more homogenous for the whole block. The example in tab. 
5 demonstrates good results even at a minimum overlap at 
P = 60% and Q = 20%. 
e Control point configuration 
Applying GPS-supported bundle block adjustment utilizing 
only one or even no ground control points presently cannot 
be recommended. To guarantee sufficient reliability and 
sufficient accuracy four terrestial control points in the cor- 
ners of a block plus high precision GPS data should be at 
hand. Empirical investigations contribute to further fine 
tuning of evaluation methods so that homogenous accura- 
cies and high reliability sufficient for many applications can 
be reache. 
e Assessment of the methods applied for GPS-supported 
bundle block adjustment 
The effect of GPS antenna coordinate differences (see sec- 
tion 2.3)on the geometry of the bundles of rays is derived 
by means of the relation antenna-camera. When apply- 
ing this method the absolute information of the original 
GPS data cannot be respected; however, relations between 
neighbouring GPS antenna coordinates can be respected. 
The practical example clearly proves that this method is 
operable with the use of only four ground control points. 
As illustrated in tables 6 and 7, a combination of the ” GPS 
antenna coordinate method" (see section 2.2) with the "an- 
tenna coordinate difference method" (see section 2.3) even 
offers the chance of limiting the amount of ground control 
point to zero. These tables together with table 5 also con- 
fain the results achieved with and without precorrection of 
the systematic GPS effects. The external accuracy of the 
adjustments is being improved varyingly by a priori correc- 
tions of systematic errors. 
Combined bundle block adjustment computed with this me- 
thod and an overlap of P = 80%, Q = 60% came up with the 
best results: Sx=+0.046m, Sy=+0.045m and Sz=+0.080m. 
As can be seen form the listed results the effects of adjust- 
ments containing linear drift parameters are also varying. 
The assumption is being confirmed that uncompensated sy- 
stematic errors and probably unconsidered correlations ef- 
fected the empirical results. At an overlap of P — 6096, Q 
— 2096 on average correlation between the coordinate of the 
projection center and the linear drift parameters turns out 
to Pxo,dox=-0.38, Pyo,doy=-0.51, Pzo,doz=-0.58. 
4 Conclusions and outlook 
This paper deals with extension of models for combined 
bundle block adjustment including GPS data. For various 
formulations have been developed allowing to compensate 
systematic effects and to defect gross errors of models as 
well as of data. Whereas many authors are starting from 
pre corrected eccentric GPS observation, a simple algorithm 
(GPS antenna coordinate differences) offers the chance to 
perform bundle block adjustment with minimum ground 
218 
control utilizing GPS data not pre corrected for systematic 
errors. In summary it may be said that introduce entering 
highly precise kinematic GPS positions plus four ground 
control points into combined bundle block adjustment re- 
sults in sufficient accuracies. Bundle block adjustment ba- 
sed on one or even no ground control points can at moment 
only be recommended in case the absolute position is of no 
interest. Besides four ground control points stable geome- 
tric properties of a block are important for achieving good 
reliability. Due to varying systematic errors bundle block 
adjustments computed without ground control points will 
most probably be limited to low accuracy requirementts. 
Writing this paper did not aim at the presentation of a com- 
plete concept for GPS-supported bundle block adjustment. 
However, for practical applications of combined bundle block 
adjustmen tutilizing kinematic GPS positioning the follo- 
wing key aspects should be taken into consideration: 
e High accuracies and thus economic processing can 
only be achieved by GPS-supported bundle block ad- 
justment when systematic errors are compensated for. 
In this respect it is quite useful to implement a bundle 
block adjustment program with appropriate algorithms 
(e.g. with error correction models or differencingsub- 
routines). 
e For fixing the excentricity between GPS antenna and 
aerial camera on board of survey aircraft the ideal 
antenna position is vertically above the camera pro- 
jection center; otherwise the excentricity has to be 
precisely determined by indirect methods. The com- 
ponents are entered into the adjustment process as 
weighted observations [Schwiertz, Dorrer 91]. 
e Continuous GPS-observations have to be synchroni- 
ted with the instances of exposure. For practical app- 
lications a new generation of GPS receivers adapted to 
photogrammetric purposes in combination with new 
camera systems Zeiss RMK TOP, LMK 2000 or Leica 
RC 20 come in handly; on one hand these camera 
systems allow to register the mid point of exposure, 
on the other hand new GPS receivers like the AS- 
HTHCH XII are able to receive and process signals of 
aerial cameras. 
A complete concept for GPS-supported bundle block 
adjustment should contain tools for respecting cor- 
relations between coordinates of the projection center 
and GPS data and linear driftparameters respectively. 
With respect to the observation of excentric camera projec- 
tion centers the accuracy requirements of aerotriangulation 
can certainly be met by kinematic GPS positioning in the 
relative mode. The image rotations at the moments of ex- 
posure may be determined with sufficient accuracy by fur- 
ther modifications. Regarding further limitation of ground 
control and gains in accuracy these techniques open a large 
field of scientific activities practical applications. 
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