High-gain long-time coherent integration for tones from moving targets via time warping

The radiated noise from ships is notably characterized by their tonal properties, making tone detection essential for passive sonar systems. The fast Fourier transform plays a crucial role in this process, but Doppler shifts can significantly diminish the integration gain. To address this issue, time warping is applied to modify the time axis of the signal, stabilizing the tonal frequency to a constant value. Traditionally, the warping operator, which determines how to modify the time axis, is designed by estimating motion parameters. In contrast, this study presents a method that eliminates the estimation step by using a set of pre-designed warping operators. The designing process involves preprocessing and clustering the delay vectors corresponding to various motion scenarios. The enhanced gain of the proposed algorithm, in comparison to the existing methods, has been validated through both simulation and experimental data.