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3. THE DIFFERENT OPERATION MODES USING CODE MEASUREMENTS 
Absolute mode : A stand alone receiver deduces its position from at least four code measurements. The quality of this 
position does not so strongly depend on the noise level of the measurements, as on the so called ‘selective availabil- 
ity’(SA), an artificial degradation introduced by the DoD for military reasons. Therefore the integration of phase meas- 
urements does not lead to an increase in the position accuracy. Typically an accuracy of 50-100 m can be achieved. 
Differential mode (DGPS) : The use of a sta- 
tionary reference station allows to operate the 
  
  
Code-only Code & Phase system in a differential mode. As the error in- 
troduced by SA is identical for all receivers, the 
Absolute mode 50 -100 m 50-100 m measurements at a reference station with known 
coordinates are used to deduce for every satellite 
Differential mode 0.5-5m 1-20 cm ; "x 
a correction value. Transmitting these range 
  
  
correction values to the moving receiver leads to 
a substantial increase of the positioning quality. 
Typically an accuracy of 1 to 5 meters can be 
achieved, depending on the quality of the code 
measurements and the satellite constellation. 
Table 1. Achievable accuracy of the position for the different op- 
eration modes 
4. RECOVERY OF HIGH PRECISION TRAJECTORIES BY INTEGRATING PHASE MEASUREMENTS 
For some applications, however, a higher accuracy as can be obtained by a differential code solution is required. In this 
case the integration of the phase measurements becomes mandatory. There are basically two important differences be- 
tween phase and code measurements: 
(1). millimeter resolution of the phase measurements compared to meter resolution of the code measurements 
(2) the phase measurements are ambiguous, leading to additional unknown parameters in the evaluation process. 
The corresponding simplified equations of observations are : 
single difference code measurement : Ap = Ad + cASync (la) 
single difference phase measurement : | Ag = Ad + cASync — AN (1b) 
with 
Ad difference of the distances (reference station - satellite) and (moving receiver satellite). 
ASync differential synchronization error of the two receivers (c speed of light). 
N Single difference ambiguity (A wavelength of the phase measurements L1 - 19 cm / L2 = 24 cm). 
The initial phase ambiguities at the double difference level are integers. (Double difference designates the between 
satellite differences of single differences.) If it is possible to fix them to their corresponding integer values, the ambi- 
guities are no longer estimated but error free values. In this case the differential phase measurement incremented by its 
associated ambiguity corresponds basically to a pseudo range but with an noise of only a few millimeters. 
5. THE KEY PROBLEM : SOLVING THE AMBIGUITIES 
The following example should illustrate the main problem in the processing of the phase measurements, i.e. the deter- 
mination of the integer values of the ambiguities. If differential code and phase measurements are introduced in a se- 
quential least square adjustment, the unknown parameters to be determined are the coordinates, the time synchroniza- 
tion error of the receiver and the initial phase ambiguities. Figure 1 shows the theoretical behavior of the rms of an ini- 
tial phase ambiguity as a function of the integration time for an average constellation of 6 satellites. 
Sigma dependent rounding strategies: It consist in statistically testing every real valued estimate whether it can be 
rounded to the next integer. This means from a pure statistical point of view (neglecting systematic errors) that the rms 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop “From Pixels to Sequences”, Zurich, March 22-24 1995