Datum Problems - Map Projections: Cartographic Information Systems - page 546

+ x 11 X x 00 Y y 00 +

ρ − ρ −

+ x 02 Y

ρ − y 00 2

+ x 30 X

ρ − x 00 3

+ x 21 X

ρ − x 00 2 Y ρ − y 00 +

y 00 3 +O(4) ,

+ x 12 X x 00 Y y 00 2 + x 03 Y

ρ − ρ − ρ −

(21.91)

y = y ( X,Y,ρ,t x ,t y ,t z ,α,β,γ,s,A 1 ,E 2 ,a 1 ,e 2 )=
= ρ y 00 + y 10 X

x 00 + y 01 Y y 00 + y 20 X x 00 2

ρ − ρ − ρ −

+ y 11 X x 00 Y y 00 +

ρ − ρ −

+ y 02 Y

ρ − y 00 2

+ y 30 X

ρ − x 00 3

+ y 21 X

ρ − x 00 2 Y ρ − y 00 +

y 00 3 +O(4) .

+ y 12 Y x 00 Y y 00 2 + y 03 Y

ρ − ρ − p −

Table 21.2 Datum transformation. Datum parameters global (WGS 84) to local (BW)

t x = 592 . 271 m , y =76 . 286 m,
t z = 407 . 335 m

1 . 092843 , β = 0 . 097832 , α = − −

γ =1 . 604106
s =8 . 537829 ppm
a 1 =6 , 377 , 397 . 155 m , A 1 =6 , 378 , 137 m
e 2 =0 . 006674372231 ,E 2 =0 . 00669437999

For space reasons, we review the results for only ten points, both for the forward and backward
transformations. Tables 21.3 and 21.4 represent the differences between the Gauss-Krueger con-
formal coordinates {X,Y } and those computed ones {X (trans) ,Y (trans) } . Indeed, the differences
of the Easting were larger than those of the Northing. We have to mention that all transformation
parameters were based on those data of “Deutsches Hauptdreiecksnetz” (DHDN). Accordingly,
the accuracy of the transformation cannot be better than a few centimeters. For a more detailed
analysis, we have chosen five points (Katzenbuckel, Gerabronn, Karlsruhe, Stuttgart, Oberkochen)
whose Gauss-Krueger conformal coordinates as well as ellipsoidal heights are given in Table 21.5 .
Tables 21.6 and 21.7 summarize those polynomial coecients given in Boxes 21.31 and 21.32
representing ( 21.92 )and( 21.93 ), respectively. Note that x 10 x/ρ is denoted as a 10 , x 10 ( x/ρ − y 00 )