340 
  
of the ambiguities must be on the order of 
1/10 of the wavelength in order to retrieve 
6 Satellites / PDOP =2.5 the integer values of the ambiguities. For 
the example in figure 1 this level is 
reached after about 20-30 minutes in the 
static mode independently of the quality 
of the code measurements. In the kine- 
matic mode, however, a new set of coor- 
dinates has to be evaluated at every new 
0 10 20 30 40 50 60 epoch leading to a weakening of the geo- 
metrical constraints. The rms of the ambi- 
guities is decreasing more slowly and re- 
    
meters 
  
  
Integration time in minutes 
  
Static mode mains more sensitive to the code quality 
FO : phase meas. only even after 30 minutes integration time. 
F1: phase & code meas. (rms single difference code meas. - 3m) Therefore a secure fixing of the ambigui- 
F2 : phase & code meas. (rms single difference code meas. - 0.50 m) ties within a very short time span requires 
a different strategy. 
- Kinematic mode 
MO : phase meas. only : : Search strategies : Search strategies are 
M1 : phase & code meas. (rms single difference code meas. =3m) not new in the GPS-processing and have 
M2 : phase & code meas. (rms single difference code meas. = 0.50 m) been widely used in the static and kine 
matic mode. The basic idea is to exploit 
the fact that all double difference ambi- 
Figure I. RMS of phase ambiguity as a function of the integration time| guities have to be integers. No ambiguity 
for different code qualities The RMS of the single difference] is therefore tested separately as in a con- 
phase measurement is always taken 5 mm. ventional sigma dependent rounding strat- 
egy. All search algorithms have two 
common features : the defining of the 
combination of interests (search space) and the validation of the correct combination. Different strategies have been 
developed as well concerning the definition of the search space [Remondi 1992, Hatch 1990, Mader 1992] as the vali- 
dation of the correct combination [Counselman and Gourevitch 1981, Euler 1992, Frei and Beutler 1991, Sauer 1994]. 
  
  
  
An often used validation method is the following discrimination factor [Euler and Schaffrin 1990], based on the rms 
error a posteriori of the unit weight. 
2G 
Dr TG Q) 
with: 
0, the rms a posteriori of the unit weight for the best integer combination. 
05 the rms a posteriori of the unit weight for the second best integer combination. 
If the value of DF exceeds a certain limit the best combination can be regarded to be the correct one. The time neces- 
sary to fix the ambiguities, however, depends strongly on the presence of the second frequency. The geometry is not 
substantially improved by the additional L2-phase measurements. The quality of the floating point solution of the am- 
biguities is similar to the single frequency mode. However, from the point of view of the discrimination potential of the 
correct solution the L2-phase measurements improve the performance of the search in a significant way [Frei 1991]. 
The key to discriminating the correct solution from all other potential candidates lies in the fact that the wavelengths are 
different but metrically the resulting double difference distances are identical. It is therefore indeed possible to retrieve 
the integer values of the ambiguities within one single epoch of GPS measurements [Hatch 1990, Mader 1992]. 
The result of a theoretical investigation is given in figure 2. It is based on the satellite constellation for mid May 1994 in 
Switzerland using a minimal elevation angle of 15 degrees and shows that under certain conditions an instantaneous 
ambiguity resolution in the dual frequency mode is possible. The requirements are code measurements of high quality, 
and a satellite constellation of 6 satellite or more. 
> 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences”, Zurich, March 22-24 1995