International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
  
Discrepancy LA | e 19 | RMSE 
X 028.189.138. 5340 
Y 44542239: 158-7163 
Cov. 
Correl.coeff. :0:27 
Plan. RMSE p 
  
  
  
Table 5. Statistics of Discrepancy of 10-minutes observations: - 
Tables 2, 3, 4, and 5 show that the deterministic error, as well 
as the stochastic error; are decreasing as a function of 
increasing the observation times (1 min, 3 mia. 3 nin. 10 min) 
4.1 Averaging Positionin 
To investigate the influence of time averaging, results of 4 
different acquisition times, namely; I min, 3min, 5min, and 
10min, are presented in the following tables for comparison. 
  
  
  
Averaging Time RMSE o 
| MINUTE 3.41 3.20 
3 MINUTES 314 2.86 
5 MINUTES 2.78 2.62 
10 MINUTES 2.15 2.06 
  
Table 6. Effect of averaging (in meters) 
Results of the table 6 show an increase in accuracy on 
averaging over longer periods, as expected. 
  
  
4.00 
2.78 
3.00 
2.00 
1.00 
RMSE in meters 
  
  
  
  
0.00 
1.00 300 500 10.00 
Averaging time in minutes 
Figure 1 RMSE Vs Observation Time 
  
3.500 —20 
3.000 
2.500 
2.000 
1.500 
1.000 
0.500 
0.000 
    
  
standard deviation 
  
  
1.00 2 3.00 500 10.00 
Averaging time in minutes 
Figure 2 Standard Deviation Vs Observation Time 
630 
Figures 1, and 2 show a decrease in RMSE, respectively 
standard deviation as a function of averaging time. 
5. TESTING DISCREPANCIES AT DIFFERENT 
CONFIDENCE LEVELS 
Estimation of the confidence interval of the errors requires 
estimation of statistical parameters, followed by evaluation of 
the statistical distribution model of the population parameters. 
A large number of samples are needed to have a valid 
conclusion. It was further assumed that the discrepancies follow 
a normal distribution, N (4,0 ). Statistical analysis of 
discrepancies consist of testing: Hy : the individual discrepancy 
belongs to the population error, against, and H, : the individual 
discrepancy is not a member of this population: 
To compute confidence intervals the values X t Z,O£& are 
used. where, Z is the standard normal confidence level, 
c 
and, X and Oz are the sample mean and standard deviation of 
the sample, respectively. 
Discrepancy scatter plot, for time-averaged positions at 1, 355, 
and 10 minutes, are presented in figure 3 (A, B, C, D) 
respectively. 
  
discrepancy In y-direction{Yret - Yc} 
  
  
discrepancy in y-direction(Yref - Yc} 
  
discrepancy in x-direction(Xref -Xc) — 
  
Interi 
— 
discrepancy in y-direction( Yref - Yc) 
discrepancy in y-direction(Yref - Yc) 
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Figi 
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