The GNSS integer ambiguities: estimation and validation

success rate
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
upper bounds
ADOP
region
simulation
0.1 0.2 0.3
f
0.4 0.5
success rate
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
lower bounds
bootstrapped
region
simulation
0.1 0.2 0.3
f
0.4 0.5
Figure 3.8: Upper and lower bounds for the success rate in the 2-D case as function of f
with vc-matrix 1
f Qâ,ref.
Evaluation of the approximations
In order to evaluate the lower and upper bounds of the success rate, simulations are
used. The procedure is explained in appendix B. The results were also presented in
Verhagen (2003).
First the two-dimensional case is considered, using:
Qˆz = 1
0.0216
f −0.0091
−0.0091
,
0.0212
0 < f ≤ 1
for different values of f. The results are shown in figure 3.8. The left panel shows the
two upper bounds and the success rates from the simulations. Obviously, the ADOPbased
upper bound is very strict and is always much better than the upper bound based
on bounding the integration region. The panels on the right show the lower bounds. It
follows that for lower success rates (< 0.93) the bootstrapped success rate is the best
lower bound. For higher success rates the success rate proposed by Kondo works very
well and is better than the bootstrapped lower bound.
Table 3.2 shows the maximum and mean differences of the approximations with the
success rate from simulation. From these differences it follows that the ADOP-based
approximation, the bootstrapped lower bound and the ADOP-based upper bound are
best.
Because of its simplicity the geometry-free model is very suitable for a first evaluation,
Quality of the integer ambiguity solution 43