Adaptive Sparse Regular Split Gaussian Kernel Least Mean Square Algorithm for Super-Low-Frequency Motion-Induced Noise Cancellation

In super-low-frequency (SLF) submarine communication, the motion-induced noise of the towed antenna is the primary noise source, and below 500 Hz, it increases with increasing speed. We propose an improved quadratic Approximate Forward–Backward Split Gaussian Kernel Least Mean Square Algorithm (ASRSG–KLMS) based on the forward–backward split criterion using noise approximation of the nonlinear kernel least mean square, which introduces an L2-paradigm regularization term and has good sparsity while maintaining optimization stability. The ASRSG–KLMS algorithm could improve the narrowband signal-to-noise ratio by approximately 6.93 dB in the frequency range of 45–55 Hz, making it suitable for motion-induced noise cancellation in the SLF band.