Transformations and OSGM02 user guide - Leica Geosystems

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The OSi/OSNI polynomial transformationTo some extent distortions within traditional triangulation networks are inevitable. Within the triangulation network of theRepublic of Ireland and Northern Ireland these distortions are not generally significant; however, regional distortions dooccur. A 3 rd order polynomial transformation has been developed to model these distortions.A polynomial expression was fitted to the coordinate differences of a number of points in the different coordinatereference systems. This is a one-dimensional fitting method that is applied to the geographical coordinate, requiringindependent parameters to be computed for both latitude and longitude.In general, the polynomial model can be expressed as:∆φ = ∑∑ Α ij(φ−φ m) i (λ−λ m) j∆ λ=∑∑ Β ij(φ−φ m) i (λ−λ m) jThe fully expanded forms of the 3 rd order polynomial are as follows:∆φ = [A 00 + A 10 U + A 01 V + A 11 UV + A 20 U 2 + A 02 V 2 + A 21 U 2 V + A 12 UV 2 + A 22 U 2 V 2 + A 30 U 3 + A 03 V 3+ A 31 U 3 V + A 13 UV 3 + A 32 U 3 V 2 + A 23 U 2 V 3 + A 33 U 3 V 3 ] / 3600∆λ = [B 00 + B 10 U + B 01 V + B 11 UV + B 20 U 2 + B 02 V 2 + B 21 U 2 V + B 12 UV 2 + B 22 U 2 V 2 + A 30 U 3 + B 03 V 3 +B 31 U 3 V + B 13 UV 3 + B 32 U 3 V 2 + B 23 U 2 V 3 + B 33 U 3 V 3 ] / 3600Where A ijand B ijare the computed parameters, and U and V are the normalised coordinates calculated as follows:U = k 0 (φ - φ m ) and V = k 0 (λ - λ m )Where φ m and λ m are the coordinates of the approximate centre of the region. The parameters A ij, B ij,K 0 , φ m and λ m aregiven in table 2 below. The transformed geographical coordinates are then obtained as follows:λ ETRS = λ IG + ∆λ and φ ETRS = φ IG + ∆φThe reverse transformation from ETRS89 to Irish Grid cannot be calculated directly and requires iteration.Conversions between geographical and grid coordinates are computed using standard Transverse Mercator projectionformulae in association with the published Irish Grid parameters.Transformations and OSGM02 user guide chapter 3v2.1 9/2002 © crown copyrightPage 23
Table of coefficients for OSi/OSNI polynomial transformationCoefficient i, j Latitude (Ai, j) Longitude (Bi, j)0, 0 0.763 -2.8100, 1 0.123 -4.6800, 2 0.183 0.1700, 3 -0.374 2.1631, 0 -4.487 -0.3411, 1 -0.515 -0.1191, 2 0.414 3.9131, 3 13.110 18.8672, 0 0.215 1.1962, 1 -0.570 4.8772, 2 5.703 -27.7952, 3 113.743 -284.2943, 0 -0.265 -0.8873, 1 2.852 -46.6663, 2 -61.678 -95.3773, 3 -265.898 -853.950Other parameters φ m = 53.5 λ m = -7.7 K 0 = 0.1Transformations and OSGM02 user guide chapter 3v2.1 9/2002 © crown copyrightPage 24
Page 2 and 3: PrefaceThis grid transformation sof
Page 4 and 5: Data copyrightUser guide copyrightT
Page 6 and 7: Appendix A Transforming ETRS89 GPS
Page 8 and 9: Orthometric heights in these system
Page 10 and 11: ETRS89 explainedBenefitsOrdnance Su
Page 12 and 13: Chapter 2Data overviewBasic princip
Page 14 and 15: Where:1 the record number is a sequ
Page 16 and 17: Where:1 the record number is a sequ
Page 18 and 19: 4 the height of the Geoid above the
Page 20 and 21: For example, to find the record for
Page 22 and 23: Shifts for x, y are:se 0= east_shif
Page 26 and 27: The Ordnance Survey Geoid model: OS
Page 28 and 29: Chapter 4Quality statementCoverageO
Page 30 and 31: Appendix ATransforming ETRS89 GPS c
Page 32 and 33: The offset values are given by:dx =
Page 34 and 35: Appendix BConverting latitude and l
Page 36 and 37: ⎛ ⎛ 5 2 5 3 ⎞ ⎛2 21 3 ⎞
Page 38 and 39: Appendix CConverting easting and no
Page 40 and 41: Worked example using Airy 1830 elli
Page 42 and 43: Geoid modelA model of the level sur

Transformations and OSGM02 user guide - Leica Geosystems

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