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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.