot be empirically derived to model the conversion from WGS84 to AGD84 (and visa versa), and replace the Higgins parameters. (The new Geocentric Datum of Australia is defined to be within one metre of WGS84 -- section 12.1.5). In the meantime, Table below summarises most of the transformation options relevant for Australian surveys.

Australian transformation options.
(STEED, 1990)

However, there is one transformation which is commonly sought, but for which no readily available transformation model is available: AGD84 <--> AGD66. The AGD66 was derived from a Least Squares adjustment of the Australian geodetic network performed in 1966 and was used until the new adjustment was performed in 1984. Because of the limitations of the adjustment model used, and the systematic errors present in some of the observations, the AGD66 coordinate set suffers significant distortions. Distortions which were clearly visible when the AGD84 coordinate set was compared with the earlier set (ALLMAN & VEENSTRA, 1984). The transformation model AGD66 <--> AGD84 is in fact defined by the maps of displacement vectors given in ALLMAN & VEENSTRA (1984).

The AGD66 coordinate set is still the official basis for the geodetic control network in several states of Australia, including New South Wales, Victoria, Tasmania and Northern Territory. An approximate transformation model AGD66 <--> WGS84 has been derived by the Land Information Centre (LIC) (see Table below). Note that in the Table the full VCV information is not available, only the estimated standard deviations of the parameters are given (shown in brackets).

Transformation parameters of relevance to Australian surveys.

Source	HINGGINS (1987)	A & Va (1984)	DMA (1987)	SEPPELIN (1974)	LIC93b
FROM TO	WGS84 AGD84	NSWC9Z2 AGD84	WGS84 WGS72	WGS72 NSWC9Z2	WGS84 AGD66
Tx (m)	116.00(2.3)	116.00(1.2)	0.00	0.00	137.98
Ty (m)	50.47(2.3)	50.47(2.3)	0.00	0.00	42.58
Tz (m)	-141.69(2.5)	-137.19(1.5)	-4.50	0.00	-162.28
(")	0.23(0.04)	0.23(0.04)	0.00	0.00	-0.015
(")	0.39(0.04)	0.39(0.04)	0.00	0.00	-0.591
(")	0.34(0.04)	-0.47(0.04)	0.554	0.26	0.298
s (ppm)	-0.098(0.07)	-0.699(0.07)	-0.226	0.827	1.017

a ALLMAN & VEENSTRA (1984) b For New South Wales only! WGS84 only approximate at one metre level

Transforming GPS Results In Australia

In summary, in Australia, to transform the results of a GPS survey into coordinate information referred to a local geodetic datum we may either:

• Use published transformation parameters (Table above), for example the Higgins parameters for WGS84 <--> AGD84, or the LIC93 parameters for WGS84 <--> AGD66(NSW).
  
• Determine the transformation parameters as an integral part of the network adjustment process.

With regards to the first option, it is of little use in relating GPS results to the local control stations because:

• It is assumed that there are no significant distortions in the local network, and that the coordinates of the control stations are related to the geodetic datum without error.

   

• It is assumed that the GPS results are related, with high accuracy, to the WGS84 system.

Neither of these conditions are usually fulfilled. In particular, the GPS network coordinates, while related to one another to a high precision, are only weakly related to the WGS84 system. For example, the uncertainty in the absolute coordinates of the Datum Station has little effect on the relative precision of the GPS network (section 6.2.6). Hence any (absolute) coordinate error will affect all stations in the network, and the previously derived transformation parameters will have little relevance in relating any GPS network to the geodetic datum.

It is therefore preferable that in order to maintain the high precision of a GPS network, any combination of the GPS results with coordinate information related to the local datum must ensure that the transformation parameters are also estimated, in some way, as part of the process of GPS result integration. In addition, the full VCV matrix of the parameters can be obtained, and used to determine the VCV of the coordinates after transformation. An example is given below.

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© Chris Rizos, SNAP-UNSW, 1999