Nicole E. Collison

Regularized matched-mode processing for source localization.

This paper develops a new approach to matched-mode processing (MMP) for ocean acoustic source localization. MMP consists of decomposing far-field acoustic data measured at an array of sensors to obtain the excitations of the propagating modes, then matching these with modeled replica excitations computed for a grid of possible source locations. However, modal decomposition can be ill-posed and unstable if the sensor array does not provide an adequate spatial sampling of the acoustic field (i.e., the problem is underdetermined). For such cases, standard decomposition methods yield minimum-norm solutions that are biased towards zero. Although these methods provide a mathematical solution (i.e., a stable solution that fits the data), they may not represent the most physically meaningful solution. The new approach of regularized matched-mode processing (RMMP) carries out an independent modal decomposition prior to comparison with the replica excitations for each grid point, using the replica itself as the a priori estimate in a regularized inversion. For grid points at or near the source location, this should provide a more physically meaningful decomposition; at other points, the procedure provides a stable inversion. In this paper, RMMP is compared to standard MMP and matched-field processing for a series of realistic synthetic test cases, including a variety of noise levels and sensor array configurations, as well as the effects of environmental mismatch.

Experimental validation of regularized array element localization

This paper examines and validates regularized inversion for array element localization (AEL) by quantitative comparison of inversion results to direct measurements of receiver positions for a full-scale AEL survey. Regularized AEL treats both receiver and source positions as unknown parameters in a ray-based inversion; prior information on source/receiver positions, inter-receiver spacing in depth, and/or a smooth array shape can be included, subject to statistically fitting the acoustic data. Uncertainties in the recovered receiver positions are estimated via Monte Carlo appraisal. To study this approach, a specially stabilized, two-dimensional receiver array and a series of impulsive sources (imploding glass light bulbs) were deployed from shore-fast (motionless) Arctic sea ice. Sources and recordings were not synchronized in time, so AEL inversions are based on relative arrival times. Receiver positions were measured to an uncertainty of ∼5 cm in each dimension [9 cm in three dimensions (3D)] using nonacoustic (optical) methods. Average AEL errors (difference between measured receiver positions and inversion results) of 13 cm in depth, 27 cm in the horizontal, and 30 cm in 3D, as well as good agreement between the measured errors and estimated AEL uncertainties validate the regularized approach and provide benchmarks for acoustic AEL. Receiver-position errors are quantitatively investigated as a function of the number of sources, source-position errors, and different regularizations.

Acoustic tracking of a freely drifting sonobuoy field

This paper develops an acoustic inversion algorithm to track a field of freely drifting sonobuoys using travel-time measurements from a series of nonsimultaneous impulsive sources deployed around the field. In this scenario, the time interval between sources can be sufficiently long that significant independent movement of the individual sonobuoys occurs. In addition, the source transmission instants are unknown, and the source positions and initial sonobuoy positions are known only approximately. The formulation developed here solves for the track of each sonobuoy (parametrized by the sonobuoy positions at the time of each source transmission), allowing arbitrary, independent sonobuoy motion between transmissions, as well as for the source positions and transmission instants. This leads to a strongly underdetermined inverse problem. However, regularized inversion provides meaningful solutions by incorporating a priori information consisting of prior estimates (with uncertainties) for the source positions and initial sonobuoy positions, and a physical model for preferred sonobuoy motion. Several models for sonobuoy motion are evaluated, with the best results obtained by minimizing the second spatial derivative of the tracks to obtain the minimum-curvature or smoothest track, subject to fitting the acoustic data to a statistically appropriate level.

Regularized Inversion for Towed-Array Shape Estimation

This chapter describes a new approach to the inverse problem of estimating the shape of a ship-towed hydrophone array using near-field acoustic measurements. The data consist of the relative travel times of arrivals along direct and reflected paths from sources deployed by two consort ships maintaining station with the moving tow ship (the “dual-shot method”). Previous inversion algorithms typically apply least-squares methods based on simplifying assumptions, such as straight-line propagation and exact knowledge of the source positions. Here, a regularized inversion is developed based on ray theory, with the source positions included as unknown parameters subject to a priori estimates and uncertainties. In addition, a minimum-structure array shape is determined by minimizing the three-dimensional curvature subject to fitting the data to a statistically meaningful level, thereby reducing spurious fluctuations (roughness) in the solution. Finally, the effect of the survey geometry is investigated by defining a mean sensor-position error measure based on the a posteriori uncertainty of the inversion. The optimal source configuration is determined by minimizing this error with respect to the source positions using an efficient hybrid optimization algorithm. The inversion and optimization procedures are illustrated using realistic synthetic examples.

Regularized matched‐mode processing

Far‐field acoustic propagation can be modeled as a discrete set of propagating normal modes. In this case, the measured fields can be decomposed into their modal components, providing the basis for matched‐mode processing (MMP). Modal decomposition is a discrete linear inverse problem that is inherently nonunique and can be unstable. Thus standard MMP generally requires the entire water column to be densely sampled (i.e., more sensors than modes) with relatively low noise. However, the inversion can be stabilized using the method of regularization to include a priori information based on the replica excitations at each trial source location of the search grid. The regularized approach gives an optimal match for each grid point for both dense and sparse arrays and noisy data. Regularized matched‐mode processing (RMMP), MMP, and matched‐field processing (MFP) are compared for a number of different array configurations, including dense and sparse arrays that span all or part of the water column. The comparis...

Localizing a large‐dimensional field of sonobuoys

For target localization, multistatic sonar systems require an adequate knowledge of both the source and receiver positions. In this paper, we use a regularized acoustic inversion method on measured direct‐arrival times from several impulsive sources to track a freely drifting sonobuoy field. The shallow‐water experiment involved 11 sonobuoys within a 6×8 km field, with 6 sources over approximately 70 min. Regularization allows prior information to be built into the inversion, which in this case consists of estimates (with associated uncertainties) of the source and initial sonobuoy drop positions determined from the GPS position of the aircraft at the instant of drop, as well as a model for smooth sonobuoy tracks. Closely spaced sonobuoys move along similar tracks, although there is considerable movement in different directions over the entire field (260–700 m). Positioning uncertainties are estimated using a Monte Carlo appraisal procedure to be approximately 100 m (absolute) and 65 m (relative). Submitt...

Regularized matched‐mode localization with environmental mismatch

This paper considers a new approach to matched‐mode processing (MMP) for source localization. The MMP consists of decomposing far‐field acoustic data to obtain the modal excitations, then matching these with modeled replica excitations. A potential advantage of MMP over matched‐field processing (MFP) is that subsets of the complete mode set can be considered. For example, if geoacoustic properties are poorly known, the matching can be applied only to low‐order modes that interact minimally with the seabed. However, modal decomposition can be ill posed and unstable if the sensor array does not adequately sample the acoustic field. For such cases, standard decomposition methods yield minimum‐norm solutions that are biased towards zero. Although these methods provide mathematical solutions (stable solutions that fit the data), they may not represent physically meaningful solutions. The new approach of regularized MMP (RMMP) carries out an independent decomposition prior to comparison with the replica excitat...

Regularized modal decomposition for matched‐mode processing

Long‐range acoustic propagation in the ocean is often well modeled by a discrete set of propagating normal modes. When this is the case, the acoustic field measured at an array of sensors can be decomposed into its modal components providing the basis for matched‐mode processing (MMP) methods. Modal decomposition represents a discrete linear inverse problem. For vertical arrays which do not adequately sample the water column or for horizontal arrays, the inverse problem is ill‐conditioned and modal decomposition can lead to poor results for noisy measurements. Regularization is a technique for stabilizing inverse problems based on trading off minimizing the data residuals (misfit) with minimizing some function of the solution. In the case of modal decomposition for MMP, an appropriate choice for the regularizing function is the deviation of the modal excitations of the solution from those of the replica field at each trial source location. This results in the best possible match between the measured and r...