The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
The organization of the paper is as follows. At the first, 
definition of system errors and their influence with respect to 
mapping results are described. The paper focuses on the 
proposed error model, and its linearization is presented. The 
subsequent discussion concerns the recovery of the main error 
parameters such as range error and bore-sight angles and the 
analysis of control and tie information. Finally, paper provides 
a brief summary, and an outlook for further work. 
2. ERROR SOURCES 
Generally speaking, there are three types of errors during a 
process of measurement: blunders, systematic biases and 
random errors. Blunders are significantly larger than the other 
two types. They can be easy detected and eliminated with use 
of empirical parameters. Random errors are always present and 
can never be eliminated, however, can be minimized by 
least-square solution and redundant observations. As to 
systematic errors, they are caused by imperfect instruments. 
They can be represented through some parameters, which are 
estimated by a mathematic model from redundant observations. 
The type of errors including range error, scan angle errors, 
bore-sight angles and level arms from the INS system to the 
laser local coordinate system are emphatically discussed in this 
section. 
2.1 Range Error and Scan Angle Errors 
The ranging measurement is determining the time-of-flight of a 
light pulse, i.e., by measuring the travelling time between the 
emitted and the received pulse. Various factors contribute to the 
range error. It has relation with not only optical and electronical 
designment but also target reflectivity because range accuracy 
is inversely proportional to the square root of the 
signal-to-noise ratio(S/N).The S/N lie on many factors, such as 
power of emitted and received signal, input bandwidth, 
background radiation, responsivity of the signal detector, etc. 
Furthermore, if airplane flies on rather a better altitude as 2000 
m, range error is dependent on the atmospheric disturbances 
because of variability of atmospheric refractive index. For 
simplicity, herein, it is regarded as unknown small constant. 
Scan angle errors are depicted in Fig.l The ideal system is 
systemtric to the z-axis with a scan angle 6. The real scanning 
system is rotated by the alignment error a and the scan angle 
is 0 . It chiefly includes the following three error sources: 
Alignment error a the zero degree direction (broken line 
Z-axis) and the plumb line (real line Z-axis) may not coincide. 
The angle bias a is amounted to adding a constant angle k to 
scan angle. 
Scan angle error AO an inaccurate scan angle affect scan angle. 
It does not suffer from non-linear effects and is therefore 
omitted. 
Scan plane error expresses that the scan plane and the X-axis 
are not perpendicular. The offset is described by the two 
exceeding small angular errors. So it is omitted as well as. 
The alignment angle influences on the mapping result more 
than the latter two errors. Therefore, we contribute the 
alignment angle to error model. These errors result to 
non-linear effect to the laser points position, in particular, at the 
end of the swath as the reported paper(Crombaghs,2000). 
2.2 Bore-sight Angles and Level-arm Vector 
Considering mounting errors of the laser scanning (LS) sensor 
with respect to the INS sensor, the LS and INS coordinate 
system are not parallel. The alignment error is expressed by the 
small rotation matrix. The bore-sight angles are the main aim of 
the recovery system errors because they are determined well by 
other means. Therefore, the bore-sight angles must be estimated 
more precisely during an in-flight calibration procedure. The 
practical influence of the bore-sight on the mapping result is 
demonstrated by Fig. 2. This figure shows a cross-section of a 
building. It is illustrated with the profile that the discrepancies 
due to bore-sight angles are clearly visible on the inclined 
planes. 
Figure 2. Effect of bore-sight errors on a cross-section profile 
of a building roof from 2 flight lines of different directions and 
heights 
The magnitude of the lever-arm vector between LS and INS 
origins can be measured quite accurately. It is usually neglected. 
As for the lever-arm vector between the center of GPS antenna 
and INS origins, the measuring accuracy can achieve to the 
level of cm after installation on the ground. As mention above, 
if the bore-sight angles are considerably larger, the level-arm 
vector is thus not as accurate as its magnitude, so larger 
level-arm quantities may be expected, i.e., they can not be 
omitted. There errors exhibit to some extent linear effect to the 
laser points (Crombaghs,2000). 
2.3 INS Errors and GPS Errors 
INS errors are derived from shift or drift of INS sensor. GPS 
errors are caused by some factors such as differential 
troposphere, ionosphere delay, multipath and clock biases, etc.. 
Certainly, they are contributing to the mapping accuracy and 
are determined as estimated parameters added to the adjusting 
model (Filin and Vosselman, 2004). However, it is difficult to 
estimate these, and even the quality of the unknown parameters 
estimates may be degraded as additional correlation. At present, 
the POSPAC software of version 4.4 produced by APPLANIX 
company can implement the difference of GPS based on 
multi-base Kalman Filter and integrated inertial navigation and 
smoothing optimization, which achieve a level that the residual 
effect in GPS/INS trajectory estimation are lower than 0.05m 
and 0.005° in position and attitude respectively under the 
optimization of the calibration area and the flight conditions. 
Fig.3 depicts the position RMS error derived from GPS/INS 
processing by POSPAC software. So the additional parameters 
of INS and GPS biases are not added to the estimated model. 
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