Zoi-Heleni Michalopoulou

An Overview of Sequential Bayesian Filtering in Ocean Acoustics

Sequential filtering provides a suitable framework for estimating and updating the unknown parameters of a system as data become available. The foundations of sequential Bayesian filtering with emphasis on practical issues are first reviewed covering both Kalman and particle filter approaches. Filtering is demonstrated to be a powerful estimation tool, employing prediction from previous estimates and updates stemming from physical and statistical models that relate acoustic measurements to the unknown parameters. Ocean acoustic applications are then reviewed focusing on source tracking, estimation of environmental parameters evolving in time or space, and frequency tracking. Spatial arrival time tracking is illustrated with 2006 Shallow Water Experiment data.

Matched-field processing for broad-band source localization

In the Hudson Canyon experiment, a sound source moved at a constant depth in 73 m of water while transmitting four tonals. The signal was received on a vertical array of hydrophones that spanned the water column. The data set from this experiment has become a standard test case for studying source tracking using matched field processing. As part of that process it was important to first determine a suitable environment model and demonstrate the feasibility of matched-field processing. In this paper, we provide the background on the original data processing that was done to accomplish this. Several interesting results emerged from that study. Frequency averaging was demonstrated to be extremely beneficial when used with the Bartlett processor. However, the popular Minimum Variance processor performed poorly. Finally we discuss a very simple approach to combining the energy coherently that provided significantly improved results.

Rapid-phase modulation of terahertz radiation for high-speed terahertz imaging and spectroscopy.

Rapid voltage-controlled phase modulation of cw terahertz (THz) radiation is demonstrated. By transmitting an infrared beam through a lithium niobate phase modulator the phase of the THz radiation, which is generated by the photomixing of two infrared beams, can be directly modulated through a 2pi phase shift. The 100 kHz modulation rate that is demonstrated with this technique is approximately 3 orders of magnitude faster than what can be achieved by mechanical scanning.

Matched-impulse-response processing for shallow-water localization and geoacoustic inversion

In this paper, impulse response matching is proposed for source localization and environmental inversion. The ocean impulse response is estimated using a cross-correlation procedure applied to data from the propagation of a broadband pulse in a shallow-water environment. Source localization and geoacoustic parameter estimation are then performed through time-domain correlations between the estimated impulse responses at spatially separated phones and synthetic replica impulse responses. The method is both spatially and temporally coherent. Parameter space search uses a hierarchical scheme designed to exploit the sensitivity of the acoustic field to the unknown parameters. Tested on the SWellEX-96 and synthetic data, the proposed method is shown to be more robust than conventional (linear), incoherent, broadband matched field processing.

Gibbs sampling for time-delay-and amplitude estimation in underwater acoustics

Multipath arrivals at a receiving sensor are frequently encountered in many signal-processing areas, including sonar, radar, and communication problems. In underwater acoustics, numerous approaches to source localization, geoacoustic inversion, and tomography rely on accurate multipath arrival extraction. A novel method for estimation of time delays and amplitudes of arrivals with maximum a posteriori (MAP) estimation is presented here. MAP estimation is optimal if appropriate statistical models are selected for the data; implementation, requiring maximization of a multidimensional function, is computationally demanding. Gibbs sampling is proposed as an efficient means for estimating necessary posterior probability distributions, bypassing analytical calculations. The Gibbs sampler includes as unknowns time delays, amplitudes, noise variance, and number of arrivals. Through Monte Carlo simulations, the method is shown to have a performance very close to that of analytical MAP estimation. The method is also shown to be superior to expectation-maximization, which is often applied to time-delay estimation. The Gibbs sampling approach is demonstrated to be more informative than other time-delay estimation methods, providing complete posterior distributions compared to just point estimates; the distributions capture the uncertainty in the problem, presenting likely values of the unknowns that are different from simple point estimates.

Particle filtering for dispersion curve tracking in ocean acoustics

A particle filtering method is developed for dispersion curve extraction from spectrograms of broadband acoustic signals propagating in underwater media. The goal is to obtain accurate representation of modal dispersion which can be employed for source localization and geoacoustic inversion. Results are presented from the application of the method to synthetic data, demonstrating the potential of the approach for accurate estimation of waveguide dispersion characteristics. The method outperforms simple time-frequency analysis providing estimates that are very close to numerically calculated dispersion curves. The method also provides uncertainty information on modal arrival time estimates, typically unavailable when traditional methods are used.

BROADBAND SOURCE LOCALIZATION IN THE GULF OF MEXICO

The Gulf of Mexico experiment involved a broadband source (100–600 Hz) transmitting pseudorandom noise. The acoustic field was received by five hydrophones positioned vertically in the water column. By performing a correlation between the received time series and the transmitted signal, an approximation of the impulse response for the ocean channel is obtained. This impulse response is readily interpretable to yield information about the experiment, especially its geometry including receiver and bottom depths. With this refined environmental information, we then apply matched-field processing to obtain the source position.

Multiple source localization using a maximum a posteriori Gibbs sampling approach

Multiple source localization in underwater environments is approached within a matched-field processing framework. A maximum a posteriori estimation method is proposed that estimates source location and spectral characteristics of multiple sources via Gibbs sampling. The method facilitates localization of weak sources which are typically masked by the presence of strong interferers. A performance evaluation study based on Monte Carlo simulations shows that the proposed maximum a posteriori estimation approach is superior to simple coherent matched-field interference cancellation. The proposed method is also tested on the estimation of the number of sources present, providing probability distributions in addition to point estimates for the number of sources.

Robust multi-tonal matched-field inversion: A coherent approach

Matched-field processing is a method for inversion of the acoustic field utilizing its spatial coherence. In this work, a matched-field processor is introduced that incorporates the spatial coherence of the acoustic field not only at a single frequency but across frequencies as well. The new processor is suitable for multitonal sources and does not require knowledge of the source spectrum which is typically unavailable in passive estimation problems. A performance evaluation on source localization under low signal-to-noise ratios shows that the new processor is significantly superior, under certain circumstances, to the conventional incoherent Bartlett processor especially in cases involving receiver arrays with a small number of phones.

Particle filtering for arrival time tracking in space and source localization.

Locating and tracking a source in an ocean environment and estimating environmental parameters of a sound propagation medium are critical tasks in ocean acoustics. Many approaches for both are based on full field calculations which are computationally intensive and sensitive to assumptions on the structure of the environment. Alternative methods that use only select features of the acoustic field for localization and environmental parameter estimation have been proposed. The focus of this paper is the development of a method that extracts arrival times and amplitudes of distinct paths from measured acoustic time-series using sequential Bayesian filtering, namely, particle filtering. These quantities, along with complete posterior probability density functions, also extracted by filtering, are employed in source localization and bathymetry estimation. Aspects of the filtering methodology are presented and studied in terms of their impact on the uncertainty in the arrival time estimates. Using the posterior probability densities of arrival times, source localization and water depth estimation are performed for the Haro Strait Primer experiment; the results are compared to those of conventional methods. The comparison demonstrates a significant advantage in the proposed approach.