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INTEGRATION OF RAW GPS MEASUREMENTS INTO A BUNDLE ADJUSTMENT 
Cameron ELLUM 
Mobile Multi-sensor Systems Research Group 
Department of Geomatics Engineering, University of Calgary, Calgary, AB, Canada 
cmellum@ucalgary.ca 
KEY WORDS: Photogrammetry, Mapping, Bundle Adjustment, GPS Integration, Software 
ABSTRACT 
GPS data is typically included in photogrammetric adjustments as externally processed position observations. This im- 
plementation has obvious benefits in its simplicity; however, a more fundamental fusion of the GPs data into the bundle 
adjustment is possible. In this paper, an investigation is made into the inclusion of GPs pseudoranges directly into a photo- 
grammetric bundle adjustment. The advantages of the technique include improved accuracy and reliability, and the ability 
to use GPS data when less than four satellites are available. Notes are made regarding pseudorange errors and their miti- 
gation using atmospheric models, linear-combinations, and precise orbits and clock corrections. Using the new technique, 
tests are performed with aerial GPS/photogrammetric data that demonstrate that the method provides accuracies that are 
superior to those obtained when exposure station position observations are used in the adjustment. The paper concludes 
with some notes regarding the design and implementation of the combined GPS/photogrammetric adjustment, with an eye 
towards maintainability, extensibility, and performance. The hierarchical structure of the program is described, and the 
benefits of an object-oriented design using inheritance and polymorphism are outlined. 
1 INTRODUCTION 2.1 Existing Technique for Including GPs Data 
With some rare exceptions (for example, Kruck et al., 1996) 
GPS data is almost always included in photogrammetric ad- 
justments as processed positions. In other words, the raw 
GPS measurements are first processed using an external 
processing program that provides position and covariance 
estimates. These positions are then included in the adjust- 
ment using parameter observation equations. The nominal 
form of these equations is (Mikhail et al., 2001) 
Kinematic GPS controlled aerial photogrammetry has be- 
come an omnipresent technology in both the scientific and 
commercial mapping communities. Virtually all airborne 
mapping systems now integrate a GPS receiver with their 
camera. This integration is done at the hardware level, 
as the GPS receiver and camera must communicate, ei- 
ther for the GPS to trigger the camera or for the camera to 
record the exposure time. Unfortunately, on the software 
side, the integration of GPS and photogrammetry is not as 
M A io M M C 
close. Typically, the GPS data is included in the photo- rGpPs(t) — r7 (t) - R7 (t)ráps 1) 
grammetric bundle adjustment only as processed positions de (bps ré dro (t in t0)) (1 
(Ackermann, 1992; Greening et al., 1994; Mikhail et al., 
2001). In effect, the GPS and photogrammetric processing 
; vals ; ie : erM.. i iti ^ M 
engines operate largely in isolation. This implementation | Where rGps(t) is the position of the GPS antenna, r7" (f) 
has obvious benefits in its simplicity; however, a more fun- — 1S the position of the camera perspective centre, Rt (t) is 
damental fusion of the GPS data into the bundle adjustment the rotation matrix that aligns the camera axes to the map- 
may provide improvements in both accuracy and reliabil- | Ping space axes, and TGps Is the offset between the GPS 
ity. antenna and camera perspective centre. The bias and drift 
terms — p. and gie; respectively — are included as un- 
known parameters in the adjustment and are intended to 
account for the errors caused by incorrect GPS ambiguity 
resolution. These terms can also account for datum incon- 
This paper outlines a tighter coupling ofthe GPS and photo- 
grammetric processing engines where the GPS code pseu- 
doranges are directly included in the bundle adjustment. 
Bari hs : sistencies. 
The goal of this integration is to improve the accuracy and 
reliability when compared to the naïve inclusion of GPS S : ; ; 1 
positions 2.2 Modification of the Collinearity Equations 
In Ellum (2001), an alternative technique was investigated 
2 THEORETICAL FOUNDATIONS for including exposure station position observations in the 
photogrammetric adjustment. Derivation of the relevant 
equations begins with the forward conformal transforma- 
In the following section, a brief theoretical background is — tion that relates the GPS positions with the image co-ordi- 
given on both the current technique for including Gps data nates, 
in a photogrammetric bundle adjustment, and on the al- 
tered technique being pursued as part of this project. vr evil ll) - Bing + pRB, (2) 
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