Probability distributions for locations of calling animals, receivers, sound speeds, winds, and data from travel time differences

Abstract

A new nonlinear sequential Monte Carlo technique is used to estimate posterior probability distributions for the location of a calling animal, the locations of acoustic receivers, sound speeds, winds, and the differences in sonic travel time between pairs of receivers from measurements of those differences, while adopting realistic prior distributions of the variables. Other algorithms in the literature appear to be too inefficient to yield distributions for this large number of variables (up to 41) without recourse to a linear approximation. The new technique overcomes the computational inefficiency of other algorithms because it does not sequentially propagate the joint probability distribution of the variables between adjacent data. Instead, the lower and upper bounds of the distributions are propagated. The technique is applied to commonly encountered problems that were previously intractable such as estimating how accurately sound speed and poorly known initial locations of receivers can be estimated from the differences in sonic travel time from calling animals, while explicitly modeling distributions of all the variables in the problem. In both cases, the new technique yields one or two orders of magnitude improvements compared with initial uncertainties. A new nonlinear sequential Monte Carlo technique is used to estimate posterior probability distributions for the location of a calling animal, the locations of acoustic receivers, sound speeds, winds, and the differences in sonic travel time between pairs of receivers from measurements of those differences, while adopting realistic prior distributions of the variables. Other algorithms in the literature appear to be too inefficient to yield distributions for this large number of variables ͑up to 41͒ without recourse to a linear approximation. The new technique overcomes the computational inefficiency of other algorithms because it does not sequentially propagate the joint probability distribution of the variables between adjacent data. Instead, the lower and upper bounds of the distributions are propagated. The technique is applied to commonly encountered problems that were previously intractable such as estimating how accurately sound speed and poorly known initial locations of receivers can be estimated from the differences in sonic travel time from calling animals, while explicitly modeling distributions of all the variables in the problem. In both cases, the new technique yields one or two orders of magnitude improvements compared with initial uncertainties. The technique is suitable for accurately estimating receiver locations from animal calls.

Locating calling mammals with signal times amongst shadows and black holes in two-dimensional models

“…We show how to obtain confidence intervals from a 2D model for TDOA measured with these errors except clocks are synchronized for simplicity. Extremely reliable confidence intervals are computed with a non-Bayesian method called Sequential Bound Estimation (SBE) 24 . It solves the non-linear equations for location without approximation.…”

“…Modeling locations in 2D is ubiquitous. Contemporary examples include locating calling mammals in the ocean 5,14,24,29 , sounds in a room via robots 6 , ships 26 , cell phones 13 , lightning 11 , wildlife radio transmitters 9 , aircraft radio emissions 10 , bistatic sonars 3 , and theoretical developments 7 . These models derive locations by translating TDOA or bistatic signal times to difference or sum of distance assuming signal speed is constant 3, [5][6][7][9][10][11]13,14,26 , the overwhelmingly-common case, or are constrained to a finite interval 24,29 , e.g.…”

Extending bioacoustic monitoring of birds aloft through flight call localization with a three‐dimensional microphone array

“…Generally, these local meteorological measurements will not be available, motivating retrieval techniques that can account for these effects. Work by Spiesberger (1999Spiesberger ( , 2005 demonstrates two methods that can solve for atmospheric conditions as well as call sources. Another addition would be the use of acoustic self-surveys as in Collier et al (2010).…”

“…Acoustic localization (sometimes referred to as "triangulation") is the process of identifying the source location of sounds using recordings from multiple time-synchronized microphones (Blumstein et al, 2011). Bioacoustic localization of calling animals has been developed theoretically (e.g., Magyar, Schleidt, & Miller, 1978;Spiesberger, 2001Spiesberger, , 2005Spiesberger & Fristrup, 1990) and demonstrated in laboratory and field trials (e.g., Gaudette & Simmons, 2014). While the utility of these techniques for wildlife monitoring has been illustrated, it is often the case that applications are limited in spatial extent or dimension.…”

Reconstructing the Acoustic Signal of a Sound Source: What Did the Bat Say?

“…These differences are sufficient to determine the position of the source, given at least four microphones in general positions. [1] and [2] describe the basic technique and ways to improve it. Bat emission directivity can be computed from knowledge of the actual shape of the bat's head, using acoustic simulation techniques [7], [8].…”