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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004 
  
  
Figure 1: Dual IMU configuration of the test flight. 
From a strict technical point of view, the authors believe 
that the optimal solution is a combination of both approaches 
where the dominant procedure is the integration at the state 
space level (sections 3.1.2 and 3.2.2) for the purpose of 
navigation and sensor calibration. The procedure at the 
observation level plays a secondary role; estimating actual 
noise figures. (This statement is subject to change as em- 
pirical validation as the analysis of actual redundant data 
sets is still in progress.) 
4 DUAL IMU TEST FLIGHT 
In order to validate the concepts and models described so 
far, in July 2003 a test flight was jointly conducted by the 
Institute of Geomatics and StereoCARTO. In the test, two 
similar IMUs were flown. As the goal of this paper is not 
to report on the test flight and its results (still undergoing 
analysis) only a short summary of it and some related re- 
sults will be given. 
4.1 Description of the experiment 
The test was performed in the outskirts of Madrid with 
a Cessna 207 aircraft owned by HIFSA and consisted of 
a photogrammetric-like flight in which two similar IMUs 
(Northrop Grumman LN-200) were placed in a non-ortho- 
gonal configuration using an special mount designed for 
this experiment (see figure 1). The IMUs were some 15 
cm apart from each other. 
The inertial units used in the experiment had different con- 
trol units and output rates. One of the inertial units was 
connected to an Applanix POS/AV 410 owned by Stereo- 
CARTO that delivered data at 200 Hz. The other LN-200 
unit belongs to the 1G, was connected to the TAG system 
and delivers data at 400 Hz. Other details about this flight 
can be seen in (Colomina et al., 2003). 
  
Wo wy, "A Az ay ü. 
(deg/h) (m/s?) 
JA 119 -125 038] -005 000 002 
T 165 177 157 251 268 215 
  
Table 1: Consistency ofthe dual-IMU configuration: resid- 
uals of inertial observations after IMU frame-to-frame 
transformation. 
4.2 Consistency analysis of the dual IMU data 
In (Colomina et al., 2003) a preliminary analysis of the 
consistency of the two IMU data sets was reported. There, 
the simplest possible comparative analysis was carried out. 
After synchronizing/interpolating the two data streams to a 
common discrete time scale at 200 Hz, the total (vector’s 
norm) angular rates and linear accelerations sensed by the 
inertial units were compared. In this paper a similar com- 
parative analysis is done for each one of the sensors. For 
this purpose, the rotation matrix R’ between the two iner- 
tial units, 4 and s was computed by means of the overde- 
termined set of equations 
Qu 7 Hw) 
eus = RME) 
© are the lin- 
ear acceleration observations of the i and s inertial units 
respectively. v*, u$, v? and v7 are the residuals of the ob- 
servation equations as usual. In the above equations, the 
amounts of interest are the precision of the RÀ determina- 
tion and, above, all the residuals. 
where (^, (?, are the angular rate and £ 
The rotation matrix R“ was parametrized by a sequence 
of Euler angles that were estimated with precisions of 4 x 
1075, 5 x 1077 and 5 x 10^? degrees respectively which 
is better than enough for the purpose of the test. 
Some residuals’ series (x- and z-accelerometers and z-ang- 
ular rate sensor) and their Fourier transforms are depicted 
in figure 2. The results, as clearly seen from the graph- 
ics cannot be more encouraging as they can be interpreted 
as white noise (left column) perturbed with engine vibra- 
tions at 20 Hz and its harmonics. Moreover, the mean (41) 
and empirical standard deviation (c) of the residuals after 
the estimation of the rotation matrix R° for each pair of 
homologous sensors in the domain space were computed. 
The i, and c values are depicted in table 1. They are con- 
sistent with the figures provided by the LN-200 vendor (1 
deg/ h angular rate sensor bias, 0.003 m /sec? accelerome- 
ter bias, 62 deg/h (1-c) angular rate sensor noise and 0.354 
m/ sec? (1-0) accelerometer noise, at 200 Hz). Therefore, 
the residuals are close to the uncertainty that characterize 
the sensors and the dual set of inertial observations can be 
considered valid to pursue further research in redundant 
inertial information as intended.