Lucky ranging in underwater acoustic environment subject to spatial coherence loss

Abstract

In principle, a passive sonar system utilizing a long line array can estimate a source’s range by measuring its wavefront curvature. However, implementation can be difficult because wavefront curvature ranging is highly sensitive to spatial coherence losses. Real-world data measured by towed arrays often exhibit rapid fluctuations in signal spatial coherence across time and frequency. Such non-stationary degradation in spatial coherence on distributed arrays bears the similarity to the atmospheric Kolmogorov Turbulence Effect present in ground based telescopes (blurring of stars). Inspired by the lucky imaging approach used in astronomy, we propose a new approach for passive ranging in underwater environments subject to time-varying spatial coherence loss. Over short time scales, we speculate that the ocean may be well-behaved in the sense that there are little or no distortion to the signal wavefronts aka lucky moments. If detected, these lucky moments can be utilized to estimate range more accurately, overcoming coherence loss degradations experienced over long integration times. Modeling the signal as either coherent or incoherent in a short time frame, we derive the maximum likelihood lucky range estimator and show that with proper time-scale and processing bands, lucky moments can be identified that yield greatly improved estimates of range.