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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part BS. Istanbul 2004 
  
ov) 
Outpyt 
Bias error 
  
Figure 8. Bias error 
Time 
Table 4. Bias errors contained in the sensors 
  
  
  
  
  
  
  
  
  
  
  
  
  
    
   
  
  
  
Time[s] 
Item X-axis | Y-axis | Z-axis 
Accelerometer [m/s] 0.005 0.020 —0.002 
Fiber optical gyro [°/s] | 0.053 | 0.018 | 0.004 
Vibration gyro [°/s] 0.788 | 0.639 | 0.082 
Accelerometer (a) 
80 rt matt qe re tr aie se té | 
Y-axis 70m , 
—60 ^ 
E A 
[5] 
eo 
= 40 y^ 
i oil 
= 20 A X-axis. 16m 
g 
ti 
0 
Z-axis -6m | 
-20 L—————— M ——————— 
0 60 
Time[s] 
Fiber optical gyro (b) 
4 KOC We eoe ei eee ee eee e | 
| X-axis’ 3.2deg 
P| 
i 
9 
En | 
82 | 
E | Y-axis 1.1deg | 
35 1 | iet 
| "axis 0.3deg 
34 ire pl ! 
0 40 
Time[s] 
Vibration gyro (c) 
50 T 
| X-axis 47deg 
_40 | 
eo "Pl 
i can 
eO t i 
S Pi 
= A 
=20 e 
£ SL axis 38deg 
m 
10 di 
VA Z-axis Sdeg 
ee uem 
0 40 
Figure 9. Positioning and angle error due to bias error 
The bias errors are estimated at each stopping point 
R,,(n-1-N) as the averages of 50 consecutive 
outputs from the sensors sampled at every 2ms during 
the time interval [t, —1,7,]. As mentioned before, the 
equipment leaves from R, , at time point 7, , so the 
averages are taken over the one-second intervals just 
before leaving times. Then, the bias errors thus estimated 
are subtracted from the measured values of accelerations 
and angular velocities during the time interval [7,, 7,] so 
as to eliminate their effects. This method of bias 
elimination should be called “the bias correction”. In 
figure 10(a) shows the trajectories projected on a 
horizontal plane estimated by means of the stop-and-go 
strategy with and without the bias correction in the case 
that the stoppage interval is 10m. In figure 10(b), the 
elevations or z-coordinates are plotted as functions of the 
horizontal distance that is defined as the length from the 
starting point along the route projected on a horizontal 
plane. As can be seen from this figure, the discrepancy 
between the estimated trajectory and the true one is 
notably reduced by correcting the bias errors. 
  
  
  
Plane alignment (a) 
pe me c 4 40 
| | 30 
£ | ur j 10 
E Y 
z 7 | 
X | bes; i 
| BR t | -10 
LI ag 
-140 -120 -100 -80  -60 -40 -20 0 20 
Y(East- West)[m] 
— True value — Before correction — After correction 
Vertical alignment (5) 
1.0 
0.0 
-].0 
Elevation Discrepancy[m] 
  
0 50 100 150 200 
Horizontal distance[m] 
  
= True value Before correction -— After correction 
Figure 10. Effects of the bias correction applied to 
the inertial survey together with the stop- 
and-go strategy.