Latency Problems

Validation of the SDP Toolkit Earth Orientation
 
For Geolocation; Part III - Latency Issues; 

Dependence on the Frequency of File Updates
 
        Peter D. Noerdlinger
 
        May  16, 1996
 
This is the third of three reports on the validation of our SDP
Toolkit functions for Earth motion in the J2000 celestial reference
frame.  It deals with the need to update the Earth motion file
"utcpole.dat" weekly and the leap seconds file "leapsec.dat"
monthly, and the effect of using "predicted" UT1 - UTC and leap
seconds.

In Part I it was explained that our Earth position in relation
to inertial space (J2000) is accurate to 10 cm, 3 coordinates,
1 sigma.  This evaluation was based on using data in the past -
albeit the recent past; it holds so long as the requisite scripts
have been run to update the Toolkit data files.

The reason that the files are required is that Earth rotation is
upredictable in the long term, and only approximately predictable
in the short term. 
 
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                SUMMARY
 
To achieve its unusually high level of geolocation accuracy and time
conversions, the SDP Toolkit depends on periodic updates of its data
files.  In Table 1 below we evaluate the gradual deterioration 
in accuracy with latency of the tabular material in the files.  Put
briefly, the accuracy will be within 1 meter if the data are not more
than two weeks old, 5 meters in three months, 11 meters in a year,
all one sigma.  

BUT, one caveat:  the updates must be done often enough to ensure an 
update of both files between the announcement of a leap second and its 
occurrence (about 5-6 months timespan). Otherwise, as with all 
geolocation systems, our accuracy will deteriorate to ~ 450 m when 
spanning the leap second.

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INTRODUCTION:

The U.S. Naval Observatory releases new tables of Earth rotation
data weekly (generally on Thursday); these contain reduced data
up to the very day of release and predictions for ~ 1 year in
advance.  Since existing (reduced, past-date) data are extremely
accurate for our purposes (~ 10 cm per coordinate), the only
problem that users may experience is in using predicted data
too far ahead. (Those who reprocess may notice geolocation 
changes at the centimeter level as well, because the Naval
Observatory frequently refines even its "final" solution; such
changes should be ignored).

The Tables contain data of UT1 - UTC (axial rotation - equivalent 
to an East-West error) and of Polar Motion (equivalent to a 
North-South error, greatest along some meridian that can be
extracted from the data).  We import not only the values, but
the 1 sigma error estimates, so the more curious can actually
look at the file "utcpole.dat", which has an explanatory header.
Here we provide summary estimates of the errors.

The main point of the present document is to inform users how
much error to expect if they process using predicted data for
up to a year past the file update.  We concentrate on UT1 - UTC 
(axial rotation) data rather than polar motion.  The polar motion 
error is comparable to the axial rotation (UT1) error for past
(as opposed to predicted) data, and it is less for predictions.
Therefore, the error in polar motion can generally be neglected,
and we supply only a few values.

The conversion of axial rotation to linear distance was done
for the equator; at other latitudes, the error decreases in
proportion to the cosine of the latitude.

Users may wish to geolocate science data in real time.  In that
case, even weekly updates will not prevent the use of predicted
data.

RESULTS OF THE LATENCY STUDY:

We have compared two sources of error estimates: The IERS 
Explanatory Supplement to Bulletins A and B and the data
tables themselves.  The Explanatory Supplement is in the
Appendix, and it agrees with our extract from the data tables
as of late March, 1996.

Here are the results for the axial error; "Latency Time" means
time since the last update.  A few error values for polar
motion are included for comparison and for those most concerned 
with North-South error:

	Table 1 - Errors due to File Latency

  File Latency  Time       	UT1 Error		Polar Motion
	(days)			(Equivalent E-W Meters 	Error (Meters
				- one sigma)		One Sigma)
	1			 0.14			-
	5			 0.45			0.02
	10			 0.76			0.09
	15			 1.03			-
	20			 1.28			-
	25			 1.51			-
	30			 1.74			0.30
	45			 2.35			-
	60			 2.92			-
	75			 3.45			-
	90			 3.96			0.50
	120			 4.91
	150			 5.82
	180			 6.66
	225			 7.87
	270			 9.03
	315			10.14
	365			11.32
	369			11.42

Obviously, since terrain corrections can be of the order of
kilometers, only those who correct their geolocation by
using digital elevation models or the like will care about
minor file latency problems of a few months.  Note that the
smallness of the errors in Table 1 gives little hint of the
much larger error (~450 m) that arises if the UT1 - UTC
value is missing or is ignored.