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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

This paper aims at estimating the azimuth, range and depth of a cooperative broadband acoustic source with a single vector sensor in a multipath underwater environment, where the received signal is assumed to be a linear combination of echoes of the source emitted waveform. A vector sensor is a device that measures the scalar acoustic pressure field and the vectorial acoustic particle velocity field at a single location in space. The amplitudes of the echoes in the vector sensor components allow one to determine their azimuth and elevation. Assuming that the environmental conditions of the channel are known, source range and depth are obtained from the estimates of elevation and relative time delays of the different echoes using a ray-based backpropagation algorithm. The proposed method is tested using simulated data and is further applied to experimental data from the Makai'05 experiment, where 8–14 kHz chirp signals were acquired by a vector sensor array. It is shown that for short ranges, the position of the source is estimated in agreement with the geometry of the experiment. The method is low computational demanding, thus well-suited to be used in mobile and light platforms, where space and power requirements are limited.

This paper proposes a single sensor based three-dimensional localization method that, by taking advantage of the spatial filtering capabilities of a vector sensor, allows for a low computational demanding implementation, suitable for light real-time systems. An acoustic vector sensor (VS) is a device that measures the three orthogonal components of the particle velocity simultaneously with the pressure field at a single position in space. Vector sensors have been long used for target localization by the US Navy, due to their inherent spatial filtering capabilities [

Taking advantage of the intrinsic spatial filtering capability of a vector sensor (a typical VS presents a figure of height directivity pattern and a directivity index of 4.8 dB [

Due to multipath, in shallow water environments, the waveform impinging on a receiver is a sum of different echoes. Rahamim

Thanks to technological advances and small size, low noise underwater acoustic vector sensors with improved dynamic range and bandwidth are becoming available [

The present paper shows that the azimuth, range and depth of a high frequency broadband cooperative source, slowly moving (<0.3 m/s) in a shallow water environment, can be tracked in the presence of multipath using a single vector sensor. The azimuth and elevation of the echoes impinging on the vector sensor are estimated from the amplitude of the particle velocity components using a least squares-based algorithm. Then, a ray backpropagation method [

This paper is organized as follows: Section 2 presents the theoretical framework considered in the data processing and analysis. In Section 3, the proposed method is tested in a simulated scenario. Section 4 shows and discusses the results obtained on a real data set, and Section 5 summarizes the paper. Preliminary results of this work were presented in [

In the following, a vector sensor is considered that measures the pressure, _{x}_{y}_{z}

Without loss of generality, it is assumed that the signal impinging on the vector sensor is in the far-field and band-limited; thus, pressure, _{0} is the medium density and ∇ is the gradient operator.

Assuming a monochromatic signal of frequency, _{0}, the wavefront is planar; thus:
_{x}_{y}_{z}

When a field due to a point source in the far-field is sampled by a vector sensor with small dimension compared to the signal wavelength, then the wavefront can by considered planar. Thus, from _{x}_{s}_{s}_{y}_{s}_{s}_{z}_{s}_{s}_{s}_{x}_{y}_{z}_{0}

Intensity-based source direction estimation was considered in the pioneering work of D'Spain _{x}_{y}_{z}^{2}(_{x}_{x}

Assuming that _{s}

If the following assumptions hold: (1) the source is in the far field; (2) 3D propagation effects can be neglected; (3) the frequency of the signal is high compared with the cutoff frequency of the acoustic channel—therefore it acts as a waveguide—and (4) the receiver is far from the boundaries—the method above can be used even in a multipath environment [

In an underwater environment, it is a common assumption to consider that the multipath structure received on a sensor well away from the channel boundaries is a sum of plane waves. Thus, the ocean acts as a linear system, and neglecting the Doppler, the waveform sampled by the pressure sensor is:
_{m}_{m}_{x}_{y}_{z}

Considering a snapshot of _{x}_{y}_{z}_{x}_{y}_{z}_{x}_{y}_{z}_{x}_{y}_{z}_{1}, …_{m}_{M}_{m}_{m}_{m}^{T}_{x}_{y}_{z}

If the amplitude matrix,

Once the coefficients,
_{m}_{m}

The elevation estimates, along with the relative echo arrival times, form the basis for the source range-depth estimation algorithm.

The source range and depth backpropagation estimation procedure used in this work was introduced by Voltz and Lu [

Source localization is possible by tracing the trajectories of, at least, two echoes impinging on the receiver from different elevation angles and searching for range-depth points, where trajectories intersect each other. Several intersection points can occur along the trajectories; however, the source position can be uniquely determined by using the knowledge of relative time delays between echoes. This can be done by time aligning the different rays, _{a}_{m}_{a}_{m}_{a}_{a}_{a}

This method is numerically very efficient, since it only requires the computation of the trajectory and respective travel time of few rays and a one-dimensional search.

Assuming that the sound speed profile is (approximately) isovelocity and that the geometry of the experiment allows for a direct and a surface-reflected echo between the source and the receiver, the source range and depth can be estimated by simple geometric relations based on the source image method (

For testing the methods presented in the previous section and anticipating their performance on real data, the environmental and geometry scenario used for simulation is based on that of the Makai Experiment [^{3} and a compressional attenuation of 0.6 dB/λ. In these simulations, it will be assumed that the azimuth is known; thus, only horizontal and vertical particle velocity components are considered. The channel pressure and particle velocity field frequency response were modeled by the cTraceo ray tracing model [

A number of 100 realizations were generated according to model

The values in brackets represent the standard deviation. The star mark appears when a sign error occurs at least once in the ensemble of realizations for the given echo. It can be seen that the absolute errors are always smaller then 1.2 degrees, and as expected, the standard deviation increases with decreasing SNR. Generally, the SNR at the receiver for distant signals decreases, which, in turn, also contributes to a higher variance of the estimates. Unsurprisingly, the sign error of the estimates increases significantly with decreasing SNR. The autocorrelation function of an LFM chirp is an oscillatory function; thus, due to the noise, the location of the absolute maximum that determines the sign of the elevation estimates can be shifted by an oscillation period, therefore resulting in a sign error. This situation is illustrated in

Next, using the elevation angle estimates for the 5 dB SNR presented in

Generally, range and depth estimation errors increase with source range, since small angle perturbations from the nominal value give rise to larger range depth perturbations. However, the errors are less than 2 m in depth and 75 m in range at the maximum range of 900 m, the worst case considered. The results obtained from the latter echoes, which are bottom reflected, present higher estimation errors than those obtained from direct and surface reflected echoes. Bottom reflection is frequency dependent, which is accounted for by the forward propagation model used to synthesize the received signal; however, the backpropagation uses only the echo path and travel time computed at a given frequency (in general, the middle frequency of the signal band). Moreover, bottom reflected echoes are more attenuated (depending on the bottom structure and the angle of incidence); thus, they are more affected by noise. One can also notice that the source image method gives reasonable estimates in the considered scenario, even at longer ranges, because the sound speed profile is almost isovelocity in the source-receiver layer.

The data set analyzed here was acquired during the Makai Experiment (Makai'05), which took place off the west coast of Kauai I. in September 2005. The Makai'05 experiment was devoted to high frequency acoustics, and details of the experimental setup are described in [

The received signal was filtered for a ship noise band (90–350 Hz) and an acoustic source band (8–14 kHz) by linear phase bandpass filtering. The ship noise was used to determine the orientation of the

As a first step to localize the source, the arrival times and amplitudes of the various echoes impinging on the vector sensor from each transmitted chirp were estimated from the arrival patterns using

The range and depth of the source were estimated with the ray backpropagation method using the elevation angles of the direct and surface reflected echoes and respective relative arrival times. In order to obtain an estimate of the standard deviation of the estimates, the objective function is an average of the objective functions computed for each single realization of the transmitted chirp signal.

For comparison purposes the results obtained using the source image method are also shown in

This paper illustrates the spatial filtering capabilities of a vector sensor applied to source localization of a known broadband signal in a multipath environment. It was shown that the estimation of the angle of arrival (elevation) of a single echo was possible. Given the estimates of the amplitudes of the echoes in the _{x}_{y}_{z}

The authors would like to thank Michael Porter, chief scientist for the Makai Experiment, Jerry Tarasek for the loan of the vector sensor array used in the experiment and Paul Hursky, Martin Siderius and Bruce Abraham for providing assistance with the data acquisition. The Makai Experiment was supported by the US Office of Naval Research. This work was funded by National Funds through Foundation for Science and Technology (FCT) under project SENSOCEAN (PTDC/EEA-ELC/104561/2008).

The authors declare no conflict of interest.

Geometry of the source image method.

Makai'05 scenario used for the simulation: the source deployed at 10 m depth moves between a 100 and 1,000 m range from the vector sensor deployed at 40 m. The sound speed profile shows a large mixed layer, characteristic of Hawaii, USA. The bottom parameters are those estimated in [

Makai'05 simulation scenario of

Zoom of the amplitude-delay curve in the neighborhood of the first echo for two signal realizations (5 dB SNR) at a source distance of 300 m showing the expected behavior (

Source localization results for the scenario of

Bathymetry of the Makai'05 experimental area for the field calibration event with the superimposed research vessel R/V Kilo Moana location (pentagon) and GPS fixes of the source rubber boat (square). The values in brackets represent the distance to the R/V Kilo Moana.

Waveforms received from a 350 m distant source for the various vector sensor components (

Zoom of the amplitude-delay curve in the neighborhood of the first echo for the

Makai'05 source range-depth estimation at min 57 of the field calibration event considering six sets of backpropagated rays (12 rays) (

Estimated source location (cross marks) relative to the R/V Kilo Moana (located at the origin) of the Makai'05 field calibration event. The square marks indicate GPS fixes obtained with a handheld GPS on board the source rubber boat. The values in brackets represent the time (in min) of

Estimated angles of the four earliest echoes impinging on the vector sensor at different source distances as given by the forward model (true) and estimated considering an signal to noise ratios (SNR) of 20 and 5 dB. The values in curved brackets represent the standard deviations. The star mark indicates that at least one sign error occurred in the ensemble of estimates for the given echo.

100 | True | 16.3 | 26.1 | −60 | −63 | model |

20 | 17.3 (0.1) | 27.3 (0.1) | −59.4 (0.5) | −62.5 (0.7) | estimate | |

5 | 17.3 (0.4) | 27.4 (0.4) | −59.4 (3.4) * | −62.1 (3.7) * | estimate | |

| ||||||

300 | True | 5.6 | 9.3 | −30.8 | −33.8 | model |

20 | 5.9 (0.1) | 9.9 (0.1) | −31.8 (0.4) | −34.4 (0.3) | estimate | |

5 | 5.9 (0.4) * | 10.1 (0.5) | −31.9 (2.3) * | −34.5 (2.0) * | estimate | |

| ||||||

500 | True | 3.3 | 5.5 | −20.7 | −22.8 | model |

20 | 3.7 (0.1) | 5.8 (0.1) | −21.8 (0.3) | −23.8 (0.3) | estimate | |

5 | 3.7 (0.5) * | 5.8 (0.5) | −21.9 (1.5) * | −24.0 (2.1) * | estimate | |

| ||||||

700 | True | 2.3 | 3.9 | −15.9 | −17.6 | model |

20 | 2.5 (0.1) | 4.1 (0.1) | −16.8 (0.2) | −18.8 (0.4) | estimate | |

5 | 2.7 (0.6) * | 4.1 (0.4) * | −16.8 (1.3) * | −18.7 (2.0) * | estimate | |

| ||||||

900 | True | 1.8 | 2.9 | −13.2 | −14.5 | model |

20 | 1.9 (0.1) | 3.1 (0.1) | −14.1(0.2) | −15.2 (0.2) | estimate | |

5 | 2.1 (0.5) * | 3.2 (0.5) * | −14.1 (1.0) * | −15.3 (1.0) * | estimate |

Estimates of range and depth of a simulated source at 10 m depth, between a 100 and 900 m range from the receiver. The backpropagation method was applied to the four echoes, the earlier two echoes (1& 2) and the last two echoes (1& 2). The source image method was applied to the earlier two echoes. The range and depth estimates were obtained using estimates of the elevation angles from simulated data with 5 dB SNR.

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100 | 102.5 | 10.0 | 99.4 | 10.2 | 104.3 | 9.7 | 95.7 | 9.9 |

300 | 299.3 | 10.2 | 300.1 | 11.3 | 290.3 | 8.9 | 282.1 | 10.5 |

500 | 499.4 | 9.8 | 500.9 | 9.5 | 469.1 | 9.4 | 477.6 | 8.8 |

700 | 649.1 | 9.6 | 668.1 | 8.2 | 640.2 | 8.3 | 649.5 | 10.9 |

900 | 829.2 | 8.6 | 804.5 | 8.4 | 830.1 | 8.4 | 857.7 | 8.3 |

Mean azimuth and elevation estimates obtained at various instants of the Makai'05 field calibration event for the ship noise (azimuth only) and for the broadband sound source at 10 m depth and a range between 100 and 400 m (estimated from acoustic data,

35 | 386.3 | 132.4 | 136.1 (0.2) | 4.1 (0.1) | 7.5 (0.1) |

48 | 357.5 | 132.2 | 137.3 (0.8) | 4.9 (0.1) | 7.5 (0.7) |

50 | 279.8 | 134.4 | 140.9 (0.4) | 5.5 (0.3) | 9.8 (1.3) |

54 | 100.8 | 133.1 | 135.1 (2.3) | 16.7 (0.2) | 25.7 (2.0) |

57 | 114.2 | 131.7 | −10.2 (1.0) | 14.0 (0.4) | 23.8 (1.0) |

60 | 145.4 | 132.2 | −12.6 (0.6) | 12.4 (0.2) | 17.8 (1.1) |

Source range and depth estimates at various instants of the Makai'05 field calibration event using the ray backpropagation method and the image method. The column marked,

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35 | 386.3 | 10.54 | 6.7 | 391.1 | 11.7 |

48 | 357.5 | 10.55 | 9.4 | 367.1 | 8.3 |

50 | 279.8 | 11.1 | 1.8 | 298.8 | 11.0 |

54 | 100.8 | 10.1 | 1.5 | 101.9 | 9.2 |

57 | 114.2 | 11.5 | 1.0 | 115.0 | 11.0 |

60 | 145.4 | 7.9 | 1.2 | 146.7 | 7.3 |