Frequency Analysis of Acoustic Data Using Multiple-Measurement Sparse Bayesian Learning

Abstract

Passive sonar systems are used to detect the acoustic signals that are radiated from marine objects (e.g., surface ships, submarines, etc.), and an accurate estimation of the frequency components is crucial to the target detection. In this paper, we introduce sparse Bayesian learning (SBL) for the frequency analysis after the corresponding linear system is established. Many algorithms, such as fast Fourier transform (FFT), estimate signal parameters via rotational invariance techniques (ESPRIT), and multiple signal classification (RMUSIC) has been proposed for frequency detection. However, these algorithms have limitations of low estimation resolution by insufficient signal length (FFT), required knowledge of the signal frequency component number, and performance degradation at low signal to noise ratio (ESPRIT and RMUSIC). The SBL, which reconstructs a sparse solution from the linear system using the Bayesian framework, has an advantage in frequency detection owing to high resolution from the solution sparsity. Furthermore, in order to improve the robustness of the SBL-based frequency analysis, we exploit multiple measurements over time and space domains that share common frequency components. We compare the estimation results from FFT, ESPRIT, RMUSIC, and SBL using synthetic data, which displays the superior performance of the SBL that has lower estimation errors with a higher recovery ratio. We also apply the SBL to the in-situ data with other schemes and the frequency components from the SBL are revealed as the most effective. In particular, the SBL estimation is remarkably enhanced by the multiple measurements from both space and time domains owing to remaining consistent signal frequency components while diminishing random noise frequency components.

Passive Sonar Target Identification Using Multiple-Measurement Sparse Bayesian Learning

“…Recall that MM-SBL effectively detects and estimates common components of signal through multiple measurements. As demonstrated in previous studies [ 34 ], frequency analysis of sparse signals using MM-SBL has advantages in term of improved resolution and noise reduction. In this paper, we proposed a target identification method from a new perspective using MM-SBL, which has been previously validated, and examined the performance using in-situ underwater acoustic data.…”

“…In a passive sonar system, received signals generally have four types of signals: tonal signals (generated by the operation of the machinery of the ship), propeller noise (generated by the cavitation which is produced by the propeller rotating), hydrodynamic noise (generated by friction between the ship and the fluid), and ambient noise [ 1 ]. A passive sonar system generally suppresses other types of signals except the tonal signal, by applying an analog filter (or low-pass filter) to the received data [ 34 ]. Therefore, in this paper, we detect marine objects using the filtered data dominated by the tonal signals.…”

“…For both the frequency analysis and the DOA estimation problems, the linear system model relates the measured data to the unknown source amplitude as where and are the transformation matrix and noise, respectively [ 29 , 34 ]. For simplicity, we define and .…”

“…SBL was first proposed for classification and regression in machine learning [ 27 ]. Recently, in underwater acoustics, SBL has been applied to beamforming [ 28 , 29 , 30 ], localization [ 31 , 32 ], mode extraction [ 33 ], and line spectral estimation [ 34 ]. In the SBL framework, the noise and source power variances are automatically obtained through an iterative optimization process.…”

“…Moreover, owing to the sparsity of the signals, the solution of the linear system using SBL is advantageous in suppressing noise and obtaining high-resolution performance. In addition, the multiple-measurement SBL (MM-SBL) has been proposed to improve performance using multiple measurements, which increasing the robustness of the SBL against noise by using the commonality of the source signals [ 28 , 34 ].…”