METHODS AND RESULTS OF COMBINED ADJUSTMENT UTILIZING 
KINEMATIC GPS POSITIONING AND PHOTOGRAMMETRIC DATA 
Keren Li 
Institute for Photogrammetry and Engineering Surveys 
University of Hannover, FRG/CHINA 
Jochen Stueckmann-Petring 
Hansa Luftbild GmbH, FRG 
ISPRS Commision III 
KEY WORDS: Accuracy, Aerotriangulation, Algorithm, GPS-Positioning 
Abstract 
The paper briefly describes the main problems of progress on GPS- supported aerotriangulation. Based on investigations and 
by means of general consideration, new algorithms for solving the combined adjustment of kinematic GPS observations and 
photogrammet ric observations with minimum ground control are discussed. The main part of the paper describes the results 
of the empirical GPS tests BLUMENTHAL and RHEINKAMP in Germany and analyzes the potential of GPS-supported 
aerotriangulation in various ways. The accuracy obtained in experiments with minimum ground control indicates that the 
use of relative kinematic GPS data will become a standard application for aerotriangulation. Some experiments of the near 
future for GPS-supported aerotriangulation are discus sed. 
1 Introduction 
In order to achieve higher performance and optimum relia- 
bility through mutual control of different type of observa- 
tions photogrammetric research has also focussed on using 
geodetic as well as navigational and astronomical data. To- 
day extended mathematical and stochastic models allow to 
treat geodetic, navigational and astronomical information 
in the same adjustment process [Ackermann 84], [Hell 79], 
[Konecny 84], [Kruck 83]. 
Due to the introduction of NAVSTAR GPS (NAVigation 
System with Time And Ranging Global Positioning System 
aerotriangulation recently gained potential for developing 
into a highly precise method of photogrammetric point de- 
termination [Andersen 89], [Brossier 88], [Jacobsen, Li 90], 
[Dorrer, Schwiertz 90], [Faig 89], [Friess 88], concerning the 
need for ground control points it will be autonomous to a 
great extend. From GPS observations registered during a 
photo flight highly accurate GPS antenna coordinates can 
be computed. In a subsequent combined bundle block ad- 
justment these serve as additional observations of the exte- 
rior orientation parameters of the aerial photos [Jacobsen 91] 
In this article the mathematical equations for combined 
bundle block adjustment are derived in separate steps for 
photogrammetic observations, geodetic observations and na- 
vigational data. Finally, the results of the empirical inve- 
stigations of GPS- supported photogrammetric point deter- 
mination are presented in datail. The article ends up with 
a summary and prospects for further developments and ap- 
plications. 
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2 Extended mathematical model 
for GPS-supported bundle block 
adjustment 
The mathematical model constitutes the mathematical re- 
presentation of an actual physical process. Concerning the 
incorporation of GPS-data into the process of bundle block 
adjustment the question for the mathematical model can be 
specified as follows: based on measured image coordinates 
and highly precise excentric GPSantenna coordinates, how 
to obtain adjusted object coordinates in the corresponding 
system and how to achive an increase in an adjustment’s 
efficiency. 
2.1 Photogrammetric observations and 
modified collinearity equations 
Provided all approximate values of the unknowns are at 
hand the linearized observation equation in matrix repre- 
sentation reads as follows [Konecny 84]: 
V 
Prior to an aerotriangulation the focal length of the used 
camera and its principal point have usually been determi- 
ned by means of a camera calibration; thus they are set 
up as weighted observations in the process of bundle block 
adjustment. Apart from the collinearity equations the re- 
gistered GPS-positions can be entered into the adjustment