Adaptive Hoyer-L-Moment Envelope Spectrum: A Method for Robust Demodulation of Ship-Radiated Noise in Low-SNR Environments

Propeller noise is the main source of ship-radiated noise. Extracting and analyzing the modulation characteristics from the propeller noise plays a crucial role in classifying and identifying vessel targets. Existing demodulation methods such as Detection of Envelope Modulation On Noise (DEMON), narrowband demodulation, and cyclostationary analysis can be used to extract modulation features. However, capturing the modulation features on the envelope spectrum may be hard under low signal-to-noise ratio scenarios, since the envelope spectrum is contaminated by interference noise. To address this challenge, selecting an optimal frequency band rich in modulation information can significantly enhance demodulation performance. This paper proposes an Adaptive Hoyer-L-moment Envelope Spectrum (AHLES) method. The method first introduces an optimal frequency band selection method based on the golden section search strategy. A Hoyer-L-moment metric is then designed to quantify the modulation intensity within narrow frequency bands. Based on this metric, the optimal spectral coherence integration band is adaptively selected according to the signal's inherent modulation characteristics, thereby enhancing demodulation performance. The effectiveness of the proposed method is validated through experiments on both simulated signals and merchant ship data.