Experiments
To study the efficiency of the proposed algorithm and math-
ematical model, an experiment was conducted using the
in-house built
MMS
. The boresight parameters estimated from
the proposed approach were also tested on a
UAV
flight, where
several
GCPs
were surveyed for accuracy assessment.
The in-house built
MMS
consisted of a Velodyne HDL 32E
lidar and Geodetics’ Geo-iNAV inertial navigation system.
The experiment was performed in a closed room where
multiple planar surfaces exist. In contrast to computing the
boresight parameters on the go (in-flight method), where
IMU
origin and coordinate system is automatically determined
through
GPS/IMU
integration, this experiment uses the physi-
cal definition of the
IMU
origin displayed on the Geo-iNAV
unit. For ground truth, a 3D point cloud of the room was
collected using an independent static Terrestrial Laser Scan-
ner (
TLS
). The
MMS
with its
GPS/IMU
axes clearly visible were
placed in the middle of the room such that the lidar sensor
could capture most of the planes in the room without having
to move the
MMS
. Leica ScanStation II static laser scanner was
used to collect the ground truth 3D point cloud along with the
high-resolution scan of the Geo-iNAV enclosure, which indi-
rectly represents the
IMU
frame axes. By default, the static
TLS
collects on a local coordinate system that has its origin at the
centroid of the scanning mirror after removing offsets. In or-
der to transform the coordinate system of the
TLS
point cloud
to
IMU
body frame, first the plane containing its X, Y axes are
extracted from
TLS
data. Then, the X, and Y axes of
IMU
that
lies on the XY plane are digitized from the point cloud. The
Z axis is perpendicular to XY plane and passing through the
origin. The geometry of the sensor setting is illustrated in
Figure 6.
Thus, the
TLS
data is transformed to
IMU
frame and used
as control surface for the 3D rigid body transformation. After
TLS
data collection, the
MMS
lidar sensor was used to col-
lect 3D data of the room. By default, the
MMS
lidar sensor
data was collected in lidar
SBF
to which misalignment needs
to be computed with respect to
IMU
body frame. After the
point cloud collection of both
TLS
and
MMS
lidar sensors and
preliminary processing of
TLS
data, there will be two point
clouds for the room, one in
IMU
frame and the other in lidar
SBF
. As discussed earlier, in order to use the Volume Mini-
mization algorithm, the lidar sensor need to be placed such
that at least three perpendicular planes are visible from both
TLS
and
MMS
lidar data (Schenk, 1999; Habib
et al
., 2001).
Three such planes and two additional planes in the dataset
are chosen from both the
TLS
and
MMS
lidar point clouds.
Then, volume between corresponding planes are determined
using 3D Delaunay triangulation. It should be noted that a
plane can be defined by as few as three points in which case
the volume between the planes would be simply the volume
of two tetrahedrons. If all conjugate planes have three points,
each will result in six tetrahedrons and therefore, six obser-
vation equations. As there are six parameters that pertain to
boresight calibration, at least seven tetrahedrons are needed
to produce a LSQ solution. Figure 7 shows the point clouds
extracted from a static
TLS
and
MMS
lidar sensor data that
consist of 260 tetrahedrons in this example data. The points
that represent the planes in the lidar sensor frame will carry
the transformation parameters that are boresight rotations
and translations. Therefore, the parameters that transform the
lidar point cloud to
IMU
frame point cloud are determined by
minimizing the volume formed between them. Figure 8 shows
the volume that needs to be minimized. Figure 9 shows co-
registered point clouds are determined after minimizing the
volume. Note that the Figures 7, 8, and 9 show just one of
the five conjugate planes used in the calibration procedure.
The derived boresight parameters are shown in Table 1. The
resulting estimated standard deviation per unit weight is
0.0361 cubic meters.
After boresight calibration was performed in the lab-envi-
ronment, the results were tested on a
UAV
flight dataset. Table
2 shows the system components that were used. The flight
duration was approximately 15 minutes at an altitude of 70 m
AGL
. The
FOV
(Field of View) of the laser scanner was 90° with
the frequency of 10 Hz (600
RPM
). Figure 10 shows the
UAV
used for the data collection and the sensor setup.
The flight plan shown in Figure 11, was designed with
multiple cross paths within the area of interest. The main
purpose of this flight pattern was to emphasize the impact
of uncertainty of boresight parameters on the georeferenced
point clouds on the crossing paths. For this reason, several
Ground Control Points (
GCP
) were marked and surveyed be-
fore the flight for data evaluation, as shown in Figure 11.
Figure 12a shows the reconstructed point cloud using ap-
proximate (uncalibrated and estimated roughly by eye-balling
the laser scanner frame with respect to the
IMU
body frame)
boresight parameters, and Figure 12 shows the geo-referenced
point clouds after applying the calibrated boresight parameters
Figure 6. Calibration Test Setup and
GPS
/
IMU
/Laser Frames.
Figure 7.
TLS
point cloud in
IMU
frame (dot) and lidar point
cloud in local sensor frame (cross) before registration.
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October 2018
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
