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LIDAR STRIP ADJUSTMENT USING CONJUGATE LINEAR FEATURES IN 
OVERLAPPING STRIPS 
A. F. Habib a ’ *, A. P. Kersting 3 , Z. Ruifang 3 , M. Al-Durgham 3 , C. Kim 3 , D. C. Lee b 
3 Dept, of Geomatics Engineering, University of Calgary, 2500 University Dr. NW, 
Calgary, Alberta, T2N 1N4, Canada, habib@geomatics.ucalgary.ca 
b Department of Geo-Informatics, Sejong University, Seoul, South Korea, dclee@sejong.ac.kr 
Commission, WG 1/1 
KEY WORDS: LIDAR, Adjustment, Semi-Automation, Matching, Accuracy 
ABSTRACT: 
LiDAR (Light Detection And Ranging) is a multisensory system consisting of three main components: laser, GPS, and IMU units. 
The basic principle is to measure distances from the sensor to the ground by converting the travel time information of the laser 
pulses sent to the earth. A scanning mechanism, usually a scanning mirror, is used to collect the data in a strip-wise fashion. The 
ground coordinates of the laser footprints are derived using the direct geo-referencing information furnished by the onboard 
GPS/IMU unit and the calibration parameters determined through a calibration procedure. When the calibration parameters are not 
accurately determined, systematic discrepancies between overlapping strips might occur. The ideal solution for the adjustment of 
neighboring strips is the implementation of an accurate calibration procedure. However, such a calibration demands the original 
observations (GPS, IMU and the laser measurements), which are not usually available to the end-user. In this work, a strip 
adjustment procedure for reducing or eliminating discrepancies between overlapping LiDAR strips is proposed. The mathematical 
model employed is similar to that used in the photogrammetric Block Adjustment of Independent Models (BAIM). Generally, a 
traditional BAIM uses conjugate points. These features, however, are not suitable for LiDAR surfaces since it is almost impossible 
to identify conjugate points in overlapping LiDAR strips. In this work, the use of linear features, which are represented by sets of 
non-conjugate points, is investigated. The non-correspondence of the selected points along the linear features is compensated for by 
artificially expanding their variance-covariance matrices. The paper presents experimental results from real data illustrating the 
feasibility of the proposed procedure. 
1. INTRODUCTION 
A LiDAR system is basically composed of a laser ranging and 
scanning unit and a position and orientation system (POS), 
which consists of an integrated differential global positioning 
system (DGPS) and an inertial measurement unit (IMU). The 
principle of laser ranging is to measure distances from the 
sensor to the ground. The GPS system provides position 
information and the IMU provides attitude information. 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 q , can be derived through the summation 
of three vectors (X 0 ,P G and p ) after applying the appropriate 
rotations: R ym pm , R^ MM and R a „. In this equation, 
X o is the vector from the origin of the ground coordinate 
system to the origin of the IMU coordinate system, P G 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 R yaw pitch roU stands for the 
rotation matrix relating the ground and IMU coordinate systems, 
R A o A/c 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 ft being the mirror 
scan angles. For a linear scanner, which is the focus of this 
paper, the mirror is rotated in one direction only leading to zero 
CC angle. 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. 
Due to systematic errors in the LiDAR components and/or 
resulting from their integration, adjacent LiDAR strips might 
exhibit discrepancies. Such systematic discrepancies are caused 
by missing or improperly employed calibration and operational 
procedures. The ideal solution for obtaining a homogeneous 
dataset, with overlapping strips coinciding properly is the 
implementation of an accurate calibration procedure. However, 
a calibration procedure demands the original observations (GPS 
and IMU measurements and laser scanner observations), which 
are not usually available to the end user. Instead, only the XYZ- 
coordinates of the LiDAR 
* Corresponding author.