n, 
ons 
cor 
als 
ons 
rix 
ans 
ion 
les 
res 
nce 
ls, 
and 
rse 
ens 
am, 
ign 
che 
an 
ion 
ing 
ion 
to 
the 
cal 
to 
73; 
ate 
is 
oot 
of 
his 
as 
al- 
73] 
are 
ne- 
no 
are 
of 
the 
his 
or, 
to 
ors 
Transportation Planning 
A brief overview of the mapping van project is 
followed by the mathematical formulation of 
conventional Givens Transformations and Givens 
without square roots. We then describe the 
implementation of Givens Transformations for 
sequential navigation of stereo-pairs. The results 
of the triangulation of a simulated strip of stereo- 
pairs are presented. Finally, we close with 
conclusions and future research plans. 
THE MAPPING VAN PROJECT 
The project Application of the Global Positioning 
System for Transportation Planning has been 
coordinated by the Center for Mapping at the Ohio 
state University. This project was initiated in 
September of 1990 with the goal of developing a 
mobile van workstation for the automatic mapping and 
recording of highway alignments and other features 
which in turn can be entered into a GIS. A working 
prototype was completed in February of 1991 
integrating a GPS receiver, a gyro-based inertial 
system, two wheel count sensors, and a stereo-vision 
system which includes two high resolution digital 
cameras and an image processing system with high- 
capacity data storage capabilities. 
The positioning portion of this project is based on 
two GPS receivers used in differential mode. One 
receiver remains stationary at a base while the other 
is mounted on the van for mobile data collection. 
All point coordinates from the mobile receiver are 
determined relative to the base station. The 
inertial system provides information of position 
change in terms of direction, pitch, roll, and 
distance traveled. Because the obstruction of GPS 
signals is a common problem, the inertial system is 
an invaluable link during periods of satellite signal 
loss. The inertial system alone can track the van 
position to better than one meter for each mile 
traveled. The GPS van positions, accurate within one 
to three meters, are used as control and the 
positional change information from the inertial 
sensors are fitted to them in a least-squares 
adjustment. 
The stereo-pairs obtained by the vision system can 
serve many purposes. Each stereo-pair, along with 
its geographic location can form an important 
component of a GIS. They can be utilized with image 
matching and feature extraction techniques for 
precisely locating features such as center and edge 
lines of roads and traffic signs. Future research 
will focus on the survey of bridges and overpasses 
and the evaluation of road surfaces for cracks and 
pavement stress [Novak, et.al., 1991]. In this paper 
however, we will show that the stereo-vision system, 
similar to the inertial system, can provide a 
solution to the positioning problem when satellite 
Signals are not available. The images captured 
Plate 1: Mapping Van of the Project Application of the Global Positioning System for 
917 
during a loss-of-lock period can be tied together by 
conjugate points. The strip of stereo-pairs can be 
sequentially triangulated using the GPS van 
coordinates just before and after loss of signal for 
control, as seen in Figure 1. 
A sequential solution is advantageous here over a 
simultaneous solution for two reasons: first, the 
stereo-pairs are captured in a sequential manner; 
second, the vehicle can be literally "navigated" from 
one stereo-pair to the next. Thus the current 
position of the vehicle is always known during loss- 
of-lock periods. At this time the triangulation has 
to be performed by an operator. It is anticipated, 
however, that by utilizing linear features(e.g. road 
edges) this procedure could be automated and 
performed in real-time [Novak, 1990]. 
Because the geometry of the vision system is assumed 
to be stable during operation, an accurate 
calibration of the entire system must be performed 
before any data collection. For this calibration, 
the interior and relative orientations of the two 
cameras, and the location of the GPS antenna relative 
to the cameras are determined using a three 
dimensional test field of retro-reflective targets. 
Local coordinates obtained by the vision system can 
be immediately transformed into a global system. 
The reference is given by the GPS antenna and the 
orientation of the van as defined by the inertial 
measurements. 
MATHEMATICAL FORMULATION OF GIVENS 
TRANSFORMATIONS 
In this section, the algorithm we used for sequential 
strip formation is explained. It is based on Givens 
Transformations and Givens Transformations without 
square roots. As estimation model, the Gauss-Markov 
model is used. 
The QR Decomposition 
Given an n x 1 coefficient vector 1 and a m x n 
design matrix A such that m z n, the problem is to 
compute the n x 1 parameter vector x so as to 
minimize the sum of the squares of the elements of 
the m x 1 residual vector v defined by 
v=ax-1. (1) 
Considering unweighted observations, the solution is 
given by 
2 = (ATA) LAT], (2)