ınbul 2004 
  
x © 
c effects 
ons that is 
(3) 
natrix 
(4) 
2; y, Z, dt), 
of columns 
- number of 
values from 
Applying 
own vector 
(5) 
n estimated 
(6) 
(7) 
n is the 
of 
edundant 
defined as 
(8) 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
Own Pay Tur 9: 
oO Oo oO 
C. ou o m mme tous 
A ET 
0 O zx Oy O zz OzT 
Or Og Or Orr 
Where the diagonal elements of the matrix refer to the are 
Oxx the variance of X, Cyy variance of y, OZ 
variance of Z , and OrT variance of time, and off-diagonal 
elements are covariances. Various dilutions of precision factors 
can now be computed: 
The horizontal dilution of precision is defined as: 
IHDOP-- ——— ——— (10) 
and the vertical dilution of precision as: 
yDOP.s. -—Z. (11) 
The semi-axis of the confidence regions are related to the 
eigenvalues of this matrix (Vanicek, P. and E.J. Krakiwsky, , 
1986) 
2. DATA COLLECTION AND VALIDATION 
To practically verify the GPS error model, and estimate the 
positional error of the measurements of ground control points 
using a GPS code receiver, the discrepancies between receiver 
coordinates and reference coordinates are computed in a study 
area around the ITC building in Enschede, The Netherlands 
using a Garmin map 76s code receiver and a Leica 300 
differential carrier phase instrument. The coordinates of the 
points obtained by carrier phase measurement were used as 
reference, to compute errors of the code measurements. 
3. COORDINATE SYSTEMS. 
For the analysis 3 different coordinate systems were used: 
-WGS 84, which is the common GPS coordinate system. 
-RD and NAP, Dutch coordinate system, used in The 
Netherlands. 
- Local (plane tangential) system, 
The transformation parameters used to transform data from 
WGS84 to RD and NAP, used in phase observation, are 
different to that applied by Garmin code receivers. Therefore 
the geodetic WGS84 coordinate ( Q, À, h) is converted Ta X, 
629 
Y, Z geocentric coordinate, and discrepancies AX, AY, AZ are 
computed. 
To be interpretable for practical use, geocentric discrepancies 
AX, AY, AZ are transformed into a plane tangent to the earth 
surface, at the centre of gravity of the study area, the local 
coordinate system (AN, AE, AH). 
The following equations were applied for the transformation of 
discrepancies from AX, AY, and AZ to the local coordinated 
system in the plane surface, which is shown (AN, AE, AH) 
AE =—AX -sinA+ AY - cosA 
AN =—AX - cosÀ - sinp — AY - sind - sinp + AZ - cos (11) 
AH = AX - cos - cos + AY - sind - cosp+ AZ - sing 
Where, @ refers to the geodetic latitude of a target point and À, 
is defined as the geodetic longitude of a target point. 
4. RESULTS 
The average of discrepancies p represents the deterministic 
error, and c indicates the stochastic error. Four different 
observation times (1, 3, 5 and 10 minutes) were used, applying 
a Garmin map76s handheld receiver. The following tables show 
the result in the local coordinate system. 
  
  
Discrepancy | u | o | s | RMSE 
AX -0.78 455 213 224 
AY -1.04 5.67, 2382 2,56 
Cov. -0.99 
Correl. oeff. -0.19 
Plani. MSE 3.40 
  
  
  
Table 2. Statistics of Discrepancy of 1-minute observations: 
  
  
Discrepancy u | c? | o | RMSE 
AX -0.72 3.02 1.74 1.87 
AY -l.04 5.14 227 2.48 
Cov -0.96 
Correl. coeff. -0.25 
Plani. RMSE 3.11 
  
  
  
Table 3. Statistics of Discrepancy of 3-minutes observations: 
  
  
Discrepancy | u | c? | o | RMSE 
AX -0.46 2.12 1.46 1.52 
AY 0.82 5.60 2.38 2.32 
Cox 0.17 
Correl.coeff. -0.06 
  
  
  
Table 4. Statistics of Discrepancy of 5-minutes observations