Brian M. Worthmann

High frequency source localization in a shallow ocean sound channel using frequency-difference matched field processing

Matched field processing (MFP) is an established technique for source localization in known multipath acoustic environments. Unfortunately, in many situations, particularly those involving high frequency signals, imperfect knowledge of the actual propagation environment prevents accurate propagation modeling and source localization via MFP fails. For beamforming applications, this actual-to-model mismatch problem was mitigated through a frequency downshift, made possible by a nonlinear array-signal-processing technique called frequency difference beamforming [Abadi, Song, and Dowling (2012). J. Acoust. Soc. Am. 132, 3018-3029]. Here, this technique is extended to conventional (Bartlett) MFP using simulations and measurements from the 2011 Kauai Acoustic Communications MURI experiment (KAM11) to produce ambiguity surfaces at frequencies well below the signal bandwidth where the detrimental effects of mismatch are reduced. Both the simulation and experimental results suggest that frequency difference MFP can be more robust against environmental mismatch than conventional MFP. In particular, signals of frequency 11.2 kHz-32.8 kHz were broadcast 3 km through a 106-m-deep shallow ocean sound channel to a sparse 16-element vertical receiving array. Frequency difference MFP unambiguously localized the source in several experimental data sets with average peak-to-side-lobe ratio of 0.9 dB, average absolute-value range error of 170 m, and average absolute-value depth error of 10 m.

Adaptive frequency-difference matched field processing for high frequency source localization in a noisy shallow ocean

Remote source localization in the shallow ocean at frequencies significantly above 1 kHz is virtually impossible for conventional array signal processing techniques due to environmental mismatch. A recently proposed technique called frequency-difference matched field processing (Δf-MFP) [Worthmann, Song, and Dowling (2015). J. Acoust. Soc. Am. 138(6), 3549-3562] overcomes imperfect environmental knowledge by shifting the signal processing to frequencies below the signals band through the use of a quadratic product of frequency-domain signal amplitudes called the autoproduct. This paper extends these prior Δf-MFP results to various adaptive MFP processors found in the literature, with particular emphasis on minimum variance distortionless response, multiple constraint method, multiple signal classification, and matched mode processing at signal-to-noise ratios (SNRs) from -20 to +20 dB. Using measurements from the 2011 Kauai Acoustic Communications Multiple University Research Initiative experiment, the localization performance of these techniques is analyzed and compared to Bartlett Δf-MFP. The results show that a source broadcasting a frequency sweep from 11.2 to 26.2 kHz through a 106 -m-deep sound channel over a distance of 3 km and recorded on a 16 element sparse vertical array can be localized using Δf-MFP techniques within average range and depth errors of 200 and 10 m, respectively, at SNRs down to 0 dB.

The frequency-difference and frequency-sum acoustic-field autoproducts

The frequency-difference and frequency-sum autoproducts are quadratic products of solutions of the Helmholtz equation at two different frequencies (ω+ and ω-), and may be constructed from the Fourier transform of any time-domain acoustic field. Interestingly, the autoproducts may carry wave-field information at the difference (ω+ - ω-) and sum (ω+ + ω-) frequencies even though these frequencies may not be present in the original acoustic field. This paper provides analytical and simulation results that justify and illustrate this possibility, and indicate its limitations. The analysis is based on the inhomogeneous Helmholtz equation and its solutions while the simulations are for a point source in a homogeneous half-space bounded by a perfectly reflecting surface. The analysis suggests that the autoproducts have a spatial phase structure similar to that of a true acoustic field at the difference and sum frequencies if the in-band acoustic field is a plane or spherical wave. For multi-ray-path environments, this phase structure similarity persists in portions of the autoproduct fields that are not suppressed by bandwidth averaging. Discrepancies between the bandwidth-averaged autoproducts and true out-of-band acoustic fields (with potentially modified boundary conditions) scale inversely with the product of the bandwidth and ray-path arrival time differences.

Wave physics of the frequency difference autoproduct: Helmholtz equation analysis

The frequency-difference autoproduct (Δf-AP) is a quadratic product of solutions of the inhomogenous Helmholtz equation that differ only in frequency, and may be easily constructed from the Fourier transform of measured time-domain signals. Recent findings involving beamforming (Abadi et al., 2012, JASA 132, 3018-3029) and matched field processing (Worthmann et al., 2015, JASA 138, 3549-3562) suggest that the Δf-AP is similar to an acoustic field at the difference frequency, even when the difference frequency lies below the recorded signal’s bandwidth. This presentation provides mathematical analysis that supports this interpretation and indicates its limitations, along with examples from a Lloyd’s mirror environment where a frequency sweep from 1-2kHz was broadcast from 100m below the reflecting surface out to a range of 2km. In particular, the Δf-AP in time-independent, inhomogeneous, multipath environments should be locally indistinguishable from an acoustic field at the difference frequency when: (i) ...

Cross-term analysis in frequency-difference-based source localization methods

In previous work, it has been shown that a quadratic product of frequency-domain acoustic fields at different frequencies but the same spatial location leads to an auxiliary field which may contain field information at frequencies below the original signal’s bandwidth (Worthmann, Song and Dowling, 2015, JASA 138, 3549-3562). This quadratic product, termed the frequency-difference autoproduct, has been shown to be valuable for beamforming and source localization in the presence of environmental mismatch and/or array sparseness. However, in a multipath environment, this quadratic product leads to undesired cross-terms. Bandwidth averaging procedures have been found to suppress some of their detrimental influences in some cases, but not all. Additionally, the poor dynamic range observed in frequency-difference beamforming and frequency-difference matched field processing are associated with the imperfect mitigation of these cross-terms. In this presentation, the nature of these cross-terms is analyzed, and signal processing tools are developed which attempt to robustly mitigate the detrimental effects of these cross terms. These signal processing tools can be used to potentially improve localization performance when using frequency-difference autoproduct-based source localization schemes. [Sponsored by ONR and NSF]

Measurement of autoproduct fields in a Lloyd's mirror environment

Conventional frequency-domain acoustic-field analysis techniques are typically limited to the bandwidth of the field under study. However, this limitation may be too restrictive, as prior work suggests that field analyses may be shifted to lower or higher frequencies that are outside the fields original bandwidth [Worthmann and Dowling (2017). J. Acoust. Soc. Am. 141(6), 4579-4590]. This possibility exists because below- and above-band acoustic fields can be mimicked by the frequency-difference and frequency-sum autoproducts, which are quadratic products of frequency-domain complex field amplitudes at a pair of in-band frequencies. For a point source in a homogeneous acoustic half-space with a flat, pressure-release surface (a Lloyds mirror environment), the prior work predicted high correlations between the autoproducts and genuine out-of-band fields at locations away from the source and the surface. Here, measurements collected in a laboratory water tank validate predictions from the prior theory using 40- to 110-kHz acoustic pulses measured at ranges between 175 and 475 mm, and depths to 400 mm. Autoproduct fields are computed, and cross-correlations between measured autoproduct fields and genuine out-of-band acoustic fields are above 90% for difference frequencies between 0 and 60 kHz, and for sum frequencies between 110 and 190 kHz.

Autoproducts in refractive waveguides near shadow zones

The frequency-difference and frequency-sum autoproducts are quadratic products of nonzero-bandwidth frequency-domain acoustic fields at different frequencies but the same spatial location. The autoproducts have been shown to mimic genuine lower- or higher-frequency, out-of-band, acoustic fields within some limitations (Worthmann and Dowling, 2017, JASA 141, 4579–4590). Previous analysis of the autoproducts considered only spatial regions of the environment that were well-ensonified by the in-band acoustic field, which itself is well-described by the ray-approximation. In this presentation, the necessity of this well-ensonified restriction is analyzed by comparing autoproduct fields with their out-of-band analogues in and near acoustic shadow zones created by refraction. The results presented are derived from exact or asymptotic solutions of the Helmholtz equation. The propagation environment chosen for this study is a horizontal, range-independent, stratified, unbounded, truncated-n 2-parabolic waveguide, which creates acoustic shadow zones in some regions of the acoustic field. By analyzing the autoproducts near the transition from well-ensonified region to shadow zone, the potentially detrimental effects of diffraction on the autoproducts’ mimicry of out-of-band acoustic fields can be analyzed and quantified. [Sponsored by ONR and NSF.] The frequency-difference and frequency-sum autoproducts are quadratic products of nonzero-bandwidth frequency-domain acoustic fields at different frequencies but the same spatial location. The autoproducts have been shown to mimic genuine lower- or higher-frequency, out-of-band, acoustic fields within some limitations (Worthmann and Dowling, 2017, JASA 141, 4579–4590). Previous analysis of the autoproducts considered only spatial regions of the environment that were well-ensonified by the in-band acoustic field, which itself is well-described by the ray-approximation. In this presentation, the necessity of this well-ensonified restriction is analyzed by comparing autoproduct fields with their out-of-band analogues in and near acoustic shadow zones created by refraction. The results presented are derived from exact or asymptotic solutions of the Helmholtz equation. The propagation environment chosen for this study is a horizontal, range-independent, stratified, unbounded, truncated-n 2-parabolic waveguide,...

Measurements of the acoustic-field autoproducts

The frequency-difference and frequency-sum autoproducts are quadratic products of acoustic fields at different frequencies extracted from a frequency-domain acoustic field with nonzero bandwidth. In well-ensonified regions of ray-path environments, the autoproducts may—in theory—mimic genuine acoustic fields at frequencies below and above the original field’s bandwidth (Worthmann and Dowling, 2017, JASA 141, 4579-4590). For example, in a Lloyd’s mirror environment, the autoproducts successfully mimic genuine out-of-band acoustic fields except near the surface or the source. In this presentation, results from a water tank experiment are shown that confirm predictions from theory. A 40- to 110-kHz pulse signal was broadcast from a source 20 cm below the surface to a hydrophone positioned at three different ranges between 20 and 50 cm and at depths from 0 to 40 cm. The measured frequency-difference autoproduct fields have cross correlations of greater than 90% with genuine acoustic fields between 0 and 60 kHz. Similarly, the measured frequency-sum autoproduct fields have cross correlations of greater than 90% with genuine acoustic fields between 110 and 190 kHz. Furthermore, the experimentally measured autoproducts correlate well with theoretically predicted autoproducts. Thus, these results serve to confirm the theory. [Sponsored by ONR and NSF.] The frequency-difference and frequency-sum autoproducts are quadratic products of acoustic fields at different frequencies extracted from a frequency-domain acoustic field with nonzero bandwidth. In well-ensonified regions of ray-path environments, the autoproducts may—in theory—mimic genuine acoustic fields at frequencies below and above the original field’s bandwidth (Worthmann and Dowling, 2017, JASA 141, 4579-4590). For example, in a Lloyd’s mirror environment, the autoproducts successfully mimic genuine out-of-band acoustic fields except near the surface or the source. In this presentation, results from a water tank experiment are shown that confirm predictions from theory. A 40- to 110-kHz pulse signal was broadcast from a source 20 cm below the surface to a hydrophone positioned at three different ranges between 20 and 50 cm and at depths from 0 to 40 cm. The measured frequency-difference autoproduct fields have cross correlations of greater than 90% with genuine acoustic fields between 0 and 60 kH...

The effects of diffraction on the frequency difference and frequency sum autoproducts

Previously, a remote sensing technique termed frequency difference matched field processing was developed for source localization in the shallow ocean (Worthmann et al., 2015, 138, 3549-3562). In this technique, field measurements at the in-band frequency are shifted down (or up) in frequency through the use of the bandwidth-averaged frequency-difference (or frequency-sum) autoproduct, a nonlinear construction made from field amplitudes and averaged over the available signal bandwidth. These bandwidth-averaged autoproducts may have phase structure similar to genuine acoustic fields at out-of-band frequencies when the original acoustic field is well-described by a sum of ray-path contributions. While ray theory may be a useful field description in many situations, it does not include diffraction. In this presentation, the effects of acoustic diffraction on the autoproduct are analyzed in an environment where diffraction varies in importance depending on the spatial location. Specifically, the behavior of t...

Target localization in a reverberant shallow ocean waveguide with environmental uncertainty using a nonlinear frequency-difference signal processing technique

Model-based signal processing for active sonar localization is typically infeasible due to insufficient knowledge of the acoustic environment. Additionally, in a shallow ocean environment, surface or bottom roughness create diffuse reverberation that can often obscure a desired target echo. Recently, a nonlinear signal processing technique was developed for passive acoustic source localization (Worthmann, et al., 2015) that is applicable to high frequency sources in uncertain shallow ocean environments. This technique exploits a nonlinear field product (the autoproduct) and uses in-band hydrophone array measurements to determine field information in a lower, out-of-band, frequency regime where environmental uncertainties are less detrimental. When extended to monostatic active sonar with a vertical array, this technique allows a model-based signal processing algorithm to combat the detrimental effects of reverberation. The nonlinear signal processing algorithm is presented, along with simulations in a 5-k...