Maximum-likelihood astrometric geometry calibration of interferometric telescopes: application to the Very Small Array

Interferometers require accurate determination of the array configuration in order to produce reliable observations. A method is presented for finding the maximum-likelihood estimate of the telescope geometry, and of other instrumental parameters, astrometrically from the visibility timelines obtained from observations of celestial calibrator sources. The method copes systematically with complicated and unconventional antenna and array geometries, with electronic bandpasses that are different for each antenna radiometer, and with low signal-to-noise ratios for the calibrators. The technique automatically focusses on the geometry errors that are most significant for astronomical observation. We apply this method to observations made with the Very Small Array and constrain some 450 telescope parameters, such as the antenna positions, effective observing frequencies and correlator amplitudes and phase shifts; this requires only ~ 1 h of CPU time on a typical workstation.