QUALITY CONTROL OF COMBINED ADJUSTMENT OF PHOTOGRAMMETRIC AND GPS DATA 
T. Bouloucos, M. Radwan, A.A. El-Sharkawey 
ITC, Department of Geoinformatics, 350 Boulevard 1945, 7500 AA  ENSCHEDE, The Netherlands 
ABSTRACT: 
Airborne Global Positioning System (GPS) data are 
incorporated in a photogrammetric block adjustment 
algorithm. The quality of the combined system was analyzed using both simulatéd and real data, and the 
statistical significance of the parameters of the 
emphasis was given to the possible reduction of ground control points. The obtained results show that a 
significant reduction can be achieved while still maintaining requirements for precision. 
KEY WORDS: GPS, Combined-Adjustment. 
INTRODUCTION 
The Global Positioning System (GPS) has been in 
operation for several years, although not all of 
the planned 24 satellites (21 plus three in-orbit 
spares) have been placed in orbit. At present, 
after the 11th Block II Navstar satellite was "set 
healthy" on August 30, 1991, 16 satellites 
(including operational Block I prototypes) are 
broadcasting usable signals accessible around the 
world. 
The potential high positioning accuracy of GPS and 
in particular the kinematic relative positioning 
in highly dynamic applications, reportedly being 
in the range of several centimeters [1,6,10,8], 
has led... to the utilization . of . GPS . in 
photogrammetric mapping. 
GPS use in photogrammetry, has focused on three 
aspects: GPS-based photo-flight navigation 
according to a given flight plan; GPS applications 
in laser profiling for digital terrain models; and 
GPS-derived positions of camera exposure stations 
and introduction of these data into block 
adjustments with the objective of minimizing the 
need for ground control points. 
In this paper we will concentrate on the third 
aspect, i.e., the combined adjustment of GPS and 
photogrammetric data. 
The introduction of GPS data into block adjustment 
is basically simple: the GPS coordinates are 
related to the block coordinate system by a set of 
transformation terms introduced as additional 
unknowns to be solved by the combined adjustment. 
Various studies conducted with simulated as well 
as real data [2,4,5,9] have shown that the 
introduction of GPS control of camera exposure 
stations in aerial triangulation adjustment 
reduces substantially the need for ground control 
points, while the precision requirements of 
mapping are maintained. They have also revealed a 
number of questions related to the degree of 
polynomials used in GPS modelling and the number 
of parameters utilized in the adjustment. 
Constant and linear terms were usually included in 
the combined adjustment for datum transfer and 
slope corrections [1,7]. When second order terms 
were  used,however, taking care of quadratic 
corrections, unfavourable results were observed 
[5]. Furthermore, the GPS correction parameters 
may be introduced stripwise or as one set of 
parameters for several strips, or even for the 
complete block. In any case, the introduction of 
an excessive number of parameters should be 
avoided and their determinability should be 
assured. 
In this study, the GPS data of the camera exposure 
stations were implemented in a block adjustment 
504 
combined functional model was investigated. Much 
with independent models based on the simultaneous 
determination of seven planimetric and height 
parameters. The statistical significance of the 
GPS correction parameters was investigated and 
their influence on the adjustment results was 
analyzed. Different control point configurations 
were used to confirm the possible reduction of 
ground controls. The experiments were performed 
using both simulated and real data. 
THE MATHEMATICAL MODEL 
The block adjustment with independent models 
(BAWIM) program developed at ITC many years ago 
(utilizing the famous 4-3 method) was modified to 
determine simultaneously the seven parameters and 
was further modified to accept the GPS data. The 
GPS coordinates of the camera stations are related 
to the block coordinate system by polynomial 
transformation terms; the transformation terms can 
be chosen stripwise or may be common for several 
strips. 
The following additional observation equations for 
each camera station i in strip k were formulated: 
V gps _ pe - ; 2. ë gps 
Xik = Xik (at a; Sik + a5 ik) X 
Voinsbs . pe - 
Yik m. (bot bi 
; 2, gps 
ik Sik + bos ik) - Yi 
k 
M Ike Lu. DOR ver C Sik € C, S Ik) - 2, PS 
ik ok "1k 2k ik 
Where: 
Xo Ys 5 + : The unknown coordinates of the 
perspective centre i in strip 
k. 
: The observation of camera 
station i given by GPS in strip 
k. 
ie 
: The unknown parameters for the 
constant term (shift 
correction) in strip k. 
(a k? Pok? ok ) 
(a 1k, ,1k,)* : The unknown parameters for the 
linear term (slope correction) 
in strip k. 
1k’ 
(851 ,D : The unknown parameters for the 
second order term (quadratic 
correction) in strip k. 
T 
2k? Pax’ Cox) 
ps T Vector of the least squares 
residuals. 
8 
(ur y 3 
S : Represent the distance of the 
exposure station i from the 
first perspective centre of 
strip k. 
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