  This paper suggests a few novel Cholesky-based square-root algorithms for the
maximum correntropy criterion Kalman filtering. In contrast to the previously
obtained results, new algorithms are developed in the so-called {\it condensed}
form that corresponds to the {\it a priori} filtering. Square-root filter
implementations are known to possess a better conditioning and improved
numerical robustness when solving ill-conditioned estimation problems.
Additionally, the new algorithms permit easier propagation of the state
estimate and do not require a back-substitution for computing the estimate.
Performance of novel filtering methods is examined by using a fourth order
benchmark navigation system example.
