SIMULTANEITY CONSIDERATIONS FOR GPS PHASE REDUCTIONS |
The construction of double- or triple-differenced observables requires that
certain constraints apply as far as field operational procedures are concerned:
The first two requirements are relatively modest, however it is necessary
to consider more closely the issue of time-tag error:
Figures 1 and 2 below illustrate the effects of relative and common
time-tag errors. In these diagrams it is assumed that the observations
by the two receivers have the same time-tags and, for simplicity, that the
signal transit times are the same from the satellite to the two receivers.
Although, this last assumption is not strictly correct, the motion of the
satellite during the time of transit can be modelled accurately (and it
allows for a simplification of the diagrams). It is also assumed that the
satellite ephemeris is free of error.
The points T1 and T2 in these diagrams refer to the true satellite positions at the time-of-transmission to receivers 1 and 2. These are both at the same point due to the assumption made above. C1 and C2 are the respective calculated positions.
Figure 1. Relative time-tag error.
In Figure 1 it is assumed that there is no time-tag error at receiver 1 but a significant error at receiver 2. The calculated and true ranges from receiver 2 are different from each other, whereas those from receiver 1 are the same.
It is the relative time-tag errors that must be kept below 1-2 microseconds. That is, in order that two ranges involving different receivers and the same satellite are modelled at the 1mm level, the time-tags must be synchronised at the microsecond level.
In the case of the same time-tag error at both receivers there is a difference between calculated and true ranges for both receivers, and this difference is nearly the same for each receiver. Such a common time-tag error would arise, for example, if the time system of the GPS receivers is not the same as for the Satellite Ephemeris Time system. The "rule-of-thumb" commonly quoted for estimating the effect of ephemeris errors on adjusted baselines (section 6.2.3) can be used to estimate the acceptable limits of the common time-tag error. (Dividing the baseline length by the satellite altitude, the ratio that propagates ephemeris error into the adjusted baseline is obtained.)
Figure 2. Common time-tag error.
For example, if the ephemeris error is of the order of 20 metres, and given that the GPS satellite altitude is about 20x106 metres, a 1ppm error will be introduced into the baseline (1cm in 10km, 10cm in 100km, etc.). As the GPS satellites travel 20m in approximately 5 milliseconds, and if it is assumed that the ephemeris data has errors of the order of 20m, then a common error in the receiver time-tags of 1 or 2 milliseconds will not add substantially to the systematic errors which have already been introduced by an inaccurate ephemeris.
In summary, the GPS receiver synchronisation issues are:
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These various time scale / time error considerations are illustrated in
Figure 3 below.
Figure 3. Elements of GPS receiver synchronisation.
The time-tag conditions (points (2) and (3) above) can be met if the
GPS navigation solution is used to individually synchronise the receiver
clocks to GPST. The receiver clock bias (which defines the offset
of the internal clock from GPST) can be determined at a better than 1 microsecond
accuracy using the pseudo-range point position solution. If the
clock is reset to always read GPST, code-correlating receivers can be considered
as being always (automatically) synchronised to each other via GPST. On
the other hand, if the receiver clock is not continuously reset to GPST
using the navigation solution, then this needs to be done during post-mission
analysis of the recorded data. Finally, in the case of earlier non-code-correlating
receivers, this synchronisation had to be effected by physically bringing
together the receivers at the start of the survey (see KING
et al, 1987).
Pseudo-range synchronisation of code-correlating receivers for simultaneous
data recording and time-tag initialisation must not be
taken for granted. The start time and data recording rate must be the same
for all receivers, hence, for example, the receivers may be programmed to
collect data at one minute intervals on the GPST minute.
Mixing receivers of different type could lead to problems due to different receiver clock operating scenarios. Some GPS receivers constantly reset their clocks to GPST using the navigation solution, in a process known as "clock steering" -- as in Figure 4. Other GPS receivers may not do this, simply allowing their receiver clocks to drift controllably, as illustrated in Figure 5, which shows the total time-tag error (thin curved line) and the "millisecond jumps" in the time-tag value actually attached to the observations at an epoch (thick stepped line). Over a day, GPS receiver clocks have been known to drift many tens of milliseconds! This may cause problems if the data analyst is unaware of the finer points of receiver operation, and the commercial GPS software being used cannot accommodate such time-tag inconsistencies. However, in extreme cases, even if the time-tag error is determined to the required level of accuracy (a few microseconds), the synchronisation condition to ensure satellite clock error elimination in between-receiver observations may not be satisfied -- that is, within 30 msec under no SA or a few milliseconds when SA is on.
Figure 4. "Steered" receiver clock and residual clock error.
Figure 5. Drifting receiver clock error and the stepping of the time-tags.
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© Chris Rizos, SNAP-UNSW, 1999