The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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• Range noise mainly affects the vertical component of the system flying height. The impact, however, is dependent 
derived coordinates. The effect is independent of the on the system’s scan angle. 
2.1 MU body frame 
Figure 1. Coordinate systems and involved quantities in the LiDAR equation 
XG *o ^yaw, pitch, roll *G ^yaw, pitch, roll ^Aa>, At)>, Ak ^a, ß 
0 
0 
- p. 
(1) 
Through the proposed simulation, it could be noticed that noise 
in some of the system measurements affects the relative 
accuracy of the derived point cloud. For instance, a given 
attitude noise in the GPS/INS derived orientation affects the 
nadir region of the flight trajectory less significantly than off 
nadir regions. Such a phenomenon is contrary to derived 
surfaces from photogrammetric mapping where the 
measurements noise does not affect the relative accuracy of the 
final product. An additional conclusion that could be drawn 
from the simulation experiments is that the introduction of noise 
in the system measurements does not lead to systematic 
discrepancies between conjugate features in overlapping strips. 
3.2 Systematic Errors 
In this work, the impact of systematic errors/biases in the bore 
sighting parameters (spatial and rotational) on the derived point 
cloud will be analysed. A simulation process was accomplished 
for that purpose. The process starts from a given simulated 
surface and trajectory, which are then used to derive the system 
measurements (ranges, mirror angles, position and orientation 
information for each pulse). Then, biases are added to the 
system parameters, which are used to reconstruct the surface 
through the LiDAR equation. The differences between the bias- 
contaminated and true coordinates of the footprints within the 
mapped area are used to represent the impact of a given bias in 
the system parameters or measurements. Due to the presence of 
systematic errors in the system parameters, the bias- 
contaminated coordinates of conjugate points in overlapping 
strips will show systematic discrepancies. The following 
conclusions could be drawn from the simulation experiments: 
(1) The discrepancies caused by the bore-sighting offset and 
angular biases can be modelled by shifts and a rotation 
across the flight direction. Therefore, a six-parameter 
rigid-body transformation (three shifts and three rotations) 
can be used to express the relationship between conjugate 
features in overlapping strips. 
(2) The discrepancies can be used for diagnosing the nature of 
the systematic errors in the system parameters. 
4. QUALITY CONTROL METHOD 
The proposed quality control tool is based on evaluating the 
degree of consistency among the LiDAR footprints in 
overlapping strips to check the intemal/relative quality of the 
LiDAR data. The conceptual basis of the QC methodology is 
that conjugate surface elements, which can be identified in 
overlapping strips, should match as well as possible. If 
consistent discrepancies are detected, then one can infer the 
presence of biases in the system parameters and/or 
measurements. Other than the ability to detect systematic errors 
in the data acquisition system, the proposed methodology will 
also evaluate the noise level in the data by quantifying the 
goodness of fit between conjugate surface elements in 
overlapping strips after removing systematic discrepancies. 
To reliably evaluate the consistency between overlapping strips, 
one must address the following questions: 
• What is the appropriate transformation function relating 
overlapping strips in the presence of systematic biases in 
the data acquisition system? 
• What are the appropriate primitives, which can be used to 
identify conjugate surface elements in overlapping strips 
comprised of irregular sets of non-conjugate points? 
• What is the possibility of automatic derivation of these 
primitives? 
• What is the possibility of automated identification of 
conjugate primitives in overlapping strips? 
• What is the appropriate similarity measure, which utilizes 
the involved primitives and the defined transformation 
function to describe the correspondence of conjugate 
primitives in overlapping strips?