Hybrid Positioning and Sensor Integration - Global Navigation Satellite Systems: Signal,Theory and Applications - page 342

x u = x' + x' (K 1 r 2 ) (1)

y u = y' + x' (K 1 r 2 ) (2)

where x'= x - x 0 ; y' = - (y - y 0 ); r 2 = x' 2 + y' 2 ; (x, y): image coordinate

x 0 1,532.9966 pixels f 24.6906 mm
y 0 1,037.3240 pixels K 1 1.5574e-008
Table 2. Interior orientation parameters of Canon EOS 10D

2.2.2 Calibration of laser scanner

Calibration of a laser scanner is not easy because the laser beam is invisible where the
wavelength is approximately 905 nm±10 nm. Thus, in this research, a solar cell is utilized for
laser beam detection. External parameters of the laser scanner are estimated by computing
the scale factor, rotation matrix and shift vector by converting the laser scanner coordinate
to the fiducial coordinate, which can be a common coordinate of the system.

3D Helmert's transformation equation, Equation (3), is used to estimate the laser scanner's
external parameter. The laser scanner coordinates (Xl, Yl, Zl) are converted to the fiducial
coordinates (Xt, Yt, Zt). Scale factor (s), rotation matrix (R), and translation matrix (Tx, Ty,
Tz) are estimated by the least square method (Shapiro, 1978). According to this calibration
methodology, external parameters of a laser scanner can be decided accurately, and it helps
to combine a laser scanner with other sensors such as digital camera or IMU.

Xt Xl Tx

⎛⎞ ⎛⎞⎛⎞
⎜⎟ ⎜⎟⎜⎟
= +
⎜⎟ ⎜⎟⎜⎟
⎜⎟ ⎜⎟⎜⎟
⎝⎠ ⎝⎠⎝⎠

(3)

Yt sR Yl Ty

Zt Zl Tz

2.2.3 Boresight offset measurement
Boresight offset must be estimated between the GPS and the IMU. In the hybrid positioning
circulation, differences in position and velocity between the IMU and the GPS, and other
sensors are used to estimate the severity of errors. If the vehicle only goes straight, this error
amount is not affected because the relative movement is constant. However, if the vehicle
turns, the error amount is not constant. The position and velocity of the near axis of gyration
are small, although those of its far axis of gyration are large. In this paper, the boresight
offset from the GPS to the IMU in the vehicle is obtained through direct measurement by
using a total station.

The transformation matrix, which includes a rotation matrix and a translation matrix from
the vehicle coordinate system to a world coordinate system, is calculated from positioning
data where the origin of the common coordinate system considered as the center of IMU. A
rotation matrix and a translation matrix are dependent on the instant posture and position
of the vehicle when the vehicle is moving. On the other hand, the transformation matrix
from the local coordinate system to the vehicle coordinate system is calculated based on the
external calibration parameter measured physically as a boresight offset. This is a physical
measurement, so it includes some measurement errors. However, this is initial information
and it can be removed by further filtering.