Multi-frequency sparse Bayesian learning for matched

Nov-2018 ASA Victoria

Multi-frequency sparse Bayesian learning for matched field processing in non-stationary noise Kay L. Gemba1, Santosh Nannuru, and Peter Gerstoft Marine Physical Laboratory of the Scripps Institution of Oceanography University of California at San Diego [email protected] 1

Presentation objectives We investigate SBL performance for the MFP application and demonstrate: 1. SBL behaves similarly to an adaptive processor and displays robustness to modest model-data mismatch and operational uncertainty. SBL performance is compared to the white noise gain constraint (WNC) and Bartlett processors. 2. SBL is implemented with 2 noise models, modeled as stationary noise (SBL1) and non-stationary noise (SBL2). The latter is useful when the noise variance evolves across snapshots (see also Gerstoft et al, Signal Processing 2018). • Results are demonstrated with simulated and the SwellEx-96 S59 data set. The twosource scenario consists of a quieter, submerged broadband source and a surface interferer. Gemba K L, Nannuru S, Gerstoft. Ocean acoustic localization with sparse Bayesian learning in nonstationary noise, IEEE J. Special Topics (Feb. 2019), under review

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Matched field processing: Bartlett and WNC Bartlett, WNC 0 dB

WNC -2 dB

WNC -6 dB

Sparse Bayesian Learning

• Model assumptions: • Constant power spectrum for each source • Amplitudes can vary from snapshot to snapshot  Same sparsity across snapshots and frequency

Stationary noise: 2 𝜎𝑛,𝑙 = 𝜎 2 = const.

Non-stationary noise (observed across snapshots) 2 𝜎𝑛,𝑙 = 𝜎𝑙2

Nannuru: Sparse Bayesian learning with uncertainty models and multiple dictionaries. Submitted to IEEE TSP (available at arXiv, www.gemba.org)

SWellEx-96 Event S59:

30 min 55 min

• Source 1 (S1) at 50 m depth (blue) • Surface Interferer (red) • 14*3=42 processed frequencies: - 166 Hz (S1 SL at 150 dB re 1 μPa) - 13 freq. ranging from 52-391 Hz (S1 SL at 122-132 dB re 1 μPa) - +/- 1 bin each • FFT Length: 4096 samples rec. at 1500 Hz • 21 Snapshots @ 50% overlap • 135 segments Experiment site (near San Diego) with Source (blue) and Interferer (red) track.

Bartlett

WNC -3dB

SBL1

• Simulation • Source 1 (50 m) • Surface Interferer • Freq. = 204 Hz • SNR = 10 dB • Int/S1 = 10 dB • Stationary noise

ROC-like Source 1 localization curve for stationary noise

Non-stationary noise at 0 dB SNR

Non-stationary noise at 0 dB + Normalized data Bartlett WNC SBL1 SBL2

Multi-frequency sources with non-stationary noise (52, 82, 166, 204, and 286 Hz) No normalization

Normalized data

Multi-frequency SWellEx-96 2-Source Localization (73/135) No normalization Bartlett

WNC -3dB

SBL1

SBL2

Normalized Data

Multi-frequency SWellEx-96 2-Source Localization (93/135) No normalization Bartlett

WNC -3dB

SBL1

SBL2

Normalized Data

SWellEx-96 Event S59 Two-Source range-localization No normalization Bartlett

WNC -3dB

SBL1

SBL2

Normalized Data

Conclusions • SBL behaves similarly to an adaptive processor and can discriminate against sidelobes.

• SBL appears robust to modest data-replica. SBL yields an ambiguity surface, only the noise models require a source count estimate. • SBL requires less tuning than Basis Pursuit and is computationally faster.

• SBL appears robust to operational uncertainty (processing of 3 adjacent bins, the interferer is present in all bins while the deep source is only present in one).

Gemba K L, Nannuru S, Gerstoft. Ocean acoustic localization with sparse Bayesian learning in nonstationary noise, IEEE J. Special Topics (Feb. 2019), under review

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SBL

CBF

Eigenrays