Modified Pairwise Spectrogram Processing for Localization of Unknown Broadband Sources

Pairwise waveform (PWW) and pairwise spectrogram (PWS) processors for 3-D localization of unknown, continuous-wave, broadband sources in shallow water have been developed and implemented. The processors use sparse hydrophone arrays and are applicable to multiple sources, which can be unknown, continuous wave, and broadband. Here, we give new formulas for these two processors that significantly reduce computational requirements, making localization at longer ranges and higher frequencies feasible. The new processors are motivated by a demonstration that an incoherent version of the PWW (IPWW) processor (in which processor outputs at different frequencies are averaged after being processed independently) is the Bartlett processor without autoreceiver terms. The new PWW processor is mathematically equivalent to the original version, though much faster. The new PWS processor is mathematically equivalent to the original version only in the limit of infinite spectrogram window length, but for window lengths that are optimal with the old PWS processor, the new PWS processor gives essentially the same results with much greater speed. Simulations comparing PWS processing to Bartlett, PWW processing, and a time difference of arrival method indicate that the main advantage of PWS processing is for multiple sources in uncertain, high-noise environments at ranges many wavelengths long. With PWS, increased robustness with respect to mismatch is obtained at the expense of reduced resolution; varying PWS processor parameters (such as the size of windows used to create spectrograms) optimizes this tradeoff. This work is motivated by the problem of localizing singing humpback whales, and simulation results use whale sources.