**Laboratories of Image, Signal processing and Acoustics - Ecole polytechnique de Bruxelles / Faculté des Sciences **

Hydrophone depth tracking by Kalman filtering of linearly frequency modulated signal between 800 Hz and 1600 Hz, MREA/BP07 active acoustic run #2, showing the resolution of acoustic measurement inversion of geometry. Pressure-and-Temperature sensor in gray, Kalman-filtered estimate in red.

In this work, the acoustic tomography (or geoacoustic inversion) problem is reformulated in a state-space form wherein the time-varying sound-speed field and geoacoustic properties are assumed to follow a random walk with a priori statistics. The state-space equations are supplemented by a measurement model, the acoustic measurements, that are a nonlinear function of the sound-speed field and the bottom properties. The state-space form enables a straightforward implementation of a nonlinear Kalman filter, leading to a data assimilation problem. Compared to conventional global optimization approaches, the filtering method takes benefit from the sequential formulation, since previous results are used as constraint for the next estimation step. Nonlinear extensions of the Kalman filter enables to consider typical acoustic measurements (full-field, transmission losses, ...). Ensemble methods are required to properly manage the nonlinearity of the measurement model. Unscented Kalman filter (UKF) and Ensemble Kalman filter (EnKF) are the typical algorithms involved in this work.

Initially motivated by the acoustic data assimilation in ocean models, this methodology opens new possibilities for acoustic characterization of shallow environments, since it combines local search and nonlinear inversion. Therefore, the developed sequential filtering approach is applied on new topics of interest that are the range-dependent acoustic tomography and the acoustic characterization with light and mobile source-receiver geometry.

Traditional OAT enables the inversion of range-integrated profiles of the environment limiting its applicability. The proposed scheme developed in this work is suitable for the recovery of range-dependent structures of a vertical slice of the environment. The (continuous) SSF of this vertical slice is then discretized into a finite number of adjacent rectangular regions characterized by an independent SSP.

The sequential nature of the filtering approach enables to integrate the tracking of the source-receiver setup jointly with the environmental inversion problem. With a slowly drifting setup, the spatial variability of the geoacoustic properties can be characterized. Assimilation of complex pressure field measurements in the kilohertz regime at shorter ranges (1-2 km) is studied to consider lighter instrumentation that is easily deployed by hand from a small high-speed boat or mounted on a remotely operated or autonomous underwater vehicles.

Example of EKF tracking of the Ushant front feature-model (FM) during two days by assimilating 15-min spaced acoustic data.

The top-left panel shows the true sound-speed field (FM-synthesized) and its filtering estimate. The acoustic source and vertical receiver array positions are indicated in black. The corresponding amplitude of pressure data on hydrophones are shown in the top-right panel, true values are shown in gray and filtered values are shown in red. The FM-parameter tracking is shown in the bottom panel (true values in gray, filtered values in red). Three frequencies (200 Hz, 400 Hz, 600 Hz) are assimilated to perform the tracking. The true values are given by the projection of oceanic model predictions (HYCOM) on the feature model parameterization scheme.

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