Subject: [IGSMAIL-2304] New broadcast Tgd values as April 29, 1999
From: Brian D. Wilson
Date: Fri, 11 Jun 1999 14:53:47 PDT

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IGS Electronic Mail      Fri Jun 11 14:53:47 PDT 1999      Message Number 2304
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Author: Brian D. Wilson
Subject: New broadcast Tgd values as April 29, 1999

To all concerned with the broadcast Tgd (L1 - L2 bias) values:

A thousand pardons for not announcing this earlier.  I thought
that a NANU was going to appear but the JPO decided not to
send one out.

JPL is now providing estimates of the Tgd values (the L1 - L2
instrumental bias for each of the satellites) to 2 SOPS every
quarter and also monitoring the values daily to identify any
abrupt changes in the Tgd values due to configuration changes
on the satellites.

The uploads of the first complete set of biases were completed
on April 29, 1999.  For the record, the table below summarizes
the Tgd values as they currently exist on the GPS constellation.

              Quantization
PRN#   JPL_Tgd  Error     New   Mult   Old_Broadcast
1	-3.34	-0.08	-3.260	 -7	 0.47
2	-1.49	-0.09	-1.397	 -3	-2.33
3	-4.60	 0.05	-4.657	-10	 1.40
4	-6.40	 0.12	-6.519	-14	 2.33
5	-4.40	-0.21	-4.191	 -9	 2.33
6	-5.12	 0.01	-5.122	-11	 1.86
7	-1.77	 0.10	-1.863	 -4	-0.93
8	-4.12	 0.07	-4.191	 -9	 1.40
9	-5.62	-0.03	-5.588	-12	 5.12
10	-1.86	 0.01	-1.863	 -4	-1.86
13	-12.20	-0.09	-12.107	-26	 5.59
14	-2.41	-0.08	-2.328	 -5	-2.33
15	-2.14	 0.19	-2.328	 -5	-0.93
16	-0.39	 0.07	-0.466	 -1	-2.33
17	-1.99	-0.13	-1.863	 -4	-0.47
18	-4.98	 0.14	-5.122	-11	-0.93
19	-2.98	-0.19	-2.794	 -6	-3.26
21	-2.27	 0.06	-2.328	 -5	-0.93
22	-3.97	 0.22	-4.191	 -9	 0.93
23	-2.86	-0.07	-2.794	 -6	-0.47
24	-0.99	-0.05	-0.931	 -2	-0.93
25	-7.52	-0.07	-7.451	-16	 1.86
26	-6.57	-0.05	-6.519	-14	 0.00
27	-4.25	-0.06	-4.191   -9	 0.47
29	-7.31	 0.14	-7.451	-16	 2.33
30	-8.10	-0.18	-7.916	-17	 3.26
31	-6.09	-0.03	-6.054	-13	 1.40

The table above lists JPL's Tgd estimate,
the new broadcast value, the multiple of 0.46566
that the new value represents, the old broadcast
value, and the quantization error due to the
limited bandwidth.  I computed the quantization
error as:  Err = JPL_Tgd - Mult * 0.46566.
The quantization errors are 0.22 or smaller for
all the satellites with new Tgd values, so we
aren't losing much due to the limited bandwidth
in the message.

One might ask (as Richard Langley of UNB did):
>How do the new values compare with what people are currently
>estimating from the IGS data?

The values we are providing are a 10-day average of daily
satellite bias estimates from our global ionospheric mapping
(GIM) software.  These estimates are exactly what we are providing
in the IONEX files (the DCB's) submitted to the IGS.  Hopefully,
this will simplify matters for many in the ionospheric community.
Now they simply need to calibrate their receiver bias in order
to compute accurate slant TEC values from the dual-frequency GPS
observables.  Since there is some quantization error and the values
will be updated only quarterly unless there is a change of greater
than 0.5 ns, those in the ionospheric community who are already
solving for biases will presumably continue to do so.

There is a slight difference in the units.  Normally, we report
the L1 - L2 satellite bias in nanoseconds (ns).  The Tgd units
also contain an additional factor of -1.5457 = 1/[1 - (f1/f2)^2]
(see the ICD200 for details).  Tgd is computed from the L2 - L1
bias (note the opposite sign) multiplied by the -1.5457.
Thus, to compute Tgd from our normal L1 - L2 biases in the iono.
community just multiply by +1.5457.

I don't mean to belabor the sign conventions but I've certainly
gotten myself confused at times.  In fact, the old broadcast Tgd
values were not that bad if they had been expressed in the proper
units.  The Tgd database contained the factory calibrations
(measured by the contractor) of the L2 - L1 bias, but unfortunately
they were *not* multiplied by -1.5457, or at least so we have
surmised.  If you take the old broadcast values and multiply them
by -1.5457, you will see some *rough* agreement between the
factory cals and JPL's estimates.

So, who is affected by Tgd?

Having the correct Tgd biases on the constellation provides
three important benefits:  (1) improved positioning accuracy for
single-frequency users that are not subject to SA (e.g., military),
(2) more consistent use of the fast clock corrections in WADGPS
systems such as WAAS, and (3) the capability to extract absolute
TEC from dual-frequency GPS observations if one has measured or
estimated the L1 - L2 bias for the receiver.  In the positioning
calculation, the Tgd values are used to convert the clocks (which
are computed using dual-frequency data) to L1 and so using an
incorrect value of Tgd degrades positioning accuracy.  This
small effect is usually hidden by SA and ionosphere errors, but
for users not subject to SA and for locations and times when
the broadcast Klobuchar ionosphere model is fairly accurate,
the accuracy degradation can be observed.  For WADGPS applications,
it's not necessarily an issue since the fast corrector can be
adjusted to account for the difference between the true Tgd value
and the (old) broadcast value the user would apply.  However, doing
this tailors the corrections for the L1 user and makes them less
useful for potential dual-frequency users.  Also, it's nice to have
the broadcast Tgd values be more consistent with the values being
solved for in the community (by WAAS, other WADGPS operators, JPL,
and other ionospheric groups).

There will be a conference paper at the upcoming ION meeting
describing the validtion that was done by JPL, Aerospace Corp.,
and folks at Holloman Air Force Base to convince the JPO to
sign off on the uploads.  Colleen Yinger of Aerospace Corp.
is lead author and will be presenting a talk at the meeting.
Bill Feess of Aerospace kindly helped to organize this
validation effort.  The bottom line is that for a single-frequency
user not subject to SA (military receiver), the improvement in
positioning accuracy that results from using the *correct*
Tgd values is significant (10-30%) and can be seen even when using
only the broadcast Klobuchar model for ionospheric correction.
As the precision of GPS increases, or SA is turned off, or a
second civilian frequency becomes available, the correct use of
Tgd (the L1 - L2 bias) and other biases (e.g., the CA1 - P1 bias)
will be even more important.

Well, that's the short description of what's going with Tgd.
More information will appear in future articles in GPS World
and elsewhere.  This is the culmination of almost three years
of convincing and lobbying by folks at JPL and many others.
The list of those to thank is quite long and I will leave most
of this to another time.  Such a list begins with Jack Klobuchar,
who has supported JPL's and many others' efforts in the GPS
ionospheric community for many years, ends with Chris Shank and
Al Gifford who provided the funding to support this on-going
effort, and contains many others in between.

 -- Brian
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 Brian D. Wilson                      |  Jet Propulsion Laboratory
 Tel:    (818) 354-2790               |  California Institute of Technology
 Fax:    (818) 393-5115               |  M/S 138-308
 Email:  [email-masked]    |  4800 Oak Grove Drive
 http://sideshow.jpl.nasa.gov/gpsiono |  Pasadena, CA 91109-8099
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