Bernese GPS Software Version 5.0 - Bernese GNSS Software

6.5 Preprocessing Phase Observations
(5) If possible, repair the cycle slips. For this purpose the difference n i Fk (t2) − n i Fk (t1)
is estimated for each slip and all observations following the epoch t1 are corrected
accordingly. If the size of the cycle slip cannot be estimated reliably, the observation
at time t2 has to be marked as outlier or a new unknown ambiguity parameter n i Fk (t2)
must be introduced.
(6) Check for clock events if zero-difference phase files are preprocessed.
6.5.1 Non-Parameter Screening
The goal of the non-parametric screening is to identify time intervals in which no cycle
slips occur with utmost certainty. Usually, a fair amount of such data (not corrupted by
cycle slips) can be found. The observed minus computed (O-C) values are calculated from
the phase observations and the input a priori information. The O-C values are checked (on
satellite difference level: one station, two satellites, one epoch for zero-difference files, and
two stations, two satellites, one epoch for single-difference files) whether they are values of
a smooth function of time and whether they may be represented within an interval of a few
minutes by a polynomial of low degree, say q, by computing the (q + 1)-st derivative and
by checking whether or not this quantity is zero within the expected RMS error.
Algorithm
It is expected that the satellite-differences of O-C are values of “smooth” time functions
with random errors of the order of a few centimeters. The program checks whether or not
the q + 2 subsequent O-C values may be represented within an interval of a few minutes by
a low degree polynomial of degree q. This is done by computing the (q + 1)–st derivative
by numerical differentiation of the O-C values time series and by checking whether or not
this quantity is zero (within 3 times its RMS error). The RMS error of the (q + 1)–st
derivative is computed from the RMS error of the O-C values which is specified in the
option “Discontinuity level” in panel “MAUPRP 5: Non-Parametric Screening”. If the condition
is met, the interval considered is shifted by one epoch, if not, the last observation of the
current interval is marked and replaced by the following one. If the current interval gets
longer than a maximum length specified in the option “Maximum time interval for polynomial
fit”, all observations of the current interval are dropped, and the process is re-initialized.
After successful re-initialization the program tests backwards to recover erroneously marked
observations. The initialization works as follows: the condition is tested using the first q +2
O-C values (for re-initialization the next q + 2 observations not yet checked). If it is wrong,
the first observation is marked, the condition is tested using value 2,3,... ,q+3. The process
is terminated as soon as the above mentioned condition is fulfilled.
6.5.2 Epoch-Difference Solution
With those data identified as “clean” in the first step an epoch-difference solution (Section
2.3.4) is performed using the standard least-squares adjustment for each baseline or
station. In the case of baselines the coordinates of the first receiver are kept fixed on their
a priori values, the coordinates of the second receiver are estimated.
Bernese GPS Software Version 5.0 Page 117