the flight mission (Lapine, 1990). This offset can be 
introduced as a constant or as stochastic apriori 
information in the adjustment. 
Generally, the moment of exposure does not 
coincide with the time when the GPS receiver collects 
an observation. Therefore, one must interpolate between 
GPS positions to determine the antenna's position at the 
instant of exposure utilizing the time tags associated 
with GPS positions and the midpoint of the exposure of 
the photograph. Linear functions or cubic splines are 
commonly used for this task (Alobaida, 1993). 
As mentioned earlier, GPS phase 
measurements are essential for achieving the accuracy 
required for  aerotriangulation. Unfortunately, 
processing of GPS phase observations is complicated 
due to the problem of the initial ambiguity number. The 
integer ambiguity corresponds to the number of whole 
cycles the signal has traveled between emission by the 
satellite and its reception at the receiver. The integer 
ambiguity can be initialized before the flight mission 
from a known reference point (Lapine, 1990) or by 
using dual-frequency receivers and on-the-fly ambiguity 
resolution techniques (Schade, 1992). 
If for any reason the satellite signals are 
interrupted during the flight, a new ambiguity number 
has to be found. Signal discontinuities are caused by 
different reasons: genuine cycle slips, interruption of the 
signal, and constellation changes of the satellites. 
Signal interruptions have been a major problem 
affecting GPS aerotriangulation. Different algorithms 
were developed for recovering the ambiguity through 
filtering and prediction techniques (Euler, 1990; 
Schade, 1992), and recently by using dual-frequency 
receivers. 
Once GPS observations have been processed, 
coordinates are available in the WGS84 reference frame. 
Most ground coordinates, however, are defined with 
respect to a national coordinate system (e.g. State Plane, 
UTM). The transformation between these coordinate 
systems can be based on published formulas (Colomina, 
1993) or a set of reference points available in both 
systems. Elevations are related to the ellipsoid and must 
be corrected for geoid undulations. 
In order to understand the limitation of GPS 
controlled aerotriangulation without any ground control 
one can assume that the triangulation process is 
accomplished in two steps: relative and absolute 
orientations. The relative orientation can be performed 
by measuring at least five tie points in each stereo-pair. 
The resulting models can be joined together for the 
whole block or strip, yielding one model in a local 
coordinate system. Performing this task does not 
require any ground control. On the other hand, in order 
to perform the absolute orientation, control is 
mandatory. The minimum control requirement for the 
absolute orientation is three control points that must not 
be collinear. For GPS controlled block triangulation this 
condition is satisfied because the GPS observations at 
the perspective centers - our control - are well 
distributed over the whole block. On the other hand this 
condition is not satisfied for strip triangulation since the 
GPS observations of the exposure stations are almost 
collinear. In that case, the roll angle (around the flight 
line) cannot be recovered, and ground control points are 
necessary for solving the absolute orientation (Alobaida, 
1993). 
In this paper a new technique of strip 
triangulation is introduced that employs GPS 
observations at the exposure stations together with the 
GPS positions of linear features on the ground. In this 
approach, point to point correspondence along the linear 
feature is not necessary. This is convenient since the 
coordinates of the linear feature (e.g. a highway or 
railroad centerline) can be gathered by a moving vehicle 
on the ground. Thus it would be practically impossible 
to associate GPS coordinates with distinct physical 
objects along the linear feature on the ground. 
Basically, the following procedure is executed: 
(1) Image coordinates of a number of points are 
measured along the linear feature in the 
captured images; this can be done 
monoscopically. 
2) An analytical function is fit through these 
points in the image. Each image has an 
individual function representing the feature. 
3) The ground feature is projected into image 
space and must belong to the corresponding 
function in the image; this serves as a 
constraint in the least squares adjustment. 
The next section contains a short overview of 
the analytics of GPS aerotriangulation. A detailed 
description of the newly developed strip triangulation 
model will be given in section 3. Results for both 
simulated and real data are reported in sections 4 and 5, 
respectively. Conclusions and recommendations are 
presented in section 6. 
2. GPS Controlled Aerotriangulation 
This section describes how GPS observations of 
the perspective centers can be included in bundle 
adjustment (Hintz and Zhao, 1989). It is assumed that 
GPS observations are interpolated at the exposure times 
of the photographs. For each camera position the 
observed GPS coordinates are introduced as additional 
Observations, via equations of the form (1). 
204 
  
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