The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008
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determine the boresight misalignment angles using overlapping
LiDAR strips, flown in different directions.
Not long ago, another rigorous class of calibration procedures
started to emerge (Filin, 2003; Friess, 2006; Skaloud and Lichti,
2006; Scaloud and Schaer, 2007). These types of approaches
model all systematic errors directly in the measurement domain
and condition groups of points to reside on a common surface
of known form.
The earlier methods, related to LiDAR strip adjustment, also
addressed the effects of systematic errors in the registration
(which was based on DEM matching) of overlapping point
clouds. For extended literature review about co-registration, see
in Pothou et al., 2006a; Pothou et al., 2006b.
Currently the most common method of calibrating a LiDAR
sensor is also the least rigorous: profiles of overlapping strips
are compared and an experienced operator manually adjusts the
misalignment angles until the strips appear to visually fit.
Although practical, this approach is time consuming and labor
intensive and the results do not immediately provide any
statistical measure on the quality of the calibration (Morin and
El-Sheimy, 2002). Furthermore, the existing methods often
cannot reliably recover all three of the angular mounting
parameters. The undetermined parameter(s) propagate into the
subsequently captured data, therefore compromising the
accuracy of any derived product. Thus, much research effort is
still devoted to improve these processes. Most of the adopted
approaches are usually based on either physical boundaries or
cross-sections (Schenk, 2001) or DTM/DSM gradients (Burman,
2000), mimicking the photogrammetric calibration approach via
signalized or intensity-deduced targets points. The drawbacks
of these methods is the lack (or simplification) of assurance
measures, correlation with the unknown terrain shape or limits
imposed by laser pointing accuracy and uncertainty due to
beam-width. Habib et al. (2007), proposed a LiDAR system
self-calibration using planar patches derived from
photogrammetric data. Not only is the mathematical model for
the LiDAR system calibration by using control planar patches
presented but also the optimal configuration for flight
conditions and the distribution of planar patches, to avoid
possible correlations have also been analysed.
Pothou et al. (2007), introduced a novel prototype algorithm for
observing, and subsequently determining the boresight
misalignment of LiDAR/IMU, using two different surfaces
(point datasets). This algorithm minimizes the distances
between points of the target surface and surface patches (TINs)
of the reference surface, along the corresponding surface
normals (based on Schenk et al., 2000). The technique can be
applied to various data combinations, such as matching LiDAR
strips or comparing LiDAR data to photogrammetrically
derived surfaces. Object of simple shape similar to man-made
structures, such as buildings, have been chosen and constructed
to perform the surface matching. The processing algorithm
includes additional testing of the validity, accuracy, and
precision of various statistical tests (QA/QC - Quality
Assurance/Quality Control) for outlier detection in positioning
and attitude data.
In this research, the feasibility of using urban areas for
boresight misalignment is investigated. Buildings are of
particular interest; in other words, what the impact of the
building shape, size, distribution, etc. is on the performance of
the boresight misalignment process. Photogrammetrically
restituted buildings were used as reference surfaces called
‘building-positions’ or ‘reference-positions’. The influence of
the number and distribution of the necessary ‘building-
positions’ on boresight’s misalignment parameter estimation is
evaluated. Experiments with various number of ‘building-
positions’ in regular as well as random distribution are
presented, analyzed and evaluated through QA/QC statistical
tests. The optimum number and distribution of ‘building-
positions’ have been determined and proposed.
In Section 2, a short review of the status of multi-sensor
calibration and boresight misalignment of LiDAR/IMU is
provided. Section 3 outlines the mathematical model of the
algorithm for the boresight misalignment and presents the
statistical analysis of the QA/QC techniques supported by the
LiDAR/IMU boresight misalignment calculation. In Section 4,
the dataset used for testing is described. The experimental
results, as well as their statistical analysis and their effects on
LiDAR points, are described in Section 5. Section 6 concludes
the research.
2. MULTI SENSOR CALIBRATION - BORESIGHT
MISALIGNMENT
The IMU frame is usually considered as the local reference
system of the MMS system, and thus, the navigation solution is
computed within this frame. The spatial relationship between
the laser scanner and the IMU is defined by the offset and
rotation between the two systems. To obtain the local object
coordinates of a LiDAR point, the laser range vector has to be
reduced to the IMU system by applying the offsets and rotations
between the two systems, which provides the coordinates of the
LiDAR point in the IMU system. The GPS/IMU based
navigation provides the orientation of the IMU frame, including
position and attitude, and thus, the mapping frame coordinates
can be subsequently derived. In our discussion, the
determination of the boresight offset (b x , b y , b z ) and the
boresight matrix (rotations co, tp, k) between the IMU and the
laser frame (provided that sufficient ground control is available)
is addressed.
Any discrepancy in boresight values results in a misfit between
the LiDAR points and the ground surface, and thus, the
calculated coordinates of the LiDAR points are not correct
(Toth, 2002). Ideally, the calibration parameters should stay
constant for subsequent missions. The description of the effects
of the different boresight misalignment angles is omitted here;
for details see (Baltsavias, 1999). For a detailed description of
multisensor calibration - boresight misalignment, see Toth and
Csanyi, 2001; Toth, 2002; Pothou et al., 2007.
3. MATHEMATICAL MODEL OF THE ALGORITHM
Two datasets, called point clouds, P (x pi , y pi , z^) (p f = 1,..., n)
and Q (Xqj, y qi , z qi ) (qj= 1,..., m), which describe the same
object are captured by different technologies and they must be
transformed into a common system. Assuming that these
datasets are connected by a 6-parameter 3D transformation, the
three offset and three rotation parameters can be estimated,
minimizing the distance between a point of Q dataset and a TIN
surface patch of P surface, which is described by points of P
dataset (Equation 1). In Figure 1, point qj (Xqj, y qi , z qi ) of Q
point cloud, has to be transformed to the closest surface patch
of the control surface P, defined by 3 points (p m , p k , pQ, through