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Two acoustic source localization techniques were applied to infrasonic data and their relative performance was assessed. The standard approach for low-frequency localization uses an ensemble of small arrays to separately estimate far-field source bearings, resulting in a solution from the various back azimuths. This method was compared to one developed by the authors that treats the smaller subarrays as a single, meta-array. In numerical simulation and a field experiment, the latter technique was found to provide improved localization precision everywhere in the vicinity of a 3-km-aperture meta-array, often by an order of magnitude. ©2009 Acoustical Society of America

Contents

• Introduction
• Numerical simulation
• Experiment
• Conclusions
• Acknowledgments
• REFERENCES
• FIGURES

A problem for military ground forces is the localization of explosions in 10×10  km² areas of operation, often of the improvised explosive device (IED) type, to a precision of order 10  m. Acoustic methods of localization have long been used for this purpose because of their relatively inexpensive nature. Detonations of more than a kilogram of conventional explosive represent a low frequency acoustic source, with energy primarily in the infrasound frequency band (f<20  Hz). In this frequency band, the traditional localization method is called data fusion, or BAZ in this paper. The BAZ technique uses an ensemble of arrays to separately estimate direction-of-arrival (DOA) information, resulting in a localization solution estimated from the various back azimuths. The DOA estimates are said to be far field, since the aperture of each subarray is assumed to be small compared to the source distance. This technique has application across a broad range of interest, from nuclear treaty monitoring,¹ to vehicle tracking,² to the conventional detonations^3,4 described in this study. DOA-based methods of localization are prone to uncertainties arising from atmospheric,⁵ environmental,⁶ and intrinsic⁷ factors. Taken together, these account for a precision of order 100  m in practical applications consistent with the aim of this study.⁴

In the literature there is a certain paucity of infrasound localization applications at ranges less than 100  km. Part of this stems from the difficulty in applying high-resolution techniques to the data, which are often contaminated by wind noise and create difficulty in forming simple signal models. For infrasonic localization, spectral-estimation-based methods are not useful, due to significant departures from 1/r pressure fluctuations.^8,9 Experience with applying techniques that directly estimate wavefront curvature to infrasound data with known ground truth for near-field sources has shown that these methods are similarly not useful for infrasonic applications. Neither BAZ nor srcLoc suffer from these limitations.

Acoustic localization across 10×10  km² areas may also be accomplished by employing near-field assumptions. Near-field methods variously make use of DOA and/or time-difference of arrival information (TDOA).^10,11,12 Efforts to apply these two techniques to infrasonic data led the authors to develop a near field, strictly TDOA-based method of acoustic localization, or srcLoc in this paper. This technique treats each of the subarrays of the BAZ method as part of a single, meta-array. While all TDOA-based methods can be shown to represent the optimal intersection of hyperbolic curves in a phase space,⁸ application of the srcLoc method to a wide variety of synthetic and actual infrasound signals has shown it to outperform other near-field techniques. Mathematically, the srcLoc method calculates an optimal, in some sense (typically least squares), intersection of sensor world lines with a source sound cone in position-velocity-time space.⁹ An analytic least squares solution of the cone intersections serves as a seed for a numerical optimization routine. For infrasound localization, the advantages of the srcLoc method lie primarily in the absence of restrictive atmospheric assumptions. The atmosphere is assumed, albeit unrealistically, to be isotropic and windless, leading to a right, circular sound cone. Too, there is no implicit model assumption governing the functional form of the signal source; since only TDOA information needs to be estimated, the isotropic atmosphere assumption is sufficient.

This paper describes a numerical simulation and field experiment to test the relative localization efficacy of BAZ and srcLoc on infrasound data. The goal of the experiments was twofold. First, to determine if the newly developed srcLoc technique would yield enhanced localization precision over the traditional BAZ method in this particular application, and second, to determine if the simple model assumptions behind srcLoc would hold up under scrutiny in the field.

The sponsor of this study placed a broad constraint on the application: an area of 10×10  km² should be covered by a dozen sensors for the purpose of low-frequency acoustic localization of explosions. In part, this constraint stems from past practice and budget limitations. Prior experience with portable infrasound array deployments lead to an array design of three subarrays, each comprising four sensors. A subarray consisted of sensors positioned at the vertices of a square, 100  m from a central point (what would become the digitizer location). The centroids of each subarray were then positioned at the vertices of an equilateral triangle, 3  km on a side (the meta-array). Such a design would give adequate spatiotemporal resolution for both the BAZ and srcLoc techniques to provide localization across much of the area.

The effects of 500 blasts at the center of each 100×100  m²  pixel in a 144  km² area were simulated. In practice, the TDOA information required for BAZ and srcLoc is estimated from generalized cross correlation of sampled waveforms. This estimation process is relatively slow, so this study made use of synthetic TDOA information representative of 10  dB signal to noise ratio (SNR) blasts when sampled at 1  kHz. Specifically, perfectly sampled TDOA information for each blast was contaminated by the appropriate (empirically determined) amount of Gaussian noise. For BAZ, the TDOA information leads to three DOA estimates (one for each subarray), from which a localization solution is calculated. For srcLoc, a single localization solution is calculated (via an analytic seed fed to a Nelder–Mead optimization¹³ routine) from the entire TDOA ensemble.

The distribution of absolute range errors (_R) was estimated for each pixel and technique. The value of _R corresponding to a cumulative sum of 0.95 on the distribution was mapped to a color, as shown in Fig. 1. No pixel in the simulation area has a larger error for srcLoc than for BAZ. By using srcLoc in lieu of the traditional BAZ, an improvement of roughly an order of magnitude is expected throughout much of the simulation area. Everywhere in the interior of the meta-array, srcLoc is predicted to exhibit the desired precision of order 10  m. The BAZ technique gives rise to large range errors when the DOA estimate from any one cluster is directed toward another. This problem is greatly exaggerated when a blast occurs outside the meta-array. Because of this, the results depicted in Fig. 1 were clipped at 6  km errors for the BAZ technique.

Figure 1.

From 27–29 August 2007, an experiment was conducted on the range complex of Ft. Greely, Alaska, in order to verify the predictions detailed in Sec. II. The actual emplacement of instruments and demolitions is depicted in Fig. 2. Each position was surveyed via 10-min averaged GPS data, to a precision of ±3  m. While the vagaries of terrain and vegetation qualitatively distorted the planned array geometry, the predictions of Sec. II still apply. Infrasound sensors used in the experiment were Chaparral Physics Mod. 25 and each cluster of four was sampled at 1  kHz. For wind-noise reduction, clusters were placed in patches of boreal forest (small, dense trees and brush) and each sensor was connected to four, 20  m porous hoses from various (unknown) manufacturers. No meteorological data were acquired, consistent with the sponsor's application; however, the weather was sunny and calm on both days. Observations of drifting smoke and dust from the detonations indicated that the winds were variable (direction) and less than about 2  m/s (walking speed).

Figure 2.

Demolitions were positioned at the sites depicted in Fig. 2. These represent a compromise between testing various critical locations in the plots of Fig. 1 and satisfying U.S. Army training requirements. Additionally, Ft. Greely Range Control criteria had to be met as the fire danger is typically high during August in interior Alaska. Explosives used in the experiment were blocks (0.57  kg) of M112 C-4 plastic explosive. The explosives were variously staked at 1  m height or placed directly on the ground. Initiation was via hand-pulled time fuse and blasting caps. Ground surface ranged from dry, hard-pack dirt road to wet, muskeg bog. Blast sites were also variously in the open or sheltered by boreal forest. At each site between three and seven separate charges, ranging in size from one-quarter to four blocks, were detonated. This amounted to a total of 55 separate blasts.

Although spectral localization methods were not employed, each of the blasts exhibited a broad peak in energy at roughly 18  Hz, across all of the sensors. Thus the data were bandpass filtered at f[0.8,36]  Hz; however, the results were not sensitive to the exact corner frequencies. This filtering resulted in further noise reduction and is a standard part of infrasonic data processing.¹ TDOA information for the subarrays (BAZ) and the meta-array (srcLoc) was then estimated via cross correlation. The TDOA information alone was used to localize each blast with srcLoc. In the case of BAZ, DOA estimates were made prior to localization. Each blast site was translated to the origin and the same translation was applied to each respective localization solution. These results are depicted in Fig. 3.

Figure 3.

Of the 55 blasts, srcLoc produced a range error _R30  m for 95% of them, compared to 11% using BAZ (as seen in the inset of Fig. 3). The srcLoc method gave better than a factor of 2 increase in localization precision over BAZ at 96% of the sites, and in no instance less than a factor of 1.4. An order of magnitude increase was obtained with srcLoc at 50% of the blast sites.

In assessing the goal of the experiment, srcLoc was found everywhere to provide enhanced localization precision over that of BAZ, both in simulation and in the field. Additionally, the simple atmospheric assumptions that underlie srcLoc were sufficient to achieve this enhancement during the testing period. A difference in the bias of each localization method was noted, but is not explained by the underlying model assumptions. Further study of this phenomenon is required. An inadvertent test of sensitivity to sensor failure was conducted as indigenous hares gnawed on the cabling at the eastern subarray, disabling a sensor for a number of blasts. The effect of sensor loss was also studied by purposefully ignoring the data from particular sensors. Single sensor failures such as this will have a large impact on a four-element subarray, manifesting itself as an increase in the uncertainty in one of the DOA estimates that feeds BAZ.⁷ This single-sensor failure mode has virtually no effect on srcLoc. Under srcLoc, there is no requirement for small clusters of sensors; with sufficient digitizers, sensors can be randomly scattered throughout the area of interest. That said, clusters are a convenient deployment strategy in case atmospheric conditions become severe enough to distort TDOA information at long (meta-array), but not short (subarrays), ranges. BAZ then can serve as a backup for srcLoc in a practical setting.

Beyond the scope of military applications, the technique can be applied to geophysical situations. Near-field volcano monitoring is an example of current interest, where enhanced, low-frequency acoustic localization can tag a particular vent as being active or lead to the location of a new fumarole.

This work represents one aspect of the research supported by NSF Grant No. IIS-0433392 and Geophysical Institute internal funding. This experiment would not have been possible were it not for the support of J. Helmericks of the Geophysical Institute, SFC Wolter and the soldiers of the 73rd ENGR CO, 1-25 SBCT, Ft. Wainwright, AK. The authors thank Dr. D. Withoff for helpful discussions and the reviewers for their cogent and insightful comments.

References and Links

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4. V. Pinsky, Y. Gitterman, A. Hofstetter, and A. Shapira, “Robust location of surface explosions by a network of acoustic arrays,” Geophys. Res. Lett. 33, L02317 (2006). first citation in article
   
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6. B. G. Ferguson and K. W. Lo, “Passive ranging errors due to multipath distortion of deterministic transient signals with application to the localization of small arms fire,” J. Acoust. Soc. Am. 111, 117–128 (2002). [ISI] [MEDLINE] first citation in article
   
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8. J. H. DiBiase, H. F. Silverman, and M. S. Brandstein, “Robust localization in reverberant rooms,” in Microphone Arrays: Signal Processing Techniques and Applications, edited by M. Brandstein and D. Ward (Springer, New York, 2001), pp. 157–180. first citation in article
   
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11. T. Duong Tran-Luu and P. Cremona-Simmons, “Acoustic sources localization by simultaneous DOA and TOA,” in Proceedings of the 2006 Meeting of the Military Sensing Symposia (MSS) Specialty Group on Battlespace Acoustic & Seismic Sensing, Magnetic & Electric Field Sensors (BAMS) (US Army CERDEC Night Vision and Electronic Sensors Directorate, Ft. Belvoir, VA, 2007), pp. 441–452. first citation in article
    
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Full figure

Fig. 1. Confidence limits (95%) for the absolute range errors in simulated source localization for each technique. The traditional DOA method of data fusion (BAZ) is depicted in the left panel and that of the strictly TDOA technique (srcLoc), in the right. To construct the panels, an ensemble of 500 TDOA vectors for each 100×100  m² pixel was synthesized. The TDOA information was representative of 10  dB SNR acoustic arrivals across the array when sampled at 1  kHz. The distributions of absolute range errors were estimated for each pixel and technique. The 95% confidence limits in the range errors are mapped to color in each panel [the left (BAZ) panel was clipped at 6  km errors]. White + symbols represent sensor locations. First citation in article

Full figure

Fig. 2. Experimental array and blast sites. Sensor locations (dotted circles) and blast sites (triangles) are depicted. Distinct charges of M112 C-4, in various sizes, were detonated at each site (see text for details). Coordinates (km) are in grid 06VWR of the MRGS coordinate system. First citation in article

Full figure

Fig. 3. Normalized results of experimental source localizations for each technique. Each blast site is translated to the origin (red star) and the same translation is applied to the corresponding localization solutions (blue circles for BAZ and green triangles for srcLoc). The inset depicts a 30×30  m² box about the origin, in which 95% of the srcLoc solutions lie, but only 11% of the BAZ solutions. First citation in article

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