The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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overlapping LiDAR strips and control surfaces. Due to the 
irregular nature of the LiDAR footprints, the identification of 
distinct points (e.g., building comers) is quite difficult and not 
reliable. More suitable primitives have been suggested by Maas 
(2000), where the correspondence is established between 
discrete points in one LiDAR strip and TIN patches in the other 
one. The correspondences are derived through a least-squares 
matching procedure where normal distances between conjugate 
point-patch pairs are minimized. The drawback of this work is 
that simple shifts were used as the transformation function 
relating conjugate point-patch pairs. The validity of such a 
model was not completely justified. Moreover, the estimated 
shifts were not used to derive an indication of the point cloud 
quality. Bretar et al., (2004) proposed an alternative 
methodology for improving the quality of LiDAR data using 
derived surfaces from photogrammetric procedures. The main 
disadvantage, which limits the practicality of this methodology, 
is relying on having aerial, imagery over the same area. In 
addition, the proposed approach uses an affine transformation to 
relate LiDAR and photogrammetric surfaces without sufficient 
justification. In Pfeifer et al. (2005) and Vosselman (2004) 
other methods were developed for detecting discrepancies 
between overlapping strips. Detected discrepancies were used 
for strip adjustment procedures rather than system and data 
evaluation. 
The objective of this paper is to propose a cost-effective and 
meaningful quality control (QC) method, which is based on 
analyzing the compatibility of LiDAR data in overlapping strips. 
More explicitly, the objective of the presented research is to 
develop a tool for detecting the presence of systematic biases as 
well as inspecting the noise level in the point cloud with a 
satisfactory level of automation (i.e., requiring minimum user 
interaction). The paper will start with a brief discussion of the 
LiDAR mathematical model relating the system measurements 
to the ground coordinates of the point cloud. Then, an analysis 
of possible systematic and random errors and their impact on 
the resulting surface will be outlined. Following the discussion 
of the error sources and their impact on the accuracy of the 
LiDAR footprints, a QC tool will be proposed. The paper will 
conclude by experimental results from a real dataset involving 
overlapping strips from operational LiDAR system. The results 
have proven the feasibility of the introduced methodology to 
evaluate the quality of the LiDAR data. More specifically, the 
proposed measure detected the presence of systematic biases 
and the data noise level. Future research will focus on relating 
the detected discrepancies between overlapping strips to the 
system biases. 
2. LIDAR MATHEMATICAL MODEL 
The coordinates of the LiDAR footprints are the result of 
combining the derived measurements from each of its system 
components, as well as the bore-sighting parameters relating 
such components. The relationship between the system 
measurements and parameters is embodied in the LiDAR 
equation (Vaughn et al., 1996; Schenk, 2001; El-Sheimy et al., 
2005), Equation 1. As it can be seen in Figure 1, the position of 
the laser footprint, X G , can be derived through the summation 
of three vectors (X o , P G and /5 ) after applying the appropriate 
rotations: R . . „ R. . , . and R In this equation, 
yaw, pitch, roll ’ Aco,A</>,Ak ct,p ^ 9 
X o is the vector between the origins of the ground and IMU 
coordinate systems, P is the offset between the laser unit and 
IMU coordinate systems (bore-sighting offset), and p is the 
laser range vector whose magnitude is equivalent to the distance 
from the laser firing point to its footprint. The term 
Ryan pitch roil stan ds for the rotation matrix relating the ground 
and IMU coordinate systems, R A(o A(A Av represents the rotation 
matrix relating the IMU and laser unit coordinate systems 
(angular bore-sighting), and R a p refers to the rotation matrix 
relating the laser unit and laser beam coordinate systems with 
a and fd being the mirror scan angles. For a linear scanner, 
which is the focus of this paper, the mirror is rotated in one 
direction only (i.e., a is equal to zero). The involved 
quantities in the LiDAR equation are all measured during the 
acquisition process except for the bore-sighting angular and 
offset parameters (mounting parameters), which are usually 
determined through a calibration procedure. 
3. LIDAR ERROR BUDGET 
The quality of the derived point cloud from a LiDAR system 
depends on the random and systematic errors in the system 
measurements and parameters. A detailed description of LiDAR 
random and systematic errors can be found in Huising and 
Pereira (1998), Baltsavias (1999), and Schenk (2001). The 
magnitude of the random errors depends on the accuracy of the 
system’s measurements, which include position and orientation 
measurements from the GPS/IMU unit, mirror angles, and 
ranges. Systematic errors, on the other hand, are mainly caused 
by biases in the bore-sighting parameters relating the system 
components as well as biases in the system measurements (e.g., 
ranges and mirror angles). In the following sub-sections, the 
impact of random and systematic errors in the system 
measurements and parameters on the reconstructed object space 
will be analyzed. 
3.1 Random Errors 
The purpose of studying the impact of random errors is to 
provide sufficient understanding of the nature of the noise in the 
derived point cloud as well as the achievable accuracy from a 
given flight and system configuration. In this work, the effect of 
random errors in the system measurements is analyzed through 
a simulation. The simulation process starts from a given surface 
and trajectory, which are then used to derive the system 
measurements (ranges, mirror angles, position and orientation 
information for each pulse). Then, noise is added to the system 
measurements, which are later used to reconstruct the surface 
through the LiDAR equation. The differences between the 
noise-contaminated and true coordinates of footprints are used 
to represent the impact of a given noise in the system 
measurements. The following list summarizes the effect of 
noise in the system measurements. 
• Position noise will lead to similar noise in the derived 
point cloud. Moreover, the effect is independent of the 
system flying height and scan angle. 
• Orientation noise (attitude or mirror angles) will affect the 
horizontal coordinates more than the vertical coordinates. 
In addition, the effect is dependent on the system flying 
height and scan angle.