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georeferencing point shape

4 messages · Häring, Tim (LWF), Roger Bivand, Tom Gottfried

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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 H?ring
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
Tom Gottfried
# 
Hi Tim,
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.
If you can assume the little differences being due to the error in gps-measurements, you could
calculate your coordinates with all your gps points as a basis and then take the mean as final value.

Tom

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Roger Bivand
    

    

      
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On Tue, 15 Jun 2010, Tom Gottfried wrote:

        

            

      
      
      
    

        
There is a problem with the known points too, in that their surveyed and 
GPS interpoint distances differ somewhat:

dist(cbind(gps_x, gps_y)[17:20,])
dist(cbind(x, y)[17:20,])
dist(cbind(gps_x, gps_y)[17:20,]) - dist(cbind(x, y)[17:20,])

This means that with only 4 GPS points, it is hard to model the 
transformation with more terms:

df <- data.frame(gps_x, gps_y, x, y)
lmx <- lm(gps_x ~ x + y, data=df[17:20,])
lmy <- lm(gps_y ~ x + y, data=df[17:20,])
nx <- predict(lmx, data.frame(x, y))
ny <- predict(lmy, data.frame(x, y))
dist(cbind(nx, ny)[17:20,])
dxy <- dist(cbind(x, y))
dnxny <- dist(cbind(nx, ny))
all.equal(dxy, dnxny, check.attributes=FALSE)

More GPS measurements would have helped, but at this scale, GPS are always 
going to be approximate. You cannot measure the centres of the GPS and 
surveyed points accurately either, I'm afraid. To fix things, you would 
need GPS measurements in the precision of the data set, so in most cases 
like this DGPS rather than GPS. If one of the surveyed points is clearly 
visible on a registered high resolution image, you could use that instead 
of the GPS - something like the corner of a building (measured to about 
1cm and known in the projection of interest). However, planning this 
before doing the fieldwork was the only effective remedy.

Roger

PS. Do you know that the GPS was using the ellipse you specify? Which 
datum are you assuming (WGS84)?

            

      
      
      
    

        

  
    

      
      
    

  


  


      

    

    
1 day later

    

      
      

        


  

        

      Tom Gottfried
    

    

      
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Am 15.06.2010 15:48, schrieb Roger Bivand:

            

      
      
      
    

        
Yes! And the surveyed interpoint distances should be more accurate. Thus, I think it's better to
rely on the surveyed (relative) coordinates, rather than transforming them to obtain the best fit
with the erroneous GPS-measurements.
But "snapping" the relative coordinates to the projected coordinate system by something like

x_new <- rep(0, times=length(x))
y_new <- x_new
for (i in 17:20){x_new <- x_new + gps_x[i]+x-x[i]; y_new <- y_new + gps_y[i]+y-y[i]}
x_new <- x_new/4; y_new <- y_new/4

(as I suggested last time), assumes that the error of GPS is random in both dimensions and has an
expected value of 0. Might this assumption be unrealistic?

            

      
      
      
    

        
Orthophotos (I think with a resolution of 40 cm) are available. This should be already much better
than the mean of the GPS measurements.

Tom