Long-Range Source Localization in the Deep Sea Using Adaptive FDSL with a Few-Element Array

Matched Field Processing (MFP) suffers from environmental mismatch in deep-sea long-range source localization. Although Frequency Difference Matched Field Processing (FDMFP) improves mismatch tolerance, it fails due to caustic phase effects. Frequency Difference Source Localization (FDSL) effectively compensates for caustic phase errors by applying frequency-difference processing to both the measured field and the replica field. However, conventional FDSL typically relies on large-aperture arrays with numerous elements, resulting in high deployment costs and bulky systems. Furthermore, it exhibits limited resolution and elevated sidelobes. These limitations are exacerbated under reduced element counts and low signal-to-noise ratio (SNR) conditions. To improve performance under low SNR and small-array configurations, this paper proposes the FDSL-MVDR and FDSL-MUSIC methods by deriving adaptive weight vectors based on the frequency-difference covariance structure and redefining the ambiguity surface. Numerical simulations in a deep-sea Munk environment (source range 195 km, depth 1000 m) using a 15-element vertical line array demonstrate that the adaptive FDSL methods outperform conventional FDSL in terms of peak sharpness and sidelobe suppression. FDSL-MUSIC achieves approximately 100% localization success at SNR = -5 dB, a 4 dB improvement over conventional FDSL. Performance analyses under representative environmental mismatches indicate that the adaptive FDSL methods maintain robust localization performance and high-resolution characteristics in complex deep-sea environments. These results validate the feasibility of high-precision deep-sea localization using a few-element array.