An Eigenvector-Based Method of Radio Array Calibration and Its Application to the Tianlai Cylinder Pathfinder

Abstract

We propose an eigenvector-based formalism for the calibration of radio interferometer arrays. In the presence of a strong dominant point source, the complex gains of the array can be obtained by taking the first eigenvector of the visibility matrix. We use the stable principle component analysis (SPCA) method to help separate outliers and noise from the calibrator signal to improve the performance of the method. This method can be applied with poorly known beam model of the antenna, and is insensitive to outliers or imperfections in the data, and has low computational complexity. It thus is particularly suitable for the initial calibration of the array, which can serve as the initial point for more accurate calibrations. We demonstrate this method by applying it to the cylinder pathfinder of the Tianlai experiment, which aims to measure the dark energy equation of state using the baryon acoustic oscillation (BAO) features in the large scale structure by making intensity mapping observation of the redshifted 21 cm emission of the neutral hydrogen (HI). The complex gain of the array elements and the beam profile in the East-West direction (short axis of the cylinder) are successfully obtained by applying this method to the transit data of bright radio sources.

The Tianlai Cylinder Pathfinder array: System functions and basic performance analysis

“…In our experiment we tried two methods of calibration. In what we termed absolute calibration, we use the transit of the strong astronomical source Cyg A to solve for the complex gain of each input channel, using the eigen-decomposition method we developed earlier [30]. At other times, we use a calibration signal broadcast from an artificial source to perform what we call relative calibration.…”

“…The present work is based on the analysis of the first light data set, which started on September 27th, 2016, (below we denote it as 2016/09/27) and was used in our early analysis [30], and a second data set, which started on March 22nd, 2018 (denoted as 2018/03/22). These two data sets consist of a total of 10 days' of observation, and cover both the autumn and spring sky.…”

“…If noise is present but small compared with the calibrator source and statistically equal in all elements, i.e., V = V 0 + N, where N is the noise covariance matrix, the vector G could be obtained by principal component analysis (PCA): solving for the eigenvectors of matrix V, with the eigenvector associated with the largest eigenvalue identified as G. This is also the least squares solution of the form V = gg † (for proof and more details see ref. [30]). Thus, for each time and frequency point, a solution of the complex gain can be obtained using this eigenvector decomposition method.…”

The Tianlai Dish Pathfinder Array: design, operation and performance of a prototype transit radio interferometer

“…A more detailed description appears in Zuo (2020). Tianlai and tlpipe use the HDF5 formats consistently.…”

“…PSCal and PScal2 both use the same robust principal value decomposition to determine the gain of each feed, but have some differences in the handling of outliers and diagnostic information. See Zuo et al (2019); Zuo (2020) for details. The computed gain is applied to the entire data set until the next point source transits.…”