Bernese GPS Software Version 5.0 - Bernese GNSS Software

14. Clock Estimation
the clock values between two epochs. The purpose of the clock jump detection is to get
a reasonable model for the clock behavior for the clock extrapolation and to update the
statistic summary in the program output.
The procedure is composed of four steps:
(1) In a first step the mean change (absolute value only) of the clock value per second is
computed for all epoch differences:
∆δ = 1
n − 1
n
δ(ti) − δ(ti−1)
ti −
ti−1
i=2
The mean noise level of the clock σ(∆δ) is the standard deviation of the mean
change ∆δ.
A jump hypothesis is setup if the change between two epochs exceeds a specified
threshold which depends on the mean value ∆δ, the noise of the clock σ(∆δ), and an
user-specified confidence interval n (option “Confidence interval”, see Figure 14.7):
δ(ti) − δ(ti−1)
ti − > ∆δ + n · σ(∆δ) .
ti−1
The mean change of the clock per second is computed iteratively without using the
epochs flagged with a jump hypothesis until no further jumps are found.
If the clock is very noisy no jump detection is done because a distinction between
noise and jumps is no longer possible. The limit is hardwired to σ(∆δ) > 100 µs
in subroutine ${LG}/CCJUMP.f90. On the other hand the computed noise level of
excellent clocks can be very small. Because it makes no sense to detect “jumps” on the
few picosecond level in a GPS derived solution, the noise σ(∆δ) needs to have a lower
limit which is a user input option (“Minimum RMS for jump detection”, see Figure 14.7).
(2) The next step is to check the list of possible clock jumps for outliers in the clock time
series. If two clock jumps are found for the same clock within a few epochs and with
the same size (but the opposite sign) the clock values between these two events are
marked as outliers:
δ(tj+1) − δ(tj) δ(ti) − δ(ti−1)
−
≤ n · σ(∆δ)
tj+1 − tj
ti − ti−1
where |ti − tj| is smaller than the user-specified limit for “few epochs” in option
“Maximum time interval for outlier detection”, see Figure 14.7. The two jumps are deleted
from the list of clock jumps as long as no jump is found just before the first or after
the second jump.
(3) To distinguish a real clock jump from noise the uncertainty of the mean clock rate
has to decrease significantly if the clock change at the jump epoch is not considered
for its computation. For this test only a few clock values around the event are used. If
no significant improvement can be found when introducing the jump the clock event
is removed from the list of clock jumps. The value n from option “Confidence interval”
is used here to define the significance level.
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