[R-sig-Geo] georeferencing point shape

[Häring, Tim (LWF)]

Hello !

I have a point shape containing field measurements in a small scale studyarea. Unfortunately these points didn`t have geographic or projected coordinates. The spatial reference for these points are theodolite measurements. For four corner points gps measurements of projected coordinates are available. I want to georeference my point shape in these projected coordinate system and have no idea how.
Here is a subset of my data:

x <- c(5.786, -3.766, -12.613, -21.836, -26.340, 3.958, -11.120, -17.266, -18.938,
  16.751, -21.507, 26.420, -19.916, 23.184, 9.660, -5.711, -18.256, 27.888, 12.634, -33.510)
y <- c(4.470, 0.797, -3.130, -7.656, -9.313, 8.700, 6.923, 8.545, 12.468, 4.748,
  -20.920, -5.396, -24.830, -11.636, 22.462, 19.210, -28.851, -9.510, 27.421, 8.035)
z <- c(1100.493, 1100.867, 1101.798, 1102.559, 1103.703, 1102.366, 1107.249, 1110.781,
 1113.920, 1096.967, 1095.284, 1088.956, 1092.869, 1086.786, 1101.300, 1110.197, NA, NA, NA, NA)
gps_x <- c(NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA, 4560136, 4560184, 4560172, 4560121)
gps_y <- c(NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA, 5289465, 5289482, 5289521, 5289502)

d <- data.frame(x,y,z,gps_x,gps_y)
d
coordinates(d) = ~x+y
plot(d, axes=T)

gps_points <- d[17:20,]
points(gps_points, pch=19, col="red")

Because both measurements - the theodolite values and the gps values - are measured in meters, my first idea was to calculate the coordinates for all points by sum the difference between a gps point and every single theodolite point in x- and y-direction. Unfortunately there are little differences depending which gps point is used as basis.
Is there a better way to transform the point pattern into the projected coordinate system?
The proj4string for my coordinate system is:
+proj=tmerc +lat_0=0 +lon_0=12 +k=1 +x_0=4500000 +y_0=0 +ellps=bessel +units=m +no_defs

Thank you very much.

TIM



----------------------------------------------------------------------------------- 
Tim Häring
Bavarian State Institute of Forestry 
Department of Forest Ecology
Hans-Carl-von-Carlowitz-Platz 1
D-85354 Freising

E-Mail: tim.haering at lwf.bayern.de
http://www.lwf.bayern.de