Post-correlation Processing for the VLBI2010 Proof-of-concept System

For the past three years, the MIT Haystack Observatory and the broadband team have been developing a proof-of-concept broadband geodetic VLBI microwave (2-12 GHz) receiver. Also on-going at Haystack is the development of post-correlation processing needed to extract the geodetic observables. Using this processing, the first fully-phase-calibrated geodetic fringes have been produced from observations conducted with the proof-of-concept system. The results we present show that the phasecalibrated phase residuals from four 512 MHz bands spanning 2 GHz have an RMS phase variation of 8 which corresponds to a delay uncertainty of 12 ps. 1. Raw Fringe Phasor Model This development begins by assuming that one has at their disposal the normalized correlation coefficients for each frequency channel (whether represented in the cross-power frequency or lag domain) for each single correlator accumulation period (AP). The raw fringe phasor Φr(f) is then defined as the phase of the cross-power spectrum produced from the correlator output data and is assumed to be the product of the fringe phasor Φg(f) due to the residual geodetic delay and the hardware (phase cal) phasor Φpc(f), where f is the sky frequency. Furthermore, since amplitudes are currently not incorporated in the phase cal processing, the magnitude of all phasors considered in this note are arbitrarily set to unity. The hardware-related phase is given by the phase calibration phasor Φpc(f) which represents the arithmetic difference between the phase cal phases obtained at each station. Φpc(f) is also sampled every f = 5n MHz, where n is the rail harmonic number. In the context of this note, Φpc(f) will be modeled as a piecewise-linear phasor function composed of as many pieces as there are frequency channels as indicated in Figure 1. It is important to note that Φpc(f) is not simply the difference of the phase cal phases obtained directly from the correlator, since the pcal phases are sampled every 5 MHz and the fringe phases in each frequency channel, generally, are sampled at a different rate. Additional processing (interpolation) is needed to obtain Φpc(f) from the correlator pcal phases. This is discussed in the section on phase calibration fitting. In regards to the phase due to the residual geodetic delay, systematic errors such as those introduced by clock drift and ionosphere delay are neglected here to place emphasis on the phase calibration processing needed to connect the raw fringe phases across several receiver bands. The residual geodetic fringe phasor (i.e., the error-free fringe phase), represented by the function Φg(f), is assumed to be linear in frequency since the aforementioned errors are ignored; estimation of Φg(f) from knowledge of Φr(f) and Φpc(f) is the goal of the correlator post-processing described in this paper. Φg(f) can be formally written as: Φg(f) = e 2πfτg (1) IVS 2010 General Meeting Proceedings 35 https://ntrs.nasa.gov/search.jsp?R=2011001182