Brief History of GB Coordinate Systems
Great Britain is one of the few countries to have two triangulations observed in the last two centuries.
The first, known simply as the “Principle Triangulation”, was published in 1858. It was not observed as a single planned scheme but was instead made up in a piecemeal fashion from observations between 1783 and 1853. Two taped bases provided scale and the origin and azimuth were defined at the Royal Observatory, Greenwich. The adjustment was performed in 21 computing blocks using the Airy 1830 ellipsoid.
The second triangulation is known as “The Retriangulation”. It was observed between 1936 and 1953 and computed by hand in 7 blocks. The original origin at Greenwich had been destroyed but was implied by holding the position of 11 stations fixed to the mean of their Principle Triangulation positions. This means that there is no one point that can be described as the origin of the Retriangulation. The coordinates are on the Airy 1830 ellipsoid and this adjustment is known as the Ordnance Survey of Great Britain 1936 Datum –
OSGB36. The OSGB36 datum is very important today since it is currently the basis for the National Grid and all Ordnance Survey map data.
The second coordinate system in Great Britain is the European Terrestrial System 1989 (ETRS89). ETRS89 is a very well defined and stable system which is fully compatible with WGS84 (the coordinate system used by GPS), and has been adopted as the primary system for accurate coordinate positioning across Europe. Unlike WGS84 however, ETRS89 is fixed at a point in time and does not move with the motion of the Earth’s tectonic plates. The difference between WGS84 and ETRS89 is now approximately >15 cm (they were synonymous in 1989). Adopting ETRS89 as the primary coordinate system in Great Britain allows an accurate and stable transformation to OSGB36 to be developed. Access to ETRS89 is provided by the National GPS Network which consists of 130 permanent GPS stations
(the Active GPS Network) supplemented by a network of over a 1000 ground stations (the Passive GPS Network), all coordinated in ETRS89. Data, coordinates and information on the National GPS Network stations is freely available at the Ordnance Survey GPS website (http://www.gps.gov.uk). If these stations are incorporated when using GPS, then the survey will automatically be coordinated in ETRS89 instead of WGS84.
Transformation Models
The function of a national ETRS89 to OSGB36 transformation is to accurately model the relationship between the two systems. This is not a simple process because OSGB36 contains randomly variable scale errors, mainly due to it being computed in blocks and the fact that scale and azimuth were controlled entirely by the 11 stations from the Principle Triangulation. These scale variations mean that OSGB36 can be described as inhomogeneous, as opposed to ETRS89 which is very stable and well defined and therefore homogeneous.
The inhomogenity of OSGB36 does not affect its adequacy as a mapping datum but it does make a simple transformation between ETRS89 and OSGB36 too inaccurate for national use. For example, the accuracy of a national 7 parameter (3 shifts, 3 rotations and a scale change) transformation is approximately 5 metres. It is these varying differences that need to be modelled in order to produce a more accurate transformation. There are two transformation models which are suitable for modelling such random datum differences.
The first type is the polynomial transformation (also known as multiple regression transformation). This type of transformation attempts to model the varying differences between two datums as a surface described by a polynomial function. Tests on polynomial transformations have shown that they cannot achieve the desired 0.1m rmse accuracy. Also, the effect of the scale variations in the OSGB36 datum makes the polynomial transformations very unstable near the edges of the transformation area. The magnitude of the residuals around the edges of the polynomial transformation is in the region of several metres.
The second type of transformation model is known as the Grid Look Up Table and it is this type which is used by the Ordnance Survey for the national ETRS89 to OSGB36 transformation.
The New Definitive Transformation – OSTN02
The main aim of OSTN02 was to improve the accuracy of the old OSTN97 transformation to 0.1m rmse. This has be achieved by significantly increasing the point density of the transformation computation data set. Many more OSGB36 points are being coordinated in ETRS89, using GNSS observations and the National GNSS Network. The observation campaign has been running since October 1999 and is complete. Over 3000+ extra points have been coordinated and all areas of Great Britain, no matter how small or remote, now contain transformation points occupied with GNSS. The size of the final data set for the transformation computation contains over 6000+ points. Apart from providing a more accurate ETRS89 to OSGB36 transformation, OSTN02 has heralded a fundamental change in the definition of Great Britain’s mapping datum. For this reason OSTN02 will also be known as the Definitive Transformation. The Definitive Transformation (OSTN02) is complete; it is used to define the National Grid in conjunction with the ETRS89 positions of the National GNSS Network stations. This change means that, for example, the National Grid coordinates of an existing OSGB36 point, refixed using GNSS from the National GNSS Network and the Definitive Transformation, will be the correct ones. The original archived OSGB36 National Grid coordinates of the point will be wrong, by definition, but the two coordinates (new and archived) will agree on average to better than 0.1 m. This is a subtle change in definition only and will not mean that existing OSGB36 coordinates need to be changed in any way.
Source: “The OS’s new Coordinate Transformation for Great Britain – GPS to OSGB36 National Grid Transformation”, by Mark Greaves, Ordnance Survey Geodetic Analyst, and Paul Cruddace, Ordnance Survey Geodetic Advisor, published in the November/December 2001 issue of the ‘Geomatics World’ trade magazine, pages 34-36