Modal scintillation index: A physics-based statistic for acoustic source depth discrimination

Abstract

A new discriminant based on the scintillation of normal mode amplitudes is introduced for the problem of passive surface/submerged source classification in a shallow water waveguide. The scintillation of modal energies is often used to characterize and understand acoustic wave propagation in a randomly fluctuating ocean waveguide [D. B. Creamer, J. Acoust. Soc. Am. 99, 2825 (1996)]. This paper proposes a variant of the traditional modal scintillation index to treat the discrimination problem in a typical littoral oceanic waveguide. The approach is based on a modal decomposition of fluctuations in the received pressure field associated with the temporal modulation of the depth of an acoustic source about its mean value. Source depth fluctuations are the result of a platform’s response to surface or internal wave motion. The rms mode excitations due to source depth modulation are shown to exhibit a depth dependent signature that may be exploited to statistically separate surface and submerged source classes. In this work, the modal scintillation index (SI) is defined as the variance in the estimated magnitude of the modal excitation normalized by its expected value over some observation interval. The statistic is self-normalizing, so knowledge of source level and source range is not required to separate the two source classes. Estimation of the modal excitation statistics requires only knowledge of the water depth and the sound speed profile at the array. Classification performance predictions in terms of receiver operating characteristic (ROC) curves will be presented based on KRAKEN Monte Carlo simulations under conditions of known and unknown source depth and range in spatially white Gaussian noise. An ad hoc decision criterion, which compares the minimum scintillation index across all modes to a threshold, was used to illustrate the phenomenology. Vertical line array and horizontal line array endfire geometries were considered. The modal scintillation approach may provide a robust alternative to matched field processing for the problem of binary source depth classification.

Depth Discrimination for Low-Frequency Sources Using a Horizontal Line Array of Acoustic Vector Sensors Based on Mode Extraction

“…The SI can reflect the fluctuation of modal functions, which is closely related to source depth. Premus et al discriminated source depth based on the value of SI [8]. However, SI can be used to discriminate source depth only if those ranges are sufficiently close, since it is influenced by the source-receiver range besides source depth.…”

“…However, SI can be used to discriminate source depth only if those ranges are sufficiently close, since it is influenced by the source-receiver range besides source depth. Considering the ill-posed problem of mode filtering when the water column is not well-sampled by the VLA, Conan et al [9] proposed a robust method for discriminating the source depth supported by previous work introduced in [6,7,8]. When the VLA spans only 50% of the water column, that method outperforms those proposed in [6,7], as is evaluated by the receiver operating characteristic curve.…”

“…However, the frequency of the moving source must be known a priori, which is difficult with passive sonar system. Next, unlike the first approach based on depth estimation, the second approach considers depth discrimination as a binary hypothesis test; examples include the matched-subspace method [6,7], the scintillation index (SI) [8], and the trapped energy ratio [9] to improve the robustness of depth discrimination.…”

A Three-Dimensional Target Depth-Resolution Method with a Single-Vector Sensor

“…Researchers such as An [ 32 ], Premus [ 33 ] and Creamer [ 34 ] introduced a way to define the modified modal scintillation index (MMSI). It has been proved in an analytical form that the index MMSI is depth-dependent and independent of source level and source range under the condition of the ideal waveguide.…”

Statistical description of matched field processing ambiguity surfaces

“…3,4 Horizontal line arrays ͑HLAs͒ rely on mode orthogonality in the range dimension to separate the propagating modes, leading to requirements on array length. 5,6 The mode correlation matrix ͑MCM͒, which describes cross-talk between modes, provides a useful way to characterize an array's ability to resolve multipath. HLA and VLA geometries can be directly compared using metrics that describe the extent to which the MCM is diagonally dominant.…”