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2.5 Variance Component Estimation
The stochastic model containing a formulation for standard
deviations (a priori) and the arising weight coefficients (a
posteriori) have great influence on the results of combined
bundle block adjustment for large blocks [Kruck 85]. For
verifying the stochastic model of each group of observati-
ons within GPS- supported bundle block adjustment the
method of variance component estimation has been app-
lied. This method plays an important role for fine tuning
the stochastic model in that it helps to find out the optimal
relation between the unknown and heterogenous accuracies.
The empirical standard deviation for each group of obser-
vations, e.q. for all GPS data, can be calculated:
V QV
er pL E
; S,[Q7!Q..,]
(11)
The actual estimation process will be repeated until all
group variances are converging. The computed empirical
standard deviations of all group of observations are com-
pared to their theoretical standard deviation. In case of a
deviation between two corresponding variances the theore-
tical one has to be altered during another adjustment proce-
dure. This way the estimate Sog a altered a postriori in an
iterative procedure until the variance components — given a
sufficient redundance - show a proper relation, that is to say
theoretical — standard — deviation
T —" 12
empirical — standard — deviation zi (a
3 Empirical investications on test-
blocks for GPS-supported block
adjustment
In cooperation with the "Institut für Erdmessung" (IFE),
the photogrammetric application of GPS has been investi-
gated on two projects within Germany, "BLUMENTHAL"
and "RHEINKAMP”. The obtained data from the base for
analyzing the systematic and stochastic propertics of GPS-
supported bundle block adjustment. Starting from the re-
sults of these investigations the mathematical models set up
in section 2 are to be tested. The aim is to find an opera-
tional solution for GPS-supported aerotriangulation using
no ground control points or only the minimum amount. In
this section the two testblocks are briefly described under
a photogrammetric aspect; the results will be presented.
215
3.1 GPS-supported bundle block adjust-
ment ”RHEINKAMP”
The testarea ”RHEINKAMP” is situated in the mining area
of the ”Ruhrkohle” Corporation. The whole area is control-
led for soil movements every three years by means of precise
point determination within conventional bundle block ad-
justment. During the second last campaign in 1988 the
object points were precisely determined once again. The
aerial photogrphs taken in the strips with an endlap of 80%
and a sidelap of 3096 have an average scale of 1:4000. Five
cross-strips were flown in order to stabilize the block geo-
metry apart from the utilized ground control points.
The technical data of the photo flight are listed below:
GPS receiver : 4 TI4100
survey aircraft : Cessna 404 of HL
ground speed : 210 km/h
flight duration : 90 min
aerial camera : RMK 30/23
focal length : 305.007mm (k=223mm)
block size : 60 km
flight altitude : 1200m
number of photos : 454
exposure interval : 3 sec
antenna-camera-offset : x=-0.33m y=0.52m z=1.16n
number of object points : 4856
number of control points: 21 full, 133 vertical
accuracy of control points : Sx=Sy=+2cm, Sz=+3cm
number of image points : 2950
With respect to satellite positioning all the data of the
"RHEINKAMP" testblock have been analyzed using two
different GPS solutions. For survey aircraft positioning the
navigational solution relying on smoothed code ranges was
applied first (absolute camera positions). The second so-
lution was computed with range corrections derived from
simultaneous GPS observations on a coordinated reference
point within the testarea (relative camera positions). As
stated in [Li 92], the second method came up with incon-
sistent GPS positions partly showing large shifts due to
technical problems and frequently changing satellite con-
stellations. On the other hand absolute positioning with
the navigational solution provides good internal accuracies
of the excentric camera positions to each other but only
poor external accuracies.
Due to the large amount of data the testblock is subdivi-
ded into sub-block for evaluation with the modified software
package BINGO (Buendelausgleichung fuer INGenieurtech-
nische Objekte). The empirical results of the photo flight
"RHEINKAMP" are presented in tables 1 to tables 4 for
both absolute and relative positioning.
