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A New Approach of Combined Block Adjustment Using GPS-Satellite Constellation 
Jacobsen, Karsten, Institut für Photogrammetrie und Ingenieurvermessung 
Schmitz, Martin, Institut für Erdmessung 
University of Hannover, Germany 
Commission Ill, WG 1 
KEY WORDS: Bundle Block Adjustment, GPS 
ABSTRACT 
The ambiguities of kinematic GPS positioning based on carrier-phase measurements in an aircraft are often not 
resolved correctly. This causes systematic errors in the GPS positions depending on time and location. In practical 
applications of combined block adjustment with projection center coordinates determined by GPS commonly shift and 
drift parameters for the fitting of the errors in the GPS-positions are introduced. However, modeling remaining GPS 
systematics by linear regression assumes a linear behavior of the errors. Non linear effects have been detected for 
poor GPS satellite geometry. A new approach of combined block adjustment is presented, which uses GPS satellite 
constellations and strictly obeys the functional GPS model. Parameters can be estimated for a complete block. The 
new approach is discussed and preliminary results are given. 
The shift and drift compensation in the traditional method has to be done individually for every flight strip. By this 
reason crossing flight strips or lines of vertical control points are required for blocks with a sidelap less than 5096. With 
the new method one correction for every continuous used satellite is required. That means, if some satellites have not 
had cycle slips during the whole flight period, these satellites are connecting the flight strips and crossing flight strips or 
additional vertical control points don't have to be used. 
1. INTRODUCTION 
The integration of the Global Positioning System (GPS) 
and bundle block adjustment for the reduction of the 
number of required control points has become an 
operational technique. For large scale mapping and also 
for height determination the GPS positioning has to be 
determined with a precision at the one decimeter level or 
even below and therefore must be based on carrier 
phases. 
The capabilities of ambiguity resolution techniques for 
kinematic GPS positioning are steadily improving and 
have already achieved a high reliability level. The 
accuracy of kinematic GPS for dynamic applications 
depends on the distance to the reference GPS station 
and the used observable. In marine applications, even 
over distances of up to 60 km accuracy's below the one 
decimeter level are reported using carrier phase 
measurements (Seeber 1995). However, for highly 
precise airborne applications the ambiguities and cycle 
slips cannot always be solved or, sometimes, are not 
correctly resolved. False ambiguity resolution introduces 
systematic errors into the GPS positions. 
The general approach in a combined bundle adjustment 
uses linear regression models or even polynoms to 
adjust the systematic distorted GPS positions to the 
projection centers. This has to be done in the block 
adjustment individually for every flight strip because the 
GPS-position errors are not only a function of the time, 
they are depending also upon the location. In addition in 
the turn around from one flight strip to the next usually 
the connection to some satellites are lost, causing a 
change in the systematic errors 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
The ambiguity errors are mainly causing deviations in the 
GPS-positions linear depending upon the time and 
location. However, non-linear effects have been found for 
poor satellite constellations. The remaining errors of the 
GPS position raised the ground height accuracy derived 
by a combined block adjustment and independent check 
points by a factor of 2 (Schmitz 1995). Such errors 
cannot be detected in an operational block without 
independent check points. 
A new approach of combined adjustment is presented, 
which uses the actual satellite constellation to determine 
GPS position corrections. Actually, the approach can be 
described as an improvement of the ambiguity terms 
using the independent position information from the 
bundle adjustment. Preliminary results are given. 
2. DATA SETS 
In 1993 an extensive test of GPS supported block 
adjustment (photo flight mission 'Vechtel has been 
performed in cooperation between the state survey of the 
German federal country Lower Saxony and the University 
of Hannover (Jacobsen 1994, Jacobsen 1996). From the 
operational production of photo flights for height 
determination additional data sets are available from the 
state survey. The investigations in this paper are based 
on the data set 'Vechtel' (1993) and ‘Gross Oesingen’ 
(1994). 
The blocks were imaged by a Zeiss RMK TOP 15 with an 
image scale of approximately 1:8000. The strips were 
flown in east-west direction with a sidelap of 60 96 and 
stabilized in the case of 'Vechtel' by 5 strips in North- 
South direction. A GPS photo flight system has been 
used for navigation. However, due to the 6096 sidelap 
also 'Oesingen' can adequately be used for a combined