International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
3. SYSTEM CALIBRATION
The system calibration can be divided into a few basic steps:
e Lever arm calibration: finding the linear offsets
between each measurement unit
e Boresight calibration: determining the angular offsets
between the IMU and the sensors due to mounting
e [nterior calibration: finding or re-fining parameters
related to sensors' interior orientation (Lidar, camera).
In principle, all these steps can but do not have to be calibrated in-
flight (Colomina, 1999; Kruck, 2001). In-flight calibration is
convenient, but may not deliver the desired accuracy when the
correlation between the estimated parameters remains significant.
In the following, we demonstrate how the calibration accuracy
(and thus mapping) improves when at least the lever arm
calibration is performed separately and time correlation of the
IMU derived attitude is properly considered.
3.1 Lever arms
Thanks to the small separation between instruments, the lever
arms relating the camera projection centre to GPS antenna phase
centre, the IMU navigation centre and the laser measurement
origin can be determined in laboratory with mm-level accuracy.
This is accomplished using tacheometric measurements and
terrestrial photogrammetry. Instead of mounting the GPS antenna,
IMU and the laser on the frame, three steel needles materialize the
physical centres of these sensors. A calibration polygon of about
twenty targets is captured with the camera mounted in the frame
from three different positions. For each position, the needles are
surveyed with a theodolite in the coordinate system with known
relation to the calibration polygon. A self-calibration bundle
adjustment is performed on the image set (Kruck, 2001) to obtain
the coordinates of the projection centre and the orientation of the
camera with respect to the lab-frame. Parameters of interior
orientation may be also estimated this way, although with lower
accuracy. With this method, the lever arms are determined in the
camera-frame with accuracy better than 1 cm.
In the following we compare the above ‘exact’ method with other
convenient, albeit less precise approaches:
A. In-flight estimation of the camera-GPS lever arm by the
rigorous approach of integrated bundle adjustment
(Kruck, 2001) with and without control points.
B. In-flight estimation of the camera-GPS lever arm by
comparing the AT-derived projection centre with GPS
antenna coordinates (needs control points).
C. In-flight estimate of GPS-IMU lever arm as additional
states in GPS/INS Kalman Filter.
Error in lever arm [cm]
X X 7 o
A: with control points 0.4 0.2 3.5 2
A: with no control pts. 1.3 5.0 26 36
B: AT/GPS - 2 steps 0.2 3 4 17
C: GPS/INS - KF 5.0 18 30 2
Table 2: Error in lever arm estimates when compared with
laboratory values in camera (A+B) and body frames (C).
Method
Table 2 summarizes the results. Just the estimates of the first (A)
approach agree well with the laboratory values but only when a
794
significant number of control points is used. The estimated lever
arm between GPS-IMU observation centres by approach (C) is
also inaccurate although the flight included several figure-eight
turns to decorrelate the relations among the Kalman Filter states,
Determining the lever arm with respect to laser scanner in-flight is
even more problematic. Hence, since neither of the considered in-
flight methods offers satisfactory solution, the lever arm values
should be determined in lab rather than estimated from airborne
data.
3.2 Boresight
Unlike the lever arms, the boresight angels are difficult to
estimate in laboratory with adequate accuracy, although methods
to do so have been proposed (Báumker and Heimes, 2001). This
is mainly due to the difficulty of achieving good IMU-alignment
without inducing sufficient dynamic. Here, in-flight calibration
offers the best solution.
For the best simultaneous estimate of boresight angles for camera
and Lidar we propose flying over a rectangular building with a
flat roof in two perpendicular stripes in both directions at different
scales. The area may or may not be equipped with accurate
Ground Control Points (GCPs), however the latter improves the
estimate. As for the camera, three approaches have been
considered before selecting the most accurate one (Skaloud and
Schaer, 2003):
L One-step procedure: the INS/GPS attitude and position are
introduced as additional observations into the bundle
adjustment and the boresight angles are estimated together
with the parameters of exterior and interior orientation
(Kruck, 2001).
II. Traditional two-steps procedure: AT including the GPS or
GPS/INS coordinates of the camera projection centre is
performed in self calibration mode and the camera
orientation is compared with INS/GPS attitude at each
photograph. The differences are formed, and boresight
angles are computed as their (weighted-) average.
III. Modified two-step procedure: As method II
accounting for the time correlations in the IMU data. As
these correlations are significant (Figure 5), the changed
weighting scheme provides unbiased boresight estimate
with realistic level of confidence.
while
= Mightine 1
.flighttine 2. .
eod
-4 r
flight line 3___
erem
image number [column]
25
30 35
variance-covariance
scale [rad]
9 5 10 18 20
image number [row]
Figure 5: Qy weighting matrix with IMU temporal correlations.
