Volume 566, June 2014
|Number of page(s)||11|
|Published online||24 June 2014|
Nonlinear Kalman filters for calibration in radio interferometry
1 GEPI, Observatoire de Paris, CNRS, Université Paris Diderot, 5 place Jules Janssen, 92190 Meudon, France
2 SKA South Africa, 3rd Floor, The Park, Park Road, 7405 Pinelands, South Africa
3 Department of Physics & Electronics, Rhodes University, PO Box 94, 6140 Grahamstown, South Africa
Received: 24 January 2014
Accepted: 20 March 2014
The data produced by the new generation of interferometers are affected by a wide variety of partially unknown complex effects such as pointing errors, phased array beams, ionosphere, troposphere, Faraday rotation, or clock drifts. Most algorithms addressing direction-dependent calibration solve for the effective Jones matrices, and cannot constrain the underlying physical quantities of the radio interferometry measurement equation (RIME). A related difficulty is that they lack robustness in the presence of low signal-to-noise ratios, and when solving for moderate to large numbers of parameters they can be subject to ill-conditioning. These effects can have dramatic consequences in the image plane such as source or even thermal noise suppression. The advantage of solvers directly estimating the physical terms appearing in the RIME is that they can potentially reduce the number of free parameters by orders of magnitudes while dramatically increasing the size of usable data, thereby improving conditioning. We present here a new calibration scheme based on a nonlinear version of the Kalman filter that aims at estimating the physical terms appearing in the RIME. We enrich the filter’s structure with a tunable data representation model, together with an augmented measurement model for regularization. Using simulations we show that it can properly estimate the physical effects appearing in the RIME. We found that this approach is particularly useful in the most extreme cases such as when ionospheric and clock effects are simultaneously present. Combined with the ability to provide prior knowledge on the expected structure of the physical instrumental effects (expected physical state and dynamics), we obtain a fairly computationally cheap algorithm that we believe to be robust, especially in low signal-to-noise regimes. Potentially, the use of filters and other similar methods can represent an improvement for calibration in radio interferometry, under the condition that the effects corrupting visibilities are understood and analytically stable. Recursive algorithms are particularly well adapted for pre-calibration and sky model estimate in a streaming way. This may be useful for the SKA-type instruments that produce huge amounts of data that have to be calibrated before being averaged.
Key words: instrumentation: interferometers / methods: data analysis / techniques: interferometric
© ESO, 2014
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