$BEG_SKIP





**********************************************************************

COLUMBUS supports OPUS File Importing. You no longer need to manually 
extract the data as described in CASE 3.

***********************************************************************






OVERVIEW:

This sample file demonstrates how to combine multiple OPUS solutions 
(for the same station) in order to compute a weighted average coordinate
position for that station.


*****
SAMPLE BELOW ASSUMES LAT/LON in decimal degrees, HEIGHT in meters. 
All standard deviations (SD's) are in meters.

SD = Standard Deviation
*****



CASE 1:

Computing an average solution is trivial when weights are not utilized. 
For example if you have three sets of coordinates for station AA, you 
simply compute the mean latitude as:

   sum lat = lat1 + lat2 + lat3
   avg lat = lat / 3

You would use a similar calculation for longitude and height.



CASE 2:

Let's complicate it just a bit by assumimg we have a standard deviation
(SD) for each latitude and we now want to compute a weighted average 
latitude. The general approach is:

   sum lat = (lat1 * wgt1) + (lat2 * wgt2) + (lat3 * wgt3)
   avg lat = lat / (wgt1 + wgt2 + wgt3)

   where: wgt1 = 1.0 / (SD squared for lat1)
          wgt2 = 1.0 / (SD squared for lat2)
          wgt3 = 1.0 / (SD squared for lat3)

You would use a similar calculation for longitude and height.



CASE 3:

OPUS solutions make it a bit more complicated, because we have more
weight data then simply a SD for Lat, Lon, and HGT. We have correlation
data as well. Each OPUS solution comes with a Covariance Matrix that
should be used to weight the coordinates for that station. This matrix 
must be inverted to get a weight matrix which is similar in meaning
to wgt1, wgt2, wgt3 from CASE 2.

The ability to perform this computation is built right into the 
existing geodetic least squares adjustment process. All you need to do 
is get your OPUS data into COLUMBUS and adjust. For our example, the
data has already been extracted from the OPUS reports and can be found
at the bottom of this sample file.



The detailed steps for calculating the average OPUS position are:

1) Start COLUMBUS and load this data file (AverageOpusPosition.txt). 

2) Set the View to be 3D Geodetic.

3) Select station AA to be included in the adjustment.

4) Enter the Select Observations dialog, select all coordinate observations.

5) Start the network adjustment. The adjusted lat, lon, hgt should be:

    N  42-49-17.53864
    W 100-04-03.36480
            274.4816 (meters)
    

$END_SKIP



! ***** BEGIN ACTUAL DATA *****


$STATION_TYPE_FOR_OBS
  3D_GEO

$DATUM
  NAD 83
  6378137.0
  298.257222101

$UNITS
  M
  D
  1


! For each OPUS solution (for the same station in this example), create a
! $GEO_COORD_ENUCOV record using the OPUS Lat. Lon, Hgt values along with
! the covariance matrix. Below is a sample covariance matrix taken from
! an OPUS report. It's also used in the first $GEO_COORD_ENUCOV record 
! below.
!
! Covariance Matrix for the enu OPUS Position (meters^2).
!    0.0000001834    -0.0000000469     0.0000003122
!   -0.0000000469     0.0000003424    -0.0000003988
!    0.0000003122    -0.0000003988     0.0000046919


! Code;            Name;     Lat;            Lon;           Hgt;   EE;            EN;           NN;           EU;            NU;           UU
$GEO_COORD_ENUCOV; AA;    42.491753872; -100.040336471; 274.482; 0.0000001834; -0.0000000469; 0.0000003424; 0.0000003122; -0.0000003988; 0.0000046919

$GEO_COORD_ENUCOV; AA;    42.491753856; -100.040336481; 274.480; 0.0000001523; -0.0000000374; 0.0000003671; 0.0000002893; -0.0000004011; 0.0000047111

$GEO_COORD_ENUCOV; AA;    42.491753863; -100.040336487; 274.483; 0.0000001654; -0.0000000399; 0.0000003446; 0.0000002981; -0.0000003945; 0.0000047001