and g
ng the
à local
rthing
order
, T is
matrix
‚is the
to the
fferent
ilter is
vector
biases
(6)
formed
del of
(7)
(8)
and
rval
p is
(9)
update.
(10)
The kalman gain matrix is defined by :
K eb EDI LR V qi
The update procedure is :
tel Se A Meu
k k (24 ia (12)
Pt =K(I-K HP"
where Z is measurements, H establishes the linear
connection between the Z and X.
To use the kalman filter to integrate the data from
different sensors are straight forward, but modeling the
statistical properties of these parameters are not always
possible. Therefore, the design of the filter is a
compromise between theory and practice. The
decentralized filter method is chosen for our case, because
it is simple and flexible. Fig. 2 shows the procedure of this
method.
[ur
E State: :
PUE Vector
pee |
Fig.2 The GPS/INS integration procedure
The Kalman filter is a very sophisticated method. After
establishing the dynamic model of the system, the kalman
prediction estimates the state vector and its covariance
matrix of the system. Whenever a measurement is
available, the kalman update will use it to calculate more
accurate state vector and covariance. This will repeat until
all data is processed. In the GPS/INS integration, the data
from the INS is very accurate for a short period, so instead
of using the kalman prediction, the INS positioning
equation (5) is used as the prediction module. To achieve
the most smooth result, the Kalman filter is used in
forward and backward. Fig. 3 shows a data set after the
GPS/INS integration.
Fig. 3 The GPSVision creates the street
map of Bayside in Wisconsin, USA
157
3.4 Positioning with stereo images
After the GPS/INS integration, every image pair taken by
the stereo cameras is georeferenced with three position
parameters and three rotation parameters. After calibration
procedure, the inerior, relative orientation parameter and
the offset parameter between the different sensors are
available. A three-dimensional coordinate of an object is
calculated by a photogrammetric intersection procedure
using its left and right image coordinate. The following
formula is used to transfer it to a Earth-Fixed coordinate
system.
=x
ins
+ BR RAR Py as)
where
X 3-D coordinate in the vision frame with the origin at
left camera, the X-axis pointing to right camera and
the Y-axis parallel to image frame and pointing up.
R} 90-degree rotation from vision frame to reference
frame. It rotate the Z-axis to the vertical direction.
DS Origin of INS body frame (b) defined in r-frame.
R° Rotation from the reference-frame (r) to INS body-
frame (b). This matrix is determined in the calibration
procedure.
R, Rotation from INS body frame (b) to the local frame
(n) defined by Easting, Northing and Upward
direction on the ellipsoid. The rotation angles (pitch,
roll and azimuth) are obtained from the INS system.
R Rotation from local frame (n) to Earth-fixed frame
(e).
X, Coordinate of the INS system in Earth fixed frame
when image pair was taken.
X* Coordinate in Earth fixed frame.
The geographic coordinate ($, A, /1) is obtained from the
Earth-Fixed coordinate Y^ by a simple transformation.
Other map coordinates, e.g. UTM, State plane, can be
also obtained according to the application requirement.
4. Feature Extraction and Applications
The stereo vision system of the GPSVision system is
designed to collect features from the real world. After data
collection in the field, the GPS and INS data are processed
and combined together. Every image pair is tagged with
its position and rotation in a global coordinate system and
is used for extracting useful information.
The Feature Extraction software is developed on
Microsoft Windows NT/95 operating system and is
external rule based driven and language neutral. The user
will interact with the software and point at features of
interest in the stereo image pairs. The software then
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996
