# Average Frequency Traceability Techniques

GPS common view is used for intercomparing frequency standards located at over 50 national time and frequency laboratories around the world. It is also available for the clients of these laboratories, providing universally acceptable traceability documentation. It can be used to demonstrate statistical control either as a simple routine check on a local frequency standard, or as a method to validate other techniques.

GPS common view is a wide-area differential-GPS technique, where each geographical region is assigned a tracking schedule for observing GPS satellites best placed to transfer average frequency. The Bureau International des Poids et Mesures (BIPM, located just outside Paris) assigns the tracking schedules to the national standards laboratories. NRC (Ottawa) makes observations on the "Eastern North America" tracking schedule - as do USNO (Washington, DC) and NIST (Boulder, CO).

From GPS common view, you can obtain:

1. direct average frequency measurements: a simple 24 hour average can have a measurement uncertainty as good as 10-13 of the reference frequency. Overlapping 24 hour averages can be used to document periods when a local quartz crystal oscillator is behaving much better (or worse) than its specifications.
2. traceability documentation for average frequency with the widest international acceptability.

NRC can help you to use GPS for establishing traceable average frequency with:

1. NRC GPS timing data (ionospheric measurements) and access to NRC primary frequency standards, (free of charge),
2. choosing the measurements and reference to be used Footnote1,
3. estimating the uncertainty to use with the measurementsFootnote1,
4. in measuring the stability of your local frequency reference and in estimating the uncertainty to use for shorter averaging times Footnote1,
5. calibration and validation of your system (antenna, site, receiver, local oscillator, software) Footnote1,
6. validation of all procedures through participation in round-robin proficiency demonstrations Footnote1.

## GPS common view explained

Each laboratory measures the time scale of its local frequency standard with respect to timing data from the chosen GPS satellites. Each laboratory collects data from one satellite at a time, chosen according to the region's tracking schedule. Data are collected for a 13 minute "track" and averaged with a standardized digital filter to obtain a single time difference number at the middle of the track: the local standard's timing reference - GPS time.

To have measurement conditions most nearly the same, each satellite is measured again two orbits later, or 23 hours and 56 minutes later (86160 seconds). Measurement reproducibility of 3 ns rms are often observed.If your laboratory has made these measurements, you can traceably compare the average frequency of your standard to NRC for this 23h 56m period. Calling your standard "REF", a double difference of the time measurements in seconds is formed: {[(REF - GPS)day2 - (REF - GPS)day1] - [(NRC - GPS)day2 - (NRC - GPS)day1]} / 86160 s. The NRC readings are available for the last 3 days (free of charge) - data can be obtained from us in other forms on a cost-recovery basis.

## GPS common view reduces common mode noise

The double differencing eliminates or reduces uncertainty due to:

1. intentional clock dither ("Selective Availability" or SA) imposed as a matter of policy to degrade accuracy for civilian users, and incidental clock noise of the satellite's on-board atomic clock and in the modelling to generate its version of GPS time,
2. errors in your GPS antenna position,
3. errors in satellite positioning in the broadcast ephemerides,
4. multipath at your antenna site, and at the NRC site,
5. tropospheric model bias,
6. diurnal variations in temperature, and
7. diurnal ionospheric delay variations.

The largest remaining effect for the most usual single-frequency GPS receiver is the ionospheric variation from one location to the other. This effect is least if the ionospheric delay is smallest (night-time readings), or if the ionosphere is highly correlated between the two sites (as it is if your lab is within a few hundred km of NRC or the reference site).A GPS ionospheric model is broadcast by the satellites as part of the GPS navigation message. A single-frequency GPS receiver can have its rms timing uncertainty reduced two-fold if this ionospheric correction is applied. (The broadcast ionospheric model is a reasonable estimate for the two-sigma uncertainty remaining after the broadcast ionospheric correction has been applied.)

Two-frequency GPS receivers at both ends can be used to measure the ionospheric density and effectively remove the variable delay due to the ionosphere. (NRC two frequency timing data from a geodetic receiver are available in the IGS (International GPS Service for Geodynamics) database, but as yet are not available referenced to UTC(NRC) in the BIPM format.)

## Frequency averaging over multiple days can be done in a similar way.

The full double differencing should be done before any other averaging or data processing is done.

## GPS Common View Digital Filter

1. Geometric delay for the antenna position (given in the header) and the satellite position from the broadcast ephemeris used for this track. The index number of this ephemeris is given in columns 78-80 in the record reporting on this track, as described below.
2. Ionospheric delay from broadcast parameters used for this track. Even if measured ionospheric corrections are available, it is the broadcast corrections which are applied for the timing results REFSV and REFGPS.
3. Tropospheric delay, calculated in the standard GPS way (NATO STANDardization AGreement 4294) for the delay caused by the lower atmosphere.
4. Sagnac correction. The surface of the earth rotates, moving your antenna while the radio signals are travelling from a GPS satellite. This correction accounts for the motion.
5. Periodic relativistic correction due to the ellipticity of the GPS satellite orbit.
6. L1-L2 time difference of the two GPS frequencies as broadcast in the ephemeris. This correction removes a satellite-to-satellite timing bias that would otherwise be present in all single-frequency receiver results.
7. GPS receiver delay, also given in header line 12 of the header as INT DLY =… .
8. Antenna cable delay minus local-clock cable delay, also given in lines 13 and 14 of the header as CAB DLY =… . and REF DLY =… .

This process is repeated for the 13 minute track forming 52 smoothed values with corrections (1) through (8) applied, each value derived from an independent group of 15 seconds of data. A linear least-squares fit is made to the 52 smoothed and corrected values, and the value of this linear fit at the midpoint of the track is output by the receiver as the REFSV (REF - SV) timing value for this track. The slope and rms deviation of the linear fit are also reported.

To obtain the column REFGPS (REF - GPS), a similar linear fit is made after the satellite vehicle time is corrected to GPS time by applying a ninth correction in addition to corrections (1) through (8):

9. The broadcast corrections of the satellite clock time are applied to obtain this satellite's estimate of GPS time. The corrections used are broadcast in the ephemeris as the coefficients and initial time of the form $\left[{a}_{o}+{a}_{1}\left(t-{t}_{o}\right)+{a}_{2}{\left(t-{t}_{o}\right)}^{2}\right]$ and are calculated for and applied to the 52 smoothed and corrected values used for REFSV.

A linear least-squares fit is made to these 52 smoothed and corrected values, and the value of this linear fit at the midpoint of the track is output by the receiver as the REFGPS (REF - GPS) timing value for this track. The slope and rms deviation of the linear fit are also reported.

Linear least-squares fits are also made, and reported, for some of the corrections. Correction (3) gives the mid-track value and slope of the modelled tropospheric correction, reported as MDTR and SMDT. Correction (2) gives the mid-track value and slope of the modelled ionospheric correction, reported as MDIO and SMDI. If measured ionospheric delays are available, then a linear least-squares fit is also made on the measured ionospheric correction with each of the 52 points averaged over the 15 s. The mid-track value of the linear fit, its slope and rms deviation are reported as MSIO, SMSI and ISG.

The definitive description of the digital filter and output format are published in Metrologia 31, pp 69-79 (1994). GPS Output Format Used for BIPM

## Tracking Schedules

A header of 16 lines provides standardized information about the GPS receiver set-up. The header is included with each file of data using the standardized common view data format. The 16 lines are:

line 1 -
GGTTS GPS DATA FORMAT VERSION = 01
The Group on GPS Time Transfer Standards defined this format 01, published in Metrologia 31, pp 69-79 (1994). Modifications to this format will each be given a different serial number, and are expected to be published in Metrologia.

line 2 -
REV DATE = YYYY-MM-DD
This gives the most recent date of any change to the header data, in all-numeric form of year (YYYY), month (MM, 01 to 12) and day (DD, 01 to 31).

line 3 -
RCVR = AOA TURBOROGUE 8000 123456 1994 V3.02
Receiver data: manufacturer's initials, model type, serial number, date of first operation, software version number.

line 4 -
CH = 01
Receiver channel number used for this file. For a single-channel receiver, CH = 01. If more than one channel has been used to collect the data following the header, channel identifiers may be appended to each line in its comment field.

line 5 -
IMS = AOA Turborogue 8000 123456 1994 V3.02
Ionosphere measurement system data: manufacturer's initials, model type, serial number, date of first operation, software version number. If no local measurements of ionospheric delay are available, i.e. for any isolated single-frequency GPS receiver, then this line is IMS = 99999.

line 6 -
LAB = NRC
Initials of the laboratory where the measurements were taken.

line 7 -
X = +XXXXXX.XX m
X coordinate of the phase centre of the GPS antenna, given in metres with at least 2 decimals. ITRF X coordinate preferred, or WGS-84, i.e. pure GPS X coordinate.

line 8 -
Y = +XXXXXX.XX m
Y coordinate of the phase centre of the GPS antenna, given in metres with at least 2 decimals. ITRF Y coordinate preferred, or WGS-84, i.e. pure GPS Y coordinate.

line 9 -
Z = +XXXXXX.XX m
Z coordinate of the phase centre of the GPS antenna, given in metres with at least 2 decimals. ITRF Z coordinate preferred, or WGS-84, i.e. pure GPS Z coordinate.

line 10 -
FRAME = ITRF
The abbreviation of the coordinate frame of the antenna coordinates X,Y,Z given above.

line 11 -
Any comments concerning the method of antenna position determination, and its uncertainty. It may use as many characters as necessary.
ITRF coordinates determined with a repeatability of 3mm rms in July of 1996 by the Geodetic Survey of Canada from global IGS (International GPS Service for Geodynamics) data.

line 12 -
INT DLY = 89.5 ns
The internal delay entered in the GPS receiver, in nanoseconds given with 1 decimal.

line 13 -
CAB DLY = 125.7 ns
The antenna cable delay, from the antenna to the GPS receiver, in nanoseconds given with 1 decimal. Normally, this line would encompass all changes in timing of the L1 C/A group delay (as measured by the receiver) of the antenna, preamplifier, filter, down-converter (if any), splitter (if any), line amplifiers, or attenuators and connectors.

line 14 -
REF DLY = 45.8 ns
The cable delay from the reference clock's output to the timing input of the GPS receiver, in nanoseconds given with 1 decimal.

line 15 -
REF = XXXXXXXXXXXXXXXXXXX
Identification of the reference clock used by the GPS receiver. As many characters as necessary. This may be the BIPM 7-digit clock code, or the BIPM 5-digit UTC code, or a full description of the timing reference.

line 16 -
CKSUM = XX
Check-sum of header. Two hexadecimal digits of the sum, modulo 256, of all characters (including blanks) of the header (excluding carriage returns and line feeds), beginning with the first G of line 1, and including the blank following the = of line 16.

line 17 -
Blank line.

Following the header, one data record is used to summarize the timing results for the GPS receiver from each 13 minute tracking session of a GPS satellite. If line 5 shows IMS = 99999, then no ionospheric delay measurements are available and columns for MSIO, SMSI and ISG will be absent. The record has different fields, and is normally printed with standardized headings:

column 1 - blank
columns 2-3 - PRN - Pseudo Random Number of the number of the GPS Gold code used for the spread-spectrum modulation by the particular satellite used for this track. The PRN specifies a unique GPS satellite. There are 36 different codes.
column 4 - blank
columns 5-6 - CL - track CLass - two hexadecimal characters used for specifying the geographic class based on the satellite vehicle (SV) latitude and longitude at the midpoint of the track: the first hexadecimal character is the integer part of (90 - SV latitude)/12, and the second hexadecimal character is the integer part of (SV longitude)/24.
column 7 - blank
columns 8-12 - MJD - Modified Julian Day - the date of the start time of the track, expressed in days after an arbitrary start (Nov. 17, 1858), according to the traditions of orbital mechanics. MJD 50449 is January 1, 1997.
column 13 - blank
columns 14-19 - STTIME - hhmmss - STart TIME of the track: hours, minutes and seconds referenced to UTC (UTC is Coordinated Universal Time, the modern implementation of Greenwich time).
column 20 - blank
columns 21-24 - TRKL - in seconds - TRacK Length - Length of track in seconds. A normal track lasts 780 s.
column 25 - blank
columns 26-28 - ELV - in units of 0.1 degrees - apparent ELeVation angle of this satellite (PRN) above the horizon, as seen by this receiver at the mid-point of the track.
column 29 - blank
columns 30-33 - AZTH - in units of 0.1 degrees - apparent AZimuTH angle of this satellite (PRN) measured from North (East=90degrees, etc), as seen by this receiver at the mid-point of the track.
column 34 - blank
columns 35-45 - REFSV - in units of 0.1 ns - time difference of the supplied REFerence and the Satellite Vehicle clock (with GPS range correction applied, but without the satellite vehicle clock model applied), evaluated using the BIPM digital filter at the midpoint of the track. Receiver delay, cable delay, tropospheric delay and modelled ionospheric delay corrections have been applied. REFSV is the time interval started by the REFerence 1 pulse per second, and stopped by the satellite's range-corrected 1 pulse per second.
column 46 - blank
columns 47-52 - SRSV - in units of 0.1 ps/s - slope of the time difference of the supplied REFerence and the Satellite Vehicle clock (with GPS range correction applied, but without the satellite vehicle clock model applied), evaluated using the BIPM digital filter at the midpoint of the track. Receiver delay, cable delay, tropospheric delay and modelled ionospheric delay corrections have been applied.
column 53 - blank
columns 54-64 - REFGPS - in units of 0.1 ns - time difference of the supplied REFerence and this satellite's estimate of GPS system time (with corrections applied from both the GPS range and the clock model), evaluated using the BIPM digital filter at the midpoint of the track. Receiver delay, cable delay, tropospheric delay and modelled ionospheric delay corrections have been applied. REFGPS is the time interval started by the REFerence 1 pulse per second, and stopped by the GPS system time 1 pulse per second as estimated from this satellite.
column 65 - blank
columns 66-71 - SRGPS - in units of 0.1 ps/s - slope of the time difference of the supplied REFerence and this satellite's estimate of GPS system time (with corrections applied from both the GPS range and the clock model), evaluated using the BIPM digital filter at the midpoint of the track. Receiver delay, cable delay, tropospheric delay and modelled ionospheric delay corrections have been applied.
column 72 - blank
columns 73-76 - DSG - in units of 0.1 ns - or Data SiGma, the rms deviation of the linear fit to the data, as described in the BIPM digital filter.
column 77 - blank
columns 78-80 - IOE - no unit - GPS broadcast Index of Ephemeris 0 - 255, indicating the ephemeris used for this computation (you may wish to check that the two receivers are using the same IOE for the same track, for best assurance of common view rejection of common mode ephemeris errors).
column 81 - blank
columns 82-85 - MDTR - in units of 0.1 ns - MoDelled TRopospheric delay at the mid-point of the track.
column 86 - blank
columns 87-90 - SMDT - in units of 0.1 ps/s - Slope of MoDelled Tropospheric delay at the mid-point of the track.
column 91 - blank
columns 92-95 - MDIO - in units of 0.1 ns - MoDelled Ionospheric delay at the mid-point of the track.
column 96 - blank
columns 97-100 - SMDI - in units of 0.1 ps/s - Slope of MoDelled Ionospheric delay at the mid-point of the track.
column 101 - blank

Optional Data from two-frequency receiver making ionospheric delay measurements. The same BIPM digital filter is applied to the ionospheric delay measurements, and reported as:
columns 102-105 - MSIO - in units of 0.1 ns -MeaSured IOnospheric delay correction at the midpoint of the track for C/A pseudorange, the L1 group delay.
column 106 - blank
columns 107-110 - SMSI - in units of 0.1 ps/s -Slope of the MeaSured Ionospheric delay correction at the midpoint of the track for C/A pseudorange, the L1 group delay.
column 111 - blank
columns 112-114 - ISG - in units of 0.1 ns -measured Ionospheric Sigma - the rms deviation of the BIPM linear fit applied to the measured ionospheric corrections.
column 115 - blank
columns 116 and 117 - CK - two hexadecimal characters of the 8-bit ChecK sum of the ASCII characters in columns 1-115.
column 118-128 freeform data. For example, if different receiver channels are used for different tracks, the comment CH = 02 could be inserted in this field to show that a particular track was made using the receiver's channel 2.

To use GPS common view for establishing traceable average frequency you will need:

1. a frequency standard that operates continuously to produce a timescale (ideally with an uninterruptable power supply of some kind). If you have a 10 MHz or a 5 MHz frequency standard, normally its output would be divided down to a 1 pulse per second signal so that its reference timing marks are unambiguous for any reasonable departure from nominal frequency
2. access to the common-view tracking schedule and data collected at a national lab responsible for average frequency (NRC, NIST).
3. measurement of the stability of your local frequency standard as a function of averaging time, out to at least one day and down to whatever minimum averaging time you wish to consider.

### Footnotes

Footnote 1

Personalized training beyond 15 minutes is charged at a rate of \$120 per hour.