called GPS-supported aerotriangulation. The early 
simulation experiments indicated that accurate 
aerotriangulation may be achievable without ground 
control points if GPS-determined camera positions reach 
the order of submeter accuracy in each coordinate [Lucas, 
1987]. Current investigations show that it is possible to 
reduce remarkably the number of essential ground control 
points in photogrammetric block adjustment to 4 points 
around the four comers of a block area [Yuan and Li, 
1997]. Moreover, in conventional bundle adjustment, the 
optimal accuracy requires full ground control points 
around the perimeter of the area at intervals of two 
airbases and elevation control points at intervals of four 
airbases in the center of the area. Consequently, GPS- 
supported aerotriangulation will avoid hard field survey 
for determining ground control points and especially 
provides a topographic map of inaccessible regions of the 
Earth, which will lead to a small technological revolution 
in photogrammetry and establish a foundation for fully 
automatic analytical photogrammetry. 
The research of GPS-supported aerotriangulation was 
started in 1984. The scholars in the USA, Germany, the 
Netherlands and Finland have made a lot of 
investigations since 1986. In early 1990’s, Chinese 
surveyors went in for this scientific research, too. Up to 
now, almost ten actual photo flight missions with airborne 
GPS receiver were performed in different parts of China, 
which achieved expected results. At present the complete 
GPS satellites constellation ensures that a receiver is 
simultaneously able to observe the GPS signals of four or 
more satellites anywhere on the Earth at any time. 
Therefore, we may say that GPS-supported 
aerotriangulation is now ready for practical application. 
This paper first derives the mathematical model of 
combined bundle block adjustment with airborne GPS 
data, and then outline the basic functions and structure of 
our developed combined adjustment software 
WuCAPS G ps. Finally, a set of actual experiments based 
on GPS-controlled photogrammetric flights over five 
sites in China are presented and discussed. 
2. MATHEMATICAL MODEL 
observations and GPS-determined data of the camera 
stations consists of kinematic GPS relative positioning 
and combined bundle adjustment with GPS navigation 
data. The intention of this paper is to detail the later. Of 
course, the adjustment methodology also deals with a lot 
of other technical details of data processing, which were 
previously described by Yuan et al.[Yuan, 1995, 1996, 
1997]. 
2.1 A Strict Relationship Between Camera 
Perspective Center and GPS Antenna Phase 
Center 
As far as the kinematic GPS relative positioning, we can 
get 3D coordinates of the phase center of airborne GPS 
antenna mounted on the fuselage at each GPS observation 
epoch. However, the 3D coordinates of the camera 
perspective centers are only solved by a bundle 
adjustment. Unfortunately, in a conventional installation, 
the phase center of the GPS antenna and the rear nodal of 
aerial camera lens cannot occupy the same point in space. 
It causes a separation problem between camera and 
antenna. Let (X A , Y A , Z A ) and (X s , Y s , Z s ) be the 
geodetic positions to the phase center of the GPS antenna 
and the perspective center of the aerial camera, 
respectively, as shown Figure 1. If the antenna offset in 
camera coordinate system is (u, v, w), then the 
transformation is accomplished with orientation matrix R. 
Fig. 1 Relative positions between camera and antenna 
If a GPS receiver on board the moving aircraft and 
another fixed receiver on the ground reference point can 
simultaneously record the successive signals of four or 
more GPS satellites at a measuring rate of 1 second or 
shorter during photo flight missions, the camera station 
positions at exposure time can be accurately determined 
by using the differential GPS carrier phase observations 
in Kalman filter. When the 3D coordinates of these 
camera stations are introduced into the bundle adjustment 
procedure to solve altogether the orientation parameters 
of aerial photographs and 3D coordinates of 
photogrammetric points, a GPS-supported bundle block 
adjustment is formed. In other words, the procedure of 
the combined bundle adjustment for photogrammetric 
X 
> 
1 
X' 
u 
Y A 
= 
Y s 
+ R • 
V 
1 
N 
> 
1 
N 
C/> 
1 
w 
Friess has reported that the kinematic GPS relative 
positioning may cause a systematic drift error which is 
linear proportion to the flight duration t during photo 
flight mission [Friess, 1991]. Taking account of 
correcting model of the linear systematic error, equation 
1 can be written as