Remote Sound Source Localization Using a Vertical Array

Synthetic Time Reversal (STR) can be used to estimate simultaneously the source signal and impulse response waveforms from a remote unknown source. Unfortunately, the unknown time shift in the reconstructed waveforms prevents elementary distance-equals-speed-times-time estimation of the source-array range. However, the relative timing between peaks in the STR impulse response can be used to estimate the source range and depth when some environmental information is available.

As a preliminary step, the correspondence between ray-path arrival angles (from beamforming outputs) and impulse response peaks must be determined. Once all possible ray path arrival angles have been considered, the arrival angles and STR-estimated relative time shifts for the various paths connecting the source and the array are known. In a multipath environment, this angle and timing information is a signature of the source location, and this location may be estimated when there is enough environmental information for propagation calculations.

Figure below illustrates propagation results via the plane-wave beamforming output, from the experiment explained in Synthetic Time Reversal section, at a source-array ranges of 100 m. At this source-array range, the direct path at 5° and surface-reflected path at 30° show up clearly throughout the signal bandwidth, while a weaker bottom reflection at –34° is also apparent.

Figure 1: Magnitude of the beamformed output at a source-array ranges of 100 m as a function of frequency (Hz) and elevation angle (degrees).

The ray-based back-propagation technique is based on acoustic time reversal (or phase conjugation in the frequency domain). First, the environmental information and the ray arrival angles are used to compute 3 rays launched at angles (which can be found from beamformer output shown in figure above) starting from the center of the array and extending out to the largest array-source range of interest, about 600 m in the current investigation. Next, the STR-determined impulse response is idealized as a series of perfect impulses that occur with the STR-determined arrival-time differences. This series of impulses is then time reversed and each impulse is launched along its associated ray path from the array. As the various impulses, located at range-depth coordinates (rm, zm) propagate away from the array along their corresponding rays, the root-mean-square (rms) impulse position, based on Euclidian distances from the impulse centroid, is monitored. The centroid location with the minimum value within the domain of interest provides an estimate of the source location. An example of such a ray-based back-propagation calculation is shown on figure below where the impulse positions are shown for three different times. In this figure, the array is on the left at r = 0 and the three rays emerge from the array-center depth of 33.5 m. In this case, a global minimum is occurs when the impulse centroid is located at (27m, 100m) when the source was actually located at (30m, 100m).

Figure 2: Sample ray trace back propagation calculation. The rays emerge from the center of receiving array at r = 0 and z = 33.5 m. Here symbols are shown at impulse locations at several different times when the rms impulse location achieves a local minimum. The actual source range and depth is 100 m and 30 m, respectively.

The root-mean-square (rms) impulse position, based on Euclidian distances from the impulse centroid, is shown below. Here, the actual source location is at 100m range. the minimum occurs at 100m range, too. The other two local minimums corresponds to the other two intersections of ray paths (shown in ray trace plot)

Figure 3: Root-mean-square impulse location vs. range for source-array ranges of 100 m.

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