Feed-forward cascaded stochastic resonance and its application in ship radiated line signature extraction

Extracting ship-radiated line signatures from intense background noise presents a significant challenge in remote passive sonar detection and identification. While stochastic resonance (SR) has shown promise for enhancing signal-to-noise ratio (SNR), cascaded stochastic resonance (CSR) offers a superior extension by gradually transitioning energy from high to low frequencies, resulting in smoother waveforms and more evident signatures. However, CSR relies heavily on the first level and lacks robustness, especially at slightly lower SNR. To overcome these limitations, we propose a feed-forward cascaded stochastic resonance (FCSR) method that leverages complete target signal information in each level and superimposes it with the output from the last level, leading to gradual improvements in SNR with high robustness. The superposition weights are designed as a function of the number of cascaded levels with an increasing trend to optimize the output of the entire cascaded system. Furthermore, a phase alignment strategy was developed to improve the superposition process. Through theoretical analysis, we demonstrate the effectiveness of the proposed FCSR method. Further simulation analyses demonstrates that FCSR outperforms CSR, with a remarkable 18 dB improvement in filtering performance under low SNR conditions, an average anti-noise ability enhancement of over 10 dB, and a robustness improvement exceeding 30% at −30 dB. We also validate the practicality and effectiveness of our proposed method through application verification, exhibiting excellent enhancement performance. This study illuminates the importance of reutilizing complete target signal information and emphasizes the potential of cascaded systems to extract signatures from heavy background noise.