Compassion of the hardware and software correlators

Contents: On 2009.10.07 a 24 hour 15 station geodetic experiment was observed. In November 2009 it was correlated in Socorro using the old hardware VLBA correlator (thereafter haco) and the new difx software correlator (thereafter soco). Unless explicitly specified otherwise, SI units are used without scaling prefixes.

The correlator outputs of the rdv77 experiment in FITS-IDI format were independently processed with PIMA and VTD/post-Solve VLBI analysis software. This included applyting approriate calibrations, normalization, and flagging; fringe fitting; evaluation of the empirical complex bandpass; scan splitting; computation of total phase delay, phase delay rate, group delay, group delay rates and fringe amplitude; writing the results in database file in the GVF format; export the database into VTD/post-Solve; computation of theoretical path delays and partial derivatives; group delay ambiguity resolution; selection of appropriate parameterization for the LSQ adjustment; outlier elimination; reweighting; and finally, estimation of station positions, source coordinates, Earth orientation parameters, atmospheric path delays, inclinations of the axis symmetry of the atmosphere, estimation of clock functions.

In addition, I extracted debugging information and used it for comparison intermediate and final results.

Comparison of final results

Listing of the haco solution.
Listing of the soco solution.

Analysis of differences reveals that

The level of agreement of the final results can be characterized as satisfactory.

Comparison of UV data

A close look shows significant discrepancies when the data are examined at a level of individual UV points.
Statistics of the haco dataset
Statistics of the soco dataset

The soco dataset has 6.4% less of non-duplicate cross-correlation UV points. Apriori time delay shows significant differences. Start time and stop time are different almost for any observation. The differences are mainly within 10–30%, but may be as much as 10 times. I can only guess that soco applied more restrictive flagging invalid data than haco. Since the time stamps are different, the algorithm for splitting the data into scans and observations give different results. Fringe search gives different corrections to apriori delay and rates, and fringe search reaches SNR. For some observations the SNR at soco was less than the detection limit, 5.0, and an observation detected with haco may be undetected at soco. The fringe reference time and scan reference time are also different. 105 baselines, over 20,000 observations makes detailed comparison difficult. Therefore, I restricted myself with three baselines: BR/HN, BR/LA, LA/HN. I kept only those observations which were detected at both haco and soco. I imported the complex bandpasses estimated using the soco data and used it for fringe search of haco data. I imported the table of scan reference time computed for the soco data and used it in computing total delays and rates for haco data. As a result, this subset of data has 1) the same number of observations; 2) the same complex bandpass; 3) the same scan reference time. Then I investigated differences in observables of this restricted dataset.

Apriori time delay

I traced and the differences are originated in differences in the original geometric path delay calculated by Calc.

Total observed group time delay at X band

BR/HN plot of the differences in group delay at X-band versus formal time delay ( σ = 7.72037⋅10-10/SNR ) suggests a strong dependence of the time delay on SNR. Considering group delay di = D + ei, where ei is the noise of the i th observation, we can compute the correlation of the noise constituent of the group delay from the haco and soco correlators as ρ = 1/2 ( &sigmah2 + &sigmas2 – &sigmad2 )/ (&sigmah2 ⋅ &sigmas2) , where &sigmad2 is the variance of the differences in group delay haco minus soco. Replacing the variances with their estimates from statistics of the three baselines under consideration, we get the following estimates of ρ: 0.821, 0.860, and 0.844 for baselines BR/HN, BR/LA, and HN/LA respectively. If 15% of the UV data are independent, we can expect that the correlation coefficient ρ will be around 0.85. Start/stop time statistics gives us similar estimate of non-overlapping UV data: circa 15%. Therefore, the differences in group delay in rdv77 experiment at three baselines can be explained by differences in UV data used for its computation. Although, I am not ready to claim that I have proved it.

Fringe amplitude at X band

I computed the ratios of the amplitudes soco/haco and subtracted one: Amplsoco/Amplhaco - 1.0

Comparison does not show any noticeable bias. However, this level of the agreement is reached if to replicate the amplitude re-normalization implemented in AIPS. This includes 1) change in the original correction for VLBA register saturation suggested by Leonid's Kogan in VLBA Memo N12 ( 1.125 for a single polarization) to 1 + w/(8*VIS_SCL*AP_LEN) (refer to AIPS routine FITLD.FOR, line 14352), where AP_LEN is the accumulation period length, w is the data weight, and VIS_SCL is mysterious "visibility scaling factor" which can be found in FITS-IDI file. I inquired many folks, but nobody could tell me who this factor has emerged. This factor is 1.0 for soco; 2) Original AIPS routine for autocorrelation re-normalization which is supposed to account for the non-linearity of the correlator amplitude response (refer to AIPS routine BRAC, file FITLD.FOR, line 14182). The origin of the underlying algorithm is mysterious. The problem is the source code apparently contradicts to the explanation in Leonid's Kogan VLBA Memo N6 based in discussion in VLBA Memo N5. If to implement the algorithm suggested in the memos, then we will get slightly different results which will lead to the bias in the amplitude ratios of -0.03. Well, it is conceivable I am still missing something in the issue of how the autocorrelation is supposed to be renormalized.

Total observed fringe phase delay at X band

This level of agreement is quite satisfactory.

Contents of FITS-IDI files

The following issues:

Logistics

Processing a 15 station astro-geo experiment using haco and soco takes about the same amount of time: 15m for data downloading and editing control files, 2h.5 for unattended processing (data loading, applying calibrations, two runs of fringe fitting, computation of the complex, bandpass, creation of the output database), and 15m of interactive astrometric data analysis with VTD/post-Solve. In total, 3 hours. Handling soco dataset is easier, since the correlator output is saved in one file.

Conclusions

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Last update: 2010.02.09_18:43:32