  In this paper, we introduce an adaptive graph normalized least mean pth power
(GNLMP) algorithm for graph signal processing (GSP) that utilizes GSP
techniques, including bandlimited filtering and node sampling, to estimate
sampled graph signals under impulsive noise. Different from least-squares-based
algorithms, such as the adaptive GSP Least Mean Squares (GLMS) algorithm and
the normalized GLMS (GNLMS) algorithm, the GNLMP algorithm has the ability to
reconstruct a graph signal that is corrupted by non-Gaussian noise with
heavy-tailed characteristics. Compared to the recently introduced adaptive GSP
least mean pth power (GLMP) algorithm, the GNLMP algorithm reduces the number
of iterations to converge to a steady graph signal. The convergence condition
of the GNLMP algorithm is derived, and the ability of the GNLMP algorithm to
process multidimensional time-varying graph signals with multiple features is
demonstrated as well. Simulations show the performance of the GNLMP algorithm
in estimating steady-state and time-varying graph signals is faster than GLMP
and more robust in comparison to GLMS and GNLMS.
