  The maximum correntropy criterion (MCC) methodology is recognized to be a
robust filtering strategy with respect to outliers and shown to outperform the
classical Kalman filter (KF) for estimation accuracy in the presence of
non-Gaussian noise. However, the numerical stability of the newly proposed
MCC-KF estimators in finite precision arithmetic is seldom addressed. In this
paper, a family of {\it factored-form} (square-root) algorithms is derived for
the MCC-KF and its improved variant, respectively. The family traditionally
consists of three factored-form implementations: (i) Cholesky
factorization-based algorithms, (ii) modified Cholesky, i.e. UD-based methods,
and (iii) the recently established SVD-based filtering. All these strategies
are commonly recognized to enhance the numerical robustness of conventional
filtering with respect to roundoff errors and, hence, they are the preferred
implementations when solving applications with high reliability requirements.
Previously, only Cholesky-based IMCC-KF algorithms have been designed. This
paper enriches a factored-form family by introducing the UD- and SVD-based
methods as well. A special attention is paid to {\it array} algorithms that are
proved to be the most numerically stable and, additionally, suitable for
parallel implementations. The theoretical properties are discussed and
numerical comparison is presented for determining the most reliable
implementations.
