Jonathan L. Odom

Exploiting array motion for augmentation of co-prime arrays

In this paper, we combine concepts from synthetic aperture processing and non-uniform linear array theory. Our objective is to use array motion to synthesize an array that can achieve the performance of a filled uniform linear array (ULA), but with fewer sensors than required for spatial Nyquist sampling. The class of physical arrays we use for synthesis are co-prime arrays constructed by nesting under-sampled ULAs with co-prime inter-element spacings. In particular, we use array motion to fill in missing co-array spacings. For co-prime M and N, a physical array of M + 2N - 1 sensors plus modest array motion is used to achieve a filled co-array corresponding to approximately 2MN elements. This facilitates spatial spectral estimation via non-adaptive beamforming over an extended aperture with low sidelobe performance.

Passive Towed Array Shape Estimation Using Heading and Acoustic Data

This paper addresses the problem of array shape estimation for passive towed sonar systems during platform maneuvers. Directional noise fields due to distant shipping lanes can be exploited as sources of opportunity for online array shape calibration. In this paper, a nonparametric noise field model is used to form field directionality maps for time-varying array shapes to exploit point and spatially spread sources. This formulation requires neither the number nor location of sources in the field to be known or estimated. Using acoustic data, a maximum-likelihood array shape estimate is derived where the shape is modeled as a polynomial in heading. Additionally, a method for fusing the shape estimate with heading sensor data is introduced. Heading sensors may permanently fail or suffer from high levels of noise during turns; thus acoustic data can be used to compensate for malfunctioning heading sensors during turns. The combined estimate is filtered using a dynamical model that is valid for sharp turns and accounts for motion of the array perpendicular to tow heading. Multisource simulations are used to demonstrate the performance of the acoustic-based estimate and robustness of the combined estimate.

Maximum-likelihood spatial spectrum estimation in dynamic environments with a short maneuverable array

This work concerns the development of field directionality mapping algorithms for short acoustic arrays on mobile maneuverable platforms that avoid the left/right ambiguities and endfire resolution degradation common to longer non-maneuverable line arrays. In this paper, it is shown that short maneuverable arrays can achieve a high fraction of usable bearing space for target detection in interference-dominated scenarios, despite their lower array gain against diffuse background noise. Two narrowband techniques are presented which use the expectation-maximization maximum likelihood algorithm under different models of the time-varying field directionality. The first, derivative based maximum likelihood, uses a deterministic model while the second, recursive Bayes maximum likelihood, uses a stochastic model for the time-varying spatial spectrum. In addition, a broadband extension is introduced that incorporates temporal spectral knowledge to suppress ambiguities when the average sensor array spacing is greater than a half-wavelength. Dynamic multi-source simulations demonstrate the ability of a short, maneuvering array to reduce array ambiguities and spatial grating lobes in an interference dominated environment. Monte Carlo evaluation of receiver operating characteristics is used to evaluate the improvement in source detection achieved by the proposed methods versus conventional broadband beamforming.

Heading and hydrophone data fusion for towed array shape estimation

This paper addresses the problem of towed array shape estimation for passive, horizontal sonar arrays. Beamforming and localization techniques significantly degrade when an assumed linear array bends due to tow platform maneuvers or ocean currents. In this paper, heading sensors along the array and acoustic hydrophone data are jointly used to estimate the shape of the array. Previously, heading data have been filtered using a dynamical motion model to reduce noise during turns. In recent work, a time-varying noise field directionality estimate that incorporates a dynamical model for the acoustic field provides a second, albeit biased, estimate of the array shape. In this paper, these two estimates are combined via adaptive weights to obtain improved shape estimates during maneuvers. A multi-source simulation is used to demonstrate the robustness of the combined array shape estimate when compared to the separate heading or acoustic sensor based techniques.

Broadband field directionality mapping with spatially-aliased arrays

This paper addresses the problem of broadband spatial spectrum estimation using multiple spatially-aliased arrays. Unlike previous approaches using sparse arrays, the signals here are assumed to be uncorrelated between multiple arrays which, in fact, may be receiving the same source during different time intervals. This paper presents an approach which jointly exploits spatial-orientation and broadband temporal diversity in order to estimate the spatial spectrum even when the inter-element spacing within each array is greater than a half-wavelength. A dynamical model for the spatial spectrum is employed to formulate a maximum likelihood estimate, which is computed via a recursive version of the expectation-maximization algorithm using data from different arrays. Simulation results are presented to demonstrate the ability of the method to suppress spatial grating lobes and increase low SNR target detection in an interference dominated environment.

Time-varying array shape estimation by mapping acoustic field directionality

This paper introduces a towed-array shape estimation technique that exploits the directional structure of the time-varying acoustic field. Unlike conventional array shape estimation methods that use discrete sources of opportunity, the proposed approach does not assume knowledge of the number of sources in the field or their estimated directions. Instead, the entire time-varying field directionality map is used. Additionally, maneuverability of the array is exploited to improve endfire resolution and left/right discrimination for a nominally linear array. The algorithm forms an approximate joint maximum-likelihood estimate of time-varying field directionality and array shape using an iterative Expectation-Maximization (EM) approach. Simulations are given to evaluate the array shape estimation error during a maneuver. In a simulated multi-source scenario, the proposed method is shown to be more robust than methods that rely on direction-of-arrival estimation when the full field around the array is considered.

Ocean acoustic waveguide invariant parameter estimation using tonal noise sources

The abundance of shipping noise sources in ocean littoral zones provides a great opportunity to estimate ocean environmental parameters. The waveguide invariant parameter β, defined as the ratio of inverse group and phase velocities between modes, has been used in a variety of applications including ranging of passive sources. Previous work utilizing the waveguide invariant in passive sonar has relied on processing the time-frequency intensity striations of broadband sources. In this paper, the reception of strong tonal components from transiting commercial ships of known location (e.g., from AIS data) are used for estimating β over the source-receiver path. A maximum likelihood estimate of β is derived by relating the fading characteristics of different tonal components over range. The method is verified on simulated data using a Pekeris waveguide model.

Time-varying spatial spectrum estimation using a maneuverable sonar array

This paper addresses the problem of spatial spectrum estimation in dynamic environments with a maneuverable sensor array. Estimation of the time-varying acoustic field directionality is of fundamental importance in passive sonar. In this paper, mobility of the array is treated as a feature allowing for left-right disambiguation as well as improved resolution toward endfire. Two new methods for on-line spatial spectrum estimation are presented: (1) recursive maximum likelihood estimation using the EM algorithm and (2) time-varying spatial spectrum estimation via derivative-based updating. A multi-source simulation is used to compare the proposed algorithms in terms of their ability to suppress ambiguous array backlobes. A broadband method is presented utilizing knowledge of the source temporal spectrum. Detection performance of weak high-bearing rate sources in interference-dominated environments is evaluated for a flat spectrum. [This work was supported by ONR under grant N000140810947.]

Microphone array beamforming with near‐field correlated sources.

As the price of omnidirectional microphone arrays has fallen, new applications have emerged for large room audio capture. Further, large room acoustics use loudspeakers, which create correlated sources and severely limit the use of optimum beamformers. Most sources are in the near field due to the large wavelength of speech. Widrow and Kailath’s work on correlation in sonar and radar assumed far field, but it cannot be directly applied to near‐field acoustics. A new beamforming method has been devel‐oped, which incorporates near field and correlation. The source bearings are estimated and an uncorrelated model is formed. A better DOA estimator was developed for the near‐field correlated case limited by the width of the mainlobe. The new beamformer is able to null strong, perfectly and nearly perfectly correlated signals using the uncorrelated model and minimum variance distortionless response beamforming.

Shallow-water waveguide invariant parameter estimation and source ranging using narrowband signals

This paper concerns waveguide invariant parameter estimation using narrowband underwater acoustic signals from multiple sources at known range, or alternatively, the ranges of multiple sources assuming known waveguide invariant parameters. Previously, the waveguide invariant has been applied to estimate the range or bottom properties from intensity striations observed from a single broadband signal. The difficulty in separating striations from multiple broadband sources, however, motivates the use of narrowband components, which generally have higher signal-to-noise ratios and are non-overlapping in frequency. In this paper, intensity fluctuations of narrowband components are shown to be related across frequency by a time-warping (i.e., stretching or contracting) of the intensity profile, assuming constant radial source velocity and the waveguide invariant β. A maximum likelihood estimator for the range with β known or for the invariant parameter β with known source range is derived, as well as Cramer-Rao...