Variable step-size LMP algorithm based on correntropy induced metric

For the problem of underwater sparse channel estimation under <italic>α</italic>-stable distributed impulsive noise, correntropy induced metric variable step-size least mean p-power (CVSS-LMP) algorithm was proposed. The correntropy induced metric was used to represent the similarity between the error vector and the zero vector, thereby suppressing the influence of impulsive noise on the steady-state accuracy of the CVSS-LMP algorithm. A Gaussian kernel-based correntropy metric was presented, and a moving average method was used to construct the variable step-size control factor, which improved the convergence speed and steady-state accuracy of the CVSS-LMP algorithm. The simulation results demonstrate that, in comparison to conventional LMP-based filtering algorithms, a 17% faster convergence rate and over 2 dB improvement in steady-state accuracy were achieved by the proposed CVSS-LMP algorithm. Furthermore, It exhibits faster convergence and superior steady-state error performance when handling <italic>α</italic>-stable distributed impulsive noise.