In passive sonar, adaptive algorithms can be used to cancel strong sinusoidal self-interferences. In order to correctly
recover low-power target signals during the early stages of processing, these adaptive algorithms must provide fast
convergence and, at the same time, narrow notches at the frequencies of the sinusoids. In this respect, the gradient
adaptive lattice (GAL) algorithm is a very attractive choice. However, the GAL algorithm with a constant step-size
parameter has to compromise between the convergence rate and notch bandwidths. Therefore, in this article, we
propose a variable step-size scheme for the GAL algorithm that can achieve both a fast convergence rate and narrow
notches. Simulation results demonstrate the efficiency of the proposed algorithm compared to both the conventional
GAL algorithm and transversal adaptive filter combined with the variable step-size scheme.