  This paper continues the research devoted to the design of numerically stable
square-root implementations for the maximum correntropy criterion Kalman
filtering (MCC-KF). In contrast to the previously obtained results, here we
reveal the first robust (with respect to round-off errors) method within the
Cholesky factorization-based approach. The method is formulated in terms of
square-root factors of the {\it covariance} matrices, i.e. it belongs to the
covariance-type filtering methodology. Additionally, a numerically stable
orthogonal transformation is utilized at each iterate of the algorithm for
accurate propagation of the Cholesky factors involved. The results of numerical
experiments illustrate a superior performance of the novel MCC-KF
implementation compared to both the conventional algorithm and its previously
published Cholesky-based variant.
