Signals as departures from random walks.

We study statistics of data ranking, focusing on the recently discovered distribution-invariant discrete eigenvalue spectrum for an independent and identically distributed (IID) process. We employ a variant of a cumulative distribution function in rank and time that maps the sampling variability for an IID process onto a set of random walks. This mapping admits confidence bounds on whether the residual (data with signal removed) arises solely from IID sampling variability.

Extraction of unknown signals in arbitrary noise.

We devise a general method to extract weak signals of unknown form, buried in noise of arbitrary distribution. Central to it is signal-noise decomposition in rank and time: only stationary white noise generates data with a jointly uniform rank-time probability distribution, U(1,N)×U(1,N), for N points in a data sequence. We show that rank, averaged across jointly indexed series of noisy data, tracks the underlying weak signal via a simple relation, for all noise distributions.

Detection of unknown signals in arbitrary noise.

We devise a simple method for detecting signals of unknown form buried in any noise, including heavy tailed. The method centers on signal-noise decomposition in rank and time: Only stationary white noise generates data with a jointly uniform rank-time probability distribution, U(1,N)×U(1,N), for N data points in a time series. Signals of any kind distort this uniformity.

Swim track kinematics and calling behavior attributed to Bryde's whales on the Navy's Pacific Missile Range Facility.

Time difference of arrival methods for acoustically localizing multiple marine mammals have been applied to recorded data from the Navy's Pacific Missile Range Facility in order to localize and track calls attributed to Bryde's whales. Data were recorded during the months of August-October 2014, and 17 individual tracks were identified. Call characteristics were compared to other Bryde's whale vocalizations from the Pacific Ocean, and locations of the recorded signals were compared to published visual sightings of Bryde's whales in the Hawaiian archipelago.

Automated acoustic localization and call association for vocalizing humpback whales on the Navy's Pacific Missile Range Facility.

Time difference of arrival (TDOA) methods for acoustically localizing multiple marine mammals have been applied to recorded data from the Navy's Pacific Missile Range Facility in order to localize and track humpback whales. Modifications to established methods were necessary in order to simultaneously track multiple animals on the range faster than real-time and in a fully automated way, while minimizing the number of incorrect localizations. The resulting algorithms were run with no human intervention at computational speeds faster than the data recording speed on over forty days of acoustic recordings from the range, spanning multiple years.

A generalized power-law detection algorithm for humpback whale vocalizations.

Conventional detection of humpback vocalizations is often based on frequency summation of band-limited spectrograms under the assumption that energy (square of the Fourier amplitude) is the appropriate metric. Power-law detectors allow for a higher power of the Fourier amplitude, appropriate when the signal occupies a limited but unknown subset of these frequencies. Shipping noise is non-stationary and colored and problematic for many marine mammal detection algorithms.