  Radio interferometric gain calibration can be biased by incomplete sky models
and radio frequency interference, resulting in calibration artefacts that can
restrict the dynamic range of the resulting images. It has been suggested that
calibration algorithms employing heavy-tailed likelihood functions are less
susceptible to this due to their robustness against outliers in the data. We
present an algorithm based on a Student's t-distribution which leverages the
framework of complex optimisation and Wirtinger calculus for efficient and
robust interferometric gain calibration. We integrate this algorithm as an
option in the newly released calibration software package, CubiCal. We
demonstrate that the algorithm can mitigate some of the biases introduced by
incomplete sky models and radio frequency interference by applying it to both
simulated and real data. Our results show significant improvements compared to
a conventional least-squares solver which assumes a Gaussian likelihood
function. Furthermore, we provide some insight into why the algorithm
outperforms the conventional solver, and discuss specific scenarios (for both
direction-independent and direction-dependent self-calibration) where this is
expected to be the case.
