Last updated 22 Aug 2021

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Check system timing accuracy (using astrometry of GNSS satellites)

Overview

Pointing the telescope

Exposure Length

Example Images

Repeat the Process

Position Measurement

Results

Periodically re-check

Non-timing errors
 

Overview

This is an outline of how to use several online software tools made available by Bill Gray (see MPML message #32538) allowing the overall timing accuracy of a telescope system to be determined by measuring the position of Global Navigation Satellite Systems (GNSS) such as the US GPS and Russian GLONASS satellites.

The orbits of these communications satellites are very well known, from where they were soon after launch, some dating back to the early 1990's to where they will be up to about 24 hours into the future and to an accuracy of just a few centimetres.

As these satellites are generally moving at apparent speeds of 2,000 - 2,400 arc seconds per minute, or 30 - 40 arc seconds per second, they can be used as a very sensitive gauge of the absolute timing accuracy of an imaging system, with all the delays and errors introduced by the camera shutter, imaging software, operating system, timing source and even observatory topocentric coordinates (see non-timing errors) combining to affect the final measurement.

The positional accuracy in RA & Dec can be expected to be of the order of 1 arc-second or better but a timing error of 1 second in the clock will manifest itself as a very obvious 30-40 arc-second discrepancy with the ephemeris, so providing a very sensitive measure of timing accuracy.


Configure capture software

The software that captures images and stamps the time of exposure within the FITS headers may need configuring to allow extra precision in the recorded time. Maxim DL is used at Great Shefford and by default it only records the time of exposure to the nearest second. However, by entering a non-zero value in the Camera Control, Expose tab, Options, Measure Shutter Latency... option, Maxim saves the exposure times to a precision of 0.01 seconds (see also here).

Of course the recorded time may not be accurate but at least it will be saved to two decimal places. However, the GNSS tools described here will allow you to determine how accurate the times really are.
 

Pointing the telescope

The first problem for the observer is to point the telescope at one of these very fast moving objects. Use the following two links to select a satellite and then generate an ephemeris for your site:
  • Choose a target from a list of GNSS satellites visible at your site (gps_find)
  • Generate an ephemeris for the selected satellite (gps_eph)

Exposure length

The GNSS satellites are generally 12th to 14th magnitude, moving at 30 - 40 arc-seconds per second. Ideally exposure times should be short enough to limit trailing so that the entire trail fits within the measurement annulus during measurement. This should allow automatic and accurate centroiding of the target, rather than trying to measure trail ends.

At Great Shefford, with a 2.2"/pixel scale and a 3-pixel radius aperture in Astrometrica, a 0.3 second exposure allows the resulting 10-12 arc-second trails to be easily measured.

With very short exposures there may not be enough reference stars recorded to achieve a good astrometric measurement, so check that there are catalogue stars distributed across the field and that the target has reference stars on all sides (in Astrometrica tick the Reference stars option within the Images/Select Markings... menu option).
 

Example images

Here is an example showing a typical short trail from a 0.3 second exposure:

The trail is short enough for the measurement annulus in Astrometrica to determine a good centroid:

 

Repeat the process

Depending on how quickly your system can take consecutive images you may need to reposition the telescope a number of times to get enough images to determine a statistically relevant result. These GNSS satellites pass through the 18 arc-minute field of view of the telescope at Great Shefford Observatory in about 30 seconds and with a gap of 1 - 3 seconds between exposures about 10 measureable images can be obtained from one telescope pointing.

It is suggested to obtain at least 10 positions, preferably more and from a number of different fields of view and in different directions in the sky, using more than one GNSS satellite.
 

Position Measurement

The next step is to measure astrometric positions of the target satellite. The date and time needs to have enough precision in the astrometry output file so that the accuracy of the method can be fully utilised. In Astrometrica this means making sure that in the CCD tab of the Program settings the "Time in File Header" precision is set to 0.1 seconds or better.

The resulting astrometry, either in the MPC's 80 column format or in the new ADES format can then be copy/pasted into the link below to work out how far off the measurements for each observation are in along-track seconds of time and cross-track arc-seconds:

Results

Here is a sample of the resulting output from gps_ast, with most of the detail lines removed for clarity:

Current time = 2021 Aug 6 8:15:55 UTC
Earth rotation parameter file date 2021 Aug 5
2003-010A C2020 02 29.84487712 11 53.44 +47 03 23.3 13.3 G J95 xresid 0.547435" along 0.0586419s G21 2003-010A
2003-010A C2020 02 29.84491812 12 03.53 +47 02 34.1 13.3 G J95 xresid 0.411983" along 0.0296576s G21 2003-010A

    ...70 lines removed...

2003-010A C2020 02 29.85459512 49 13.99 +43 23 30.7 13.0 G J95 xresid 0.730248" along -0.0056586s G21 2003-010A
2003-010A C2020 02 29.85462812 49 21.00 +43 22 42.6 13.1 G J95 xresid 0.087513" along -0.0330421s G21 2003-010A

74 observations found

Avg cross-track : -0.018644 +/- 0.338065"
Avg along-track (timing): -0.0050475 +/- 0.0382892 seconds
Negative along-track errors mean your clock was 'ahead' of the actual time;
i.e., the times reported in the astrometry are later than the positions
of the GPS satellites would indicate.

From a number of similar determinations the average along-track (timing) value indicated there was about 0.07 seconds of latency in the overall system at Great Shefford.

This value was then configured in Maxim/DL (in the Camera Control, Expose tab, Options, Measure Shutter Latency... option) so that every subsequent image taken has the 0.07 second system latency automatically applied to the time recorded in the FITS header. In the gps_ast output above, this adjustment has already been applied, reducing the overall timing latency to -0.005 0.038 seconds.

Combining measurements made on three different nights and plotting timing errors horizontally in seconds of time and cross-track errors vertically in arc-seconds, the random distribution of measurements can be seen here:

 

Periodically re-check

This method should be used to periodically check timing accuracy to make sure any change to the overall telescope system that may affect timing (e.g. hardware or operating system upgrades) is detected and can then be taken into account.

Non-timing errors

When initially obtaining readings using this method in 2017 it was noticed that there were systematic trends in the cross track residuals the further from the meridian a satellite was imaged. Investigation eventually uncovered that the coordinates of the observatory issued by the Minor Planet Center back in 2002 had not correctly included the adjustment of the geoid height to the height above mean sea level. The geoid height at Great Shefford is 47.6 meters and the effect of the incorrect coordinates on the cross track residuals can be seen in this figure where the GNSS satellites plotted in green were observed to the west of the meridian and those in orange observed to the east of the meridian.


(Satellites are identified in the figure with the 3-character codes from gps_find)

After the observatory coordinates were corrected, both sets of points are now properly centred around 0 arc seconds on the cross track (Y) axis:


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