process as they were ”pseudo aerial control points”. Equa- 
tion (2) describes the transformation of the GPS antenna 
coordinates into image space [Li 92]: 
The application of differencing makes use of the fact that 
certain effects on neighbouring GPS positions within strips 
or blocks are of a systematic nature. After experimental in- 
vestigations [Jacobsen 91], [Li 92] the effects of spacial ex- 
  
  
  
  
  
Vie : : Th 
| Xeps—Xo = R-E (2) centricity, time shifts, interpolation and of geoid undulation 
y p 8 i de 
| [Haug 80] have appeared to be systematic. The same ap- Po 
| In the collinearity equations (1) used for conventional aero plies to transformations onto excentric GPS antennas. By bu 
| triangulation the coordinates of the camera projection cen- means of appropriate coordinate differencing these syste- 
| ters have to be replaced by the ones of the GPS antenna matic effects can be eliminated. sel 
| [Dorrer 88], [Dorrer, Schwiertz 88]. on: 
| me 
| Differencing two GPS antenna positions results in an ob- lie: 
servation equation for coordinate differences: the 
2.2 Excentric GPS observations of the ; a ios i rel 
. ° 5 = — : J — : > 7 —t : 
camera projection center OXON CAUEQU-Ryer(0-0-D, (9 th 
val 
In comparison to equation (3) term DO and thus part of 
Recent developments in Satellite Geodesy resulted in obser- the sy stematic errors of the GP 5 data is canceled. The 
vation methods allowing the determination of the camera expression (t; - t): D } is depending on the time shift. For 
station with sufficient accuracy during the moment of ex- neighbouring GPS positions within the same strip it has the 
posure [Seeber 91]. Utilizing these observations in aerotri- same order; thus they are nearly eliminated by differencing. 
angulation leads to a significant reduction of the amount of 
necessary ground control points. 
For incorporating kinematic positioning of the GPS antenna 2.4 GPS-based geodetic observations Th 
into a terrestrial geodetic system the formulation of GPS- gro 
supported aerotriangulation has to be extended. Compon- sta 
ents which describe the spatial excentricity between the Besides utilizing GPS antenna coordinates in the image pat 
GPS antenna and the camera projection center plus the system also incorporating geodetic GPS information into de 
corresponding coordinate transformation have to be added combined bundle block adjustment raises the economic ef- tic 
as well as parameters treating systematic effects within the ficiency of photogrammetric point determination. Further- du 
GPS-data. In matrix representation this is expressed by more this measure allows for an improvementin accuracy Me 
[Li 90]: and reliability of the results. suf 
«scs X. 1 - dM): Ro (Xo - R- t-D,+D es M iiis : iid 
9p ior ) Ro-(Xor Re) 1+ Do (3) Summarizing all possibilities of applying geodetic informa- 
The components of the spatial excentricity between the ca- tion derived from GPS observations leads to observation 
mera projection center and the GPS antenna are defined equations that are based on simular formulations [Kruck 83] 
in the image coordinate system. To be able to meet the set up for: Object coordinates derived from GPS observa- 
requirements of practical applications it showed be intro- tions: 3 
duced as observed unknown. The high precision determi- V 3 
nation of the excentricity is possible only via indirect and xgps(terr.) = dXaps — (Xaps,, — X^) (7) 
time consuming measurements [Schwiertz, Dorrer 91]. The ; ; 
: . ; Coordinate differences: 
resulting components can be entered into the adjustment 
through equation: Yar =. 0% wn d% (A + x? 4 X9) (8) 
a = 0 
Vers dem (en — ef (4) Height differences: 
Apart from the fixed relation between camera projection 0 In 
center and GPS antenna the coordinates of the antenna Vas; = Ah o Ah; - (Aha, — AR) the 
may serve as "aerial control point" coordinates. They are Ah, = Xi, X Y y, Ge Z aZ, gat 
direct observations of the unknowns and the cooresponding x ,f y anc 
observation euqation reads: Ah; z Md Xi + zd, + d, ana 
R R R sup 
Vxorslüeri.) = dXops—c unn, X 05 (9) sul 
in 
tion 
2.3 GPS antenna coordinate differences Distances: UR 
ap 
. 30 ; = —(s— s° 
A widely used practice for eliminating errors common in the Vs s = Sa (s AY. ) AZ. 
measurements is to form differences of these measurements. S, = 2dX ;+ — dy, + : dZ; 
Based on this principle and on equation (3) a formulation s X. m T Z. 
for combined bundle block adjustment will be developed, S mo 7 dX; — 7 dy; — $ dz; 
the utilized GPS antenna coordinates have been interpola- 
ted onto each instant of exposure. 
(10) 
214 
a