  The maximum correntropy criterion (MCC) has been employed to design
outlier-robust adaptive filtering algorithms, among which the recursive MCC
(RMCC) algorithm is a typical one. Motivated by the success of our recently
proposed proportionate recursive least squares (PRLS) algorithm for sparse
system identification, we propose to introduce the proportionate updating (PU)
mechanism into the RMCC, leading to two sparsity-aware RMCC algorithms: the
proportionate recursive MCC (PRMCC) algorithm and the combinational PRMCC
(CPRMCC) algorithm. The CPRMCC is implemented as an adaptive convex combination
of two PRMCC filters. For PRMCC, its stability condition and mean-square
performance were analyzed. Based on the analysis, optimal parameter selection
in nonstationary environments was obtained. Performance study of CPRMCC was
also provided and showed that the CPRMCC performs at least as well as the
better component PRMCC filter in steady state. Numerical simulations of sparse
system identification corroborate the advantage of proposed algorithms as well
as the validity of theoretical analysis.
