[teqc] Interpolation/upsampling of rinex

[Gerry Creager]

Bjorn,

A lot of work has gone into sub- and super-Nyquist sampling over the 
years.  I agree with Lou, however, that it is problemmatical to attempt 
to interpolate observables to a pseudo-10 hz rate simply because we can.

I consider it a bit less questionable to use interpolated data, as 
referenced by Mader, et al, for calculations of ionospheric estimates. 
I'm no so sure one can trust such high frequency kinematic updates, 
however.  I'm concerned about rapid iono and tropo changes that can 
effect large changes in propagation which would take longer to recover 
in the true observables, and will thus skew your interpolation efforts.

Bob, super-Nyquist sampling can prove acceptable and not result in a 
high noise figure if one is willing to determine the high frequency 
components of all the perturbation factors.  In this case, the iono and 
tropo elements are significant, especially in a wet troposphere.  This 
doesn't imply one can upsample with impunity, but simply that it's 
possible to sample higher than the classic Nyquist rate without inducing 
too much noise in the sampled result, and still be able to reconstruct 
the core signal.

gerry

bg at lysator.liu.se wrote:
> Hi Lou and Bob,
> 
> Clearly teqc does not, and will not, do interpolation.
> 
> The following might be slightly off topic for the teqc list.
> 
> I am well aware of Nyquist. My application involves 10Hz kinematic rover
> data and bought 1Hz reference station data. 10Hz ref station data is not
> available.
> 
> Here are two published papers discussing successful interpolation in the
> application I have.
> 
>      ngs.woc.noaa.gov/CORS/Articles/interp_extrap.doc
>      http://www.springerlink.com/content/v26k5452118h7367/
> 
> --
>      Björn
> 
>> Hi Lou:
>>
>> I agree with your sentiments, but under the correct conditions
>> interpolated data is perfectly OK and valid. IF, and that is a BIG IF,
>> the frequency content of the analog signal before sampling has no energy
>> above Nyquist (half the sampling rate) then one can reconstruct the
>> continuous, analog signal at any arbitrary time, not just at the
>> samples. The IF is SO BIG, however, that anyone proposing to
>> upsample/interpolate is most probably not doing something valid (just
>> the fact that they are asking indicates they probably don't understand).
>>
>>
>> Bob
>>
>>
>>
>>
>>>> Teqc is a versatile tool for manipulating rinex files. Does it also do
>>>> upsampling/interpolation of rinex data? I have not found any
>>>> description
>>>> in the manual/tutorial.
>>>>
>>> Teqc make data up out of thin air?  That's a big "no".
>>>
>>> --lou
>>>
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-- 
Gerry Creager -- gerry.creager at tamu.edu
Texas Mesonet -- AATLT, Texas A&M University
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