  High precison calibration is essential for a new generation of radio
interferometers looking for Epoch of Reionization and Baryon Acoustic
Oscillation signatures in neutral hydrogen. These arrays have so far been
calibrated by redundant calibration, which usually assumes baselines intended
to be identical are perfectly so. We present a new calibration scheme that
relaxes the assumption of explicit redundancy by calculating the expected
covariance of baselines. The technique also allows one to take advantage of
partial knowledge of the sky, such as point sources with known positions but
unknown fluxes. We describe a 2-level sparse matrix inverse to make the
calibration tractable for 1,000-element class interferometers. We provide a
reference implementation and use it to test the calibration of simulations of
an array with imperfectly located antennas observing Euclidean-distributed
point sources. Including position information for a handful of the brightest
sources, we find the amplitude/phase reconstruction improves by a factor of
$\sim$2/5 over redundant calibration for the noise levels/position errors
adopted in the simulations. Inclusion of source positions also allows us to
measure the overall phase gradient across the array, information which is lost
in traditional redundant calibration.
