Abstract
The cascade of blind deconvolution and array invariant has been successful to localize and track a surface ship radiating random waveforms, using a 56-m long vertical array in 100-m deep shallow water. In this paper, it is shown that a 60-m long, bottom-mounted horizontal array can be utilized for blind deconvolution to extract the Green's functions from the same ship (100-800 Hz), in conjunction with the array invariant for source-range estimation. The additional information obtained with a horizontal array is the source bearing (azimuth angle, ϕ) from the well-resolved ray angle identified for blind deconvolution to extract the phase component of the unknown source waveforms. The overall tracking performance shows good agreement with global positioning system (GPS) measurements to less than 11% in terms of standard deviation of relative range error at ranges of 0.3-1.5 km, except when the ship is around the broadside (e.g., ) of the horizontal array. On the other hand, the source bearings are in excellent agreement with the GPS data except near the endfire due to the lower angular resolution. The potential for simultaneous localization of multiple ships is also discussed.
Highlights
The array invariant method, a robust approach to source-range estimation, is based on the dispersion characteristics of broadband signals in ideal waveguides.[1]
The overall tracking performance shows good agreement with global positioning system (GPS) measurements to less than 11% in terms of standard deviation of relative range error at ranges of 0.3–1.5 km, except when the ship is around the broadside (e.g., j/j < 25) of the horizontal array
Simultaneous localization of multiple ships was investigated for a simple two-ship scenario where the two ships were well separated in the azimuth angle with similar power
Summary
The array invariant method, a robust approach to source-range estimation, is based on the dispersion characteristics of broadband signals in ideal waveguides.[1] It involves conventional plane-wave beamforming, utilizing multiple arrivals (i.e., eigenrays) separated in beam angle and travel time, referred to as “beam-time migration,” which contains the source-range information. The array invariant (v) in the beam-time domain corresponds to the waveguide invariant (b) in the phase- versus group-velocity (or slowness) domain. The array invariant derived from ideal waveguides is applicable to general waveguides by incorporating b, which is fully supported by the waveguide invariant physics.[2] For many surface/bottom interacting environments, b is approximately unity for small grazing angles (e.g., h < 20), similar to the ideal waveguides.[3]. The array invariant has been extended to a mildly range-dependent environment with a sloping bottom using an iterative approach.[4]
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