[Difx-users] On delay modelling

Tue Apr 25 04:52:47 EDT 2017

Hi Mugundhan,

For VLBI the fringe rates are high enough that the delay is usually
calculated for every single voltage sample.  However, the full delay
calculation is not performed for every single sample - that would be
computationally very intensive.  Rather, the delays are calculated every
second or every few seconds and a polynomial interpolator is formed, that
lets you interpolate cheaply to any instant of time.  Some correlators
calculate every second and store these delays, and during the correlation
they pick the nearest 3 delays to form a quadratic interpolator.  DiFX
initially calculates a 6th order polynomial using 7 computed delays spaced
by 20 seconds each (I think? Something like that, anyway), and then during
the correlation uses this more compressed form to recalculate a quadratic
interpolator that covers one second at a time.

Once again, though, you don't normally want to use the baseline vector *b =
a1 - a2*.  You want to use the antenna vectors *a1* and *a2* separately.
Maybe you already understood this but just used the wrong terminology.

And I would rotate the *s* vector for the earth orientation effects before
performing the dot product.  *b.s* is a scalar, not a vector.

I'm not sure what your goal is here, but if it is just to do VLBI
correlation I strongly recommend using one of the existing VLBI delay
packages.  If your goal is to develop a new VLBI delay model, then
obviously you need to do that, but I'd caution once again that this will be
hugely complex!

Cheers,
Adam

On 25 April 2017 at 17:40, Mugundhan vijayaraghavan <
v.vaishnav151190 at gmail.com> wrote:

> Hi Adam and David,
>
> Based on your mails and references, and from this reference (
> https://ipnpr.jpl.nasa.gov/progress_report2/VII/VIIG.PDF), I tried to
> construct what we require to estimate the geometric delay only (I'm not
> bringing in the other delays for the sake of simplicity).
>
> So, first, we have the raw data, which has to be correlated. Before
> correlation, we have to estimate the delays that the data streams have to
> be given.
>
> For this I need two vectors: the source direction vector & the baseline
> vector. The baseline vector for both the observing antennas when referenced
> to the earth's center will be [x1 , y1, z1]  & [x2 , y2 , z2 ] of ITRF
> system respectively. Let the position of the source in the celestial
> coordinate be some RA and dec. In the earth centered coordinate system like
> ITRF, the positions of the antennas are not time variable, but the source
> vector \hat(s) is time variant (?).
>
> So for calculating the hour angle of the source, if I'm observing from
> India and my local sidereal time is say 20 hrs, since my observations are
> referenced to earth center, the hour angle wrt earth center is 300 degrees
> (Is this correct ?).
>
> Now for the obtained *b.s *vector, I can multiply the earth orientation
> parameter matrix to factor in the earth rotation effects & add the excess
> relativistic delays to this. Have I understood the process correctly ?
>
> Now, what is the ideal rate at which these delays have to be updated ? Is
> this determined by the fringe rate of the baseline ? Lets say if the fringe
> rate of my particular baseline is 1 second, then is it sufficient that my
> source position is updated for every 0.5 s ? Or calculation and correction
> of these parameters every sampling instant is necessary?
>
> Thank you,
> Regards,
> Mugundhan
>
>
>
> On Tue, Apr 25, 2017 at 10:12 AM, Mugundhan vijayaraghavan <
> v.vaishnav151190 at gmail.com> wrote:
>
>> Dear David,
>>
>> Thank you so much for the reference. I'll go through it first and come
>> back with more questions (if any) :)
>>
>> Thanks,
>> Best regards,
>> Mugundhan
>>
>> On Mon, Apr 24, 2017 at 8:56 PM, David Gordon <geovlbi at gmail.com> wrote:
>>
>>> Hi Mugundhan,
>>>
>>> Maybe I can add a little to what Adam has said. I recommend you download
>>> the IERS Conventions (2010) technical note
>>> (https://www.iers.org/TN36) for more details. But briefly, the calc
>>> programs compute a terrestrial-to-celestial rotation matrix
>>> at the desired epoch using the value of UT1 at that epoch and smaller
>>> rotations for polar motion and precession/nutation.
>>> It also computes the first and second time derivatives of that rotation
>>> matrix. The X,Y, Z site positions, velocities and accelerations
>>> are then rotated into the J2000 celestial reference frame. Then some
>>> elastic and other corrections are computed and applied at
>>> each station - such as the solid earth tide, the ocean loading, the pole
>>> tide, short period UT1 and polar motion corrections, etc.
>>> An atmosphere delay is also computed. We use the 'concensus' delay
>>> model, described in chapter 11 of the conventions.
>>> The source vector used is the un-abberrated direction to the source as
>>> seen from the solar system barycenter. Corrections for
>>> aberration and the retarded baseline are contained in the concensus
>>> model. The 'geocenter'  is just the (0,0,0) point in the
>>> VLBI reference frame (which we try to align with the ITRF), but does not
>>> strictly represent the earth's center of mass. It only
>>> needs to be the same point for all the antennas in a correlation.
>>>
>>> Cheers,
>>> David (David.Gordon-1 at nasa.gov)
>>>
>>>
>>> On Mon, Apr 24, 2017 at 3:19 AM, Mugundhan vijayaraghavan <
>>> v.vaishnav151190 at gmail.com> wrote:
>>>
>>>> Hi Adam,
>>>>
>>>> Thank you so much for the clarifications.
>>>>
>>>> Regards,
>>>>
>>>> Mugundhan
>>>>
>>>> On Mon, Apr 24, 2017 at 12:44 PM, Adam Deller <
>>>> adeller at astro.swin.edu.au> wrote:
>>>>
>>>>> Hi Mugundhan,
>>>>>
>>>>> Since the x axis of the ITRF is nominally aligned with longitude 0 on
>>>>> the Earth, if you want to think of things in terms of hour angles then yes
>>>>> the hour angle will be GMST.  You don't then make any further adjustment
>>>>> for the latitude and longitude of the observing stations.  To be properly
>>>>> precise, though, you will have to take into account precession and nutation
>>>>> as well as polar offset (orientation of the Earth in space c.f. the best
>>>>> model including precession and nutation) and UT1-UTC (Earth's rotational
>>>>> phase c.f. "average").  They are changing the tilt and rotation of the xyz
>>>>> ITRF frame with respect to the J2000 positions, which you can "undo" by
>>>>> offsetting the hour angle and declination of the source very slightly.
>>>>>
>>>>> Cheers,
>>>>> Adam
>>>>>
>>>>> On 24 April 2017 at 14:41, Mugundhan vijayaraghavan <
>>>>> v.vaishnav151190 at gmail.com> wrote:
>>>>>
>>>>>> Dear Adam,
>>>>>>
>>>>>> Thank you for your clarifications.
>>>>>>
>>>>>> One more question:
>>>>>> The unit vector \hat(s) originates from the center of the earth, in
>>>>>> this case, the hour angles of the sources will have to be calculated as
>>>>>> GMST-RA ? In this case, do we have to offset the obtained hour angles and
>>>>>> the declination by the lat and long of the observing stations ?
>>>>>>
>>>>>> Thank you,
>>>>>>
>>>>>> Mugundhan
>>>>>>
>>>>>> On Mon, Apr 24, 2017 at 6:10 AM, Adam Deller <
>>>>>> adeller at astro.swin.edu.au> wrote:
>>>>>>
>>>>>>> Hi Mugundhan,
>>>>>>>
>>>>>>> On 21 April 2017 at 15:30, Mugundhan vijayaraghavan <
>>>>>>> v.vaishnav151190 at gmail.com> wrote:
>>>>>>>
>>>>>>>> Dear All,
>>>>>>>>
>>>>>>>> I have a few queries about how delay modelling is carried out in
>>>>>>>> VLBI for compensating the same.
>>>>>>>>
>>>>>>>> 1.) The geometric delay is calculated as tg=*b.s*, where *b *is
>>>>>>>> the baseline vector and *s *is the source vector. Lets say I have
>>>>>>>> two antennas, both located about 100 kms apart. How do standard VLBI delay
>>>>>>>> modelling software calculate this delay ? Based on some preliminary reading
>>>>>>>> I understood that the baseline distance are first calculated referenced to
>>>>>>>> the earth center, if this is done, are delays estimated assuming the earth
>>>>>>>> center to be the phase reference ? How is this earth centered reference
>>>>>>>> then transformed to the celestial frame ? because both *b *and *s *must
>>>>>>>> be in the same coordinate system for carrying out a dot product operation,
>>>>>>>> right ?
>>>>>>>>
>>>>>>>
>>>>>>> VLBI delay modeling is very complicated, involving considerably more
>>>>>>> than just a *b.s* operation.  Other propagation effects are taken
>>>>>>> into account too, and the length of the baseline *b* is changing
>>>>>>> with time due to tidal forces and what-not, plus the whole system is
>>>>>>> wobbling around due to the changing earth orientation.
>>>>>>>
>>>>>>> But stripping it back to the minimum: yes, the Earth centre is
>>>>>>> usually used as the reference.  Look up the International Terrestrial
>>>>>>> Reference Frame (ITRF) to see the definition of the axes.  Then you
>>>>>>> obviously need to know the *time* (and the Earth orientation
>>>>>>> parameters) to figure out where the unit vector \hat(s) that points at the
>>>>>>> direction of the source is pointing in this reference frame.  For each
>>>>>>> telescope, we then compute the station-based delay from the telescope back
>>>>>>> to the geocentre at the desired instant of time, and each telescope's data
>>>>>>> stream is delayed by the computed amount (rather than shifting only one
>>>>>>> data stream by the difference between \tau_a and \tau_b).  That's what it
>>>>>>> means to use the geocentre as the reference.
>>>>>>>
>>>>>>>
>>>>>>>>
>>>>>>>> 2.) In some books/articles i find a reference to a RA and Dec of
>>>>>>>> Baseline ? What does this physically mean ? I'm not able to visualize this
>>>>>>>> clearly. any help will be greatly appreciated !
>>>>>>>>
>>>>>>>
>>>>>>> Like I said above, it makes more sense to figure out where the
>>>>>>> source unit vector is pointing relative to a telescope coordinate system.
>>>>>>> You can equivalently rotate the telescope coordinates and keep the source
>>>>>>> unit vector fixed, but that is (I think) less intuitive.
>>>>>>>
>>>>>>>
>>>>>>>>
>>>>>>>> 3.) In the complete delay model, tm, which is the sum of geometric
>>>>>>>> delay+clock delay+ionospheric/atmospheric delay+fixed delays due to analog
>>>>>>>> component, the fastest varying component will be geometric delay only, once
>>>>>>>> this is compensated, if the other quantities are contributing to some
>>>>>>>> excess time varying delay, this will be seen as a residual fringe. Now, for
>>>>>>>> clock delay, is this estimated using the allan deviation of the clock being
>>>>>>>> used? Lets say my clock loses 10^-9 seconds in 30 minutes, and if I sample
>>>>>>>> my signal at 16 MHz which is ~ 62.5 ns, will I be able to integrate the
>>>>>>>> data without any degradation due to clock upto 30 minutes ?
>>>>>>>>
>>>>>>>>
>>>>>>> The sampling time is irrelevant.  It's the sky frequency that
>>>>>>> determines the visibility phase.  Your signal might only be 16 MHz wide,
>>>>>>> but if you were observing at 100 GHz then a change of 1 nanosecond
>>>>>>> translates to 100 turns of phase.  So in that example you could only
>>>>>>> integrate for maximally a fraction of a second.  Normally VLBI clock drifts
>>>>>>> are monitored to a level of at worst a few ns/day or so. If they are
>>>>>>> unknown then a test correlation is performed to determine the clock offset
>>>>>>> and drift, and then the observation is recorrelated having applied the best
>>>>>>> available clock model.
>>>>>>>
>>>>>>>
>>>>>>>> 4.) There is also an associated baseline velocity component which
>>>>>>>> will lead to a time difference between the wavefronts received at both the
>>>>>>>> antennas. Is this baseline velocity the same as the orbital velocity of the
>>>>>>>> earth ? Or is this modelled differently ?
>>>>>>>>
>>>>>>>>
>>>>>>> By delay tracking to the geocentre, this problem is naturally taken
>>>>>>> into account. When you use the geocentre, you are automatically forced to
>>>>>>> account for the rotation of the reference frame between the time the signal
>>>>>>> is received at the antenna and the time that it would pass through the
>>>>>>> geocentre.  So you've corrected for the velocity of both of the stations,
>>>>>>> rather than their difference.  The process is known as retarded baseline
>>>>>>> correction.
>>>>>>>
>>>>>>> Unfortunately the documentation for VLBI delay packages is not
>>>>>>> extensive.  You can look up CALC (https://lupus.gsfc.nasa.gov/s
>>>>>>> oftware_calc_solve.htm) or VTD (http://astrogeo.org/vtd/) but
>>>>>>> neither have an excellent explanation of the theory.
>>>>>>>
>>>>>>> Cheers,
>>>>>>> Adam
>>>>>>>
>>>>>>>
>>>>>>>> I would greatly appreciate if the experts here clarify my doubts.
>>>>>>>> Kindly do point me to references that may lead to clarification of these
>>>>>>>> doubts too !
>>>>>>>>
>>>>>>>> Thanking you,
>>>>>>>> With best regards,
>>>>>>>>
>>>>>>>> Mugundhan V.
>>>>>>>>
>>>>>>>>
>>>>>>>> _______________________________________________
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>>>>>>>> Difx-users at listmgr.nrao.edu
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>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> --
>>>>>>> !=============================================================!
>>>>>>> Dr. Adam Deller
>>>>>>> ARC Future Fellow, Senior Lecturer
>>>>>>> Centre for Astrophysics & Supercomputing
>>>>>>> Swinburne University of Technology
>>>>>>> John St, Hawthorn VIC 3122 Australia
>>>>>>> phone: +61 3 9214 5307 <+61%203%209214%205307>
>>>>>>> fax: +61 3 9214 8797 <+61%203%209214%208797>
>>>>>>>
>>>>>>> office days (usually): Mon-Thu
>>>>>>> !=============================================================!
>>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>> --
>>>>>> the giver of moksha
>>>>>>
>>>>>
>>>>>
>>>>>
>>>>> --
>>>>> !=============================================================!
>>>>> Dr. Adam Deller
>>>>> ARC Future Fellow, Senior Lecturer
>>>>> Centre for Astrophysics & Supercomputing
>>>>> Swinburne University of Technology
>>>>> John St, Hawthorn VIC 3122 Australia
>>>>> phone: +61 3 9214 5307 <+61%203%209214%205307>
>>>>> fax: +61 3 9214 8797 <+61%203%209214%208797>
>>>>>
>>>>> office days (usually): Mon-Thu
>>>>> !=============================================================!
>>>>>
>>>>
>>>>
>>>>
>>>> --
>>>> the giver of moksha
>>>>
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>>>>
>>>>
>>>
>>
>>
>> --
>> the giver of moksha
>>
>
>
>
> --
> the giver of moksha
>

-- 
!=============================================================!
Dr. Adam Deller
ARC Future Fellow, Senior Lecturer
Centre for Astrophysics & Supercomputing
Swinburne University of Technology
John St, Hawthorn VIC 3122 Australia
phone: +61 3 9214 5307
fax: +61 3 9214 8797

office days (usually): Mon-Thu
!=============================================================!
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