GPS Monitoring Statistics
-------------------------

Software version: 0.09. 
Document version: 1. 

The statistics for the GPS Monitoring Service are calculated using 
several steps, detailed below. The values of the parameters used are 
output to the daily *.LOG log files, and *.DAT results files. They are 
not given in the final automatic report, as this is unnecessary detail 
for the end user. 


Calibration
-----------

The diagram below shows schematically the systems involved in this 
service. 

         /--------<-----------\
         |                    |
      GPS SVs                 |
         |                    |
monitoring GPS receiver       |
         |                    |
      UTC(NPL)                |
         |                    | 
 time transfer at NPL        /|\
         |                    |
 time transfer at USNO        |
         |                    |
     UTC(USNO)                |
         |                    |
 GPS ground control           |
         |                    |
         \--------->----------/

To calculate UTC(NPL)-GPS_time from GPS measurements at NPL, the total 
absolute delays through this chain must be calibrated. For this service, 
a single calibration value is used, called [{UTC(NPL)-GPS_time} - REFSYS}]_cal, 
and this is attributed to the delay through the receiver (which was 
previously uncalibrated). A separate value is needed for each receiver used. 

The calibration was calculated as the mean value of 
[{UTC(NPL)-GPS_time} - REFSYS}]_cal = 
   [UTC(NPL)-UTC(USNO)]_cal
 + [UTC(USNO)-GPS_time]_usno 
 - [UTC(USNO)-UTC(NPL)]_tw 
 - [UTC(NPL) - GPS_time]_meas 
averaged over all available days where
[UTC(NPL)-UTC(USNO)]_cal is the result of the last GPS common view receiver 
  trip differential calibration, 
[UTC(USNO)-GPS_time]_usno are the daily results as reported on USNO's website, 
[UTC(USNO)-UTC(NPL)]_tw are the daily interpolated results of the thrice-weekly 
  two-way satellite time and frequency tranfers, 
[UTC(NPL) - GPS_time]_meas are the daily mean results as measured using the 
  receiver of interest. 

A conservative estimate of the uncertainty at +/-20ns (95%) was obtained, dominated by 
considering the drifts in the equipment since the last differential calibration, 
in comparison with similar systems, for example the known drift rates between two-way 
equipment and GPS receivers. It is expected that forthcoming calibration results will 
reduce this uncertainty. 

The value obtained by this method was compared against that obtained using the 
BIPM's Circular T UTC results, which is founded on independent calibrations, 
and found to be consistent. 


Data health
-----------

(1) add calibration - 
extract an entry from the REFSYS data column of the raw BIPM common 
view file. Add the calibration value, [{UTC(NPL)-GPS_time} - REFSYS}]_cal, 
to give a single measurement, [UTC(NPL)-GPS_time]_meas. 

(2) initial data filter - 
ignore tracks that are evidently invalid, currently those which 
are not 780s in length (the BIPM schedule), and not GPS. 

(3) if [UTC(NPL)-GPS_time]_meas passed the filter, then check for 
outliers against assumed reasonable values - 
check whether the value lies less than a given number 
of standard deviations (SD) from an assumed mean. Currently the mean is 
0ns, the SD is 100ns, and the detection limit is 5 SDs. 

(4) if [UTC(NPL)-GPS_time]_meas is consistent with the assumed values, 
then check for outliers against a running mean - 
if there are enough good previous points, then a running mean is 
formed from them, and the same consistency test applied as in step (3). 
Currently 20 points are used. 


Statistics results
------------------

Mean - 
A mean is calculated for all consistent points, those passing 
(2), (3) and (4) above. This is the reported single daily value, 
UTC(NPL)-GPS_time, which is thus a mean of all available measurements, 
without weighting the mean in any way. 

Others - 
Various other statistics are calculated for the distribution, and may be 
used internally at NPL to check the data quality, but are not reported to the 
end-user as this is unnecessary detail. 

Confidence interval - 
In the absence of selective availability (SA), variation of the measured 
daily means due to noise on the receiver measurements is of the order of 
10ns (95%), so combined in quadrature with that due to the calibration 
uncertainty, a conservative total uncertainty of +/-22ns (95%) is obtained. 
This will be revised in the event that the measurement noise changes 
significantly. 


Anomaly detection
-----------------

Those outliers failing either (3) or (4) above are checked to 
see whether they may be explained as "glitches" due solely to the 
GPS receiver used at NPL. Points classified as receiver problems are: 

(a) single points -
either at the start or end of a satellite track, or neighboured by 
consistent measurements of the same satellite. 

(b) low elevation - 
points below a certain limit (currently 10 degrees), where reception 
and/or atmospheric corrections may have caused difficulties. 

Any outlier that is NOT explained as a receiver problem is reported 
to the output files, along with a message, as these require
further investigation, and may indicate a problem with the GPS
constellation itself. 

Jon Clarke, 2000-07-03.