  For identifying the non-Gaussian impulsive noise systems, normalized LMP
(NLMP) has been proposed to combat impulsive-inducing instability. However, the
standard algorithm is without considering the inherent sparse structure
distribution of unknown system. To exploit sparsity as well as to mitigate the
impulsive noise, this paper proposes a sparse NLMP algorithm, i.e., Correntropy
Induced Metric (CIM) constraint based NLMP (CIMNLMP). Based on the first
proposed algorithm, moreover, we propose an improved CIM constraint variable
regularized NLMP(CIMVRNLMP) algorithm by utilizing variable regularized
parameter(VRP) selection method which can further adjust convergence speed and
steady-state error. Numerical simulations are given to confirm the proposed
algorithms.
