[Difx-users] On delay modelling

Tue Apr 25 05:17:26 EDT 2017

Hi Adam,

Oh sorry, by baseline I meant vector of ant1 and geocenter & ant2 and
geocenter. Yes, the antenna vectors are what I meant, sorry for the wrong
usage. My goal was to just understand the process before I use any of the
existing VLBI delay packages, for which the material was scarce. I will use
CALC/SOLVE for calculating my delays :) No, my goal is not to develop a new
VLBI delay model now, just wanted to understand it.

Thank you for your time.

Regards,
Mugundhan

On Tue, Apr 25, 2017 at 2:22 PM, Adam Deller <adeller at astro.swin.edu.au>
wrote:

> 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.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> _______________________________________________
>>>>>>>>> Difx-users mailing list
>>>>>>>>> Difx-users at listmgr.nrao.edu
>>>>>>>>> https://listmgr.nrao.edu/mailman/listinfo/difx-users
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> --
>>>>>>>> !=============================================================!
>>>>>>>> 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
> !=============================================================!
>

-- 
the giver of moksha
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