  This technical note is aimed to derive the Chandrasekhar-type recursion for
the maximum correntropy criterion (MCC) Kalman filtering (KF). For the
classical KF, the first Chandrasekhar difference equation was proposed at the
beginning of 1970s. This is the alternative to the traditionally used Riccati
recursion and it yields the so-called fast implementations known as the
Morf-Sidhu-Kailath-Sayed KF algorithms. They are proved to be computationally
cheap because of propagating the matrices of a smaller size than $n \times n$
error covariance matrix in the Riccati recursion. The problem of deriving the
Chandrasekhar-type recursion within the MCC estimation methodology has never
been raised yet in engineering literature. In this technical note, we do the
first step and derive the Chandrasekhar MCC-KF estimators for the case of
adaptive kernel size selection strategy, which implies a constant scalar
adjusting weight. Numerical examples substantiate a practical feasibility of
the newly suggested MCC-KF implementations and correctness of the presented
theoretical derivations.
