A Bayesian method to estimate the depth and the range of phonating sperm whales using a single hydrophone
Summary (3 min read)
Introduction
- Submitted on 7 Mar 2013 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not.
- A Bayesian method to estimate the depth and the range of phonating sperm whales using a single hydrophone.
- Journal of the Acoustical Society of America, Acoustical Society of America, 2007, Vol. 121, pp. 1519-1528. pp. 1519-1528. ISSN 0001-4966 Open Archive Toulouse Archive Ouverte is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.
A Bayesian method to estimate the depth and the range of phonating sperm whales using a single hydrophone
- Christophe Laplanchea Laboratoire Images, Signaux et Systèmes Intelligents, Groupe Ingénierie des Signaux Neuro-Sensoriels, Université Paris 12, Créteil, France Some bioacousticians have used a single hydrophone to calculate the depth/range of phonating diving animals.
- The author’s tests using synthetic data show that the accurate estimation of the depth/range of sperm whales is possible using a single hydrophone and without using any seafloor reflections.
- Therefore, if the unidimensional array is vertical, then the circle is horizontal, and its depth and radius give the depth and the horizontal range of the sound source.
- One can seldom clearly detect the seafloor echoes of clicks emitted by sperm whale using a hydrophone close to the sea surface towed by a research vessel.
- The Bayesian approach has already proven to be efficient to locate sound sources using TOADs Spiesberger, 2005 .
A. Trajectory model
- First, one would need a representation of the underwater trajectory of the whale using a mathematical model.
- Let t A be the time when the sperm whale flukes-up and starts diving, t B the time when the whale starts clicking, t C the time when the whale stops clicking, and t D the time when the whale resurfaces.
- One can then define the trajectory T using the depth, range, and heading of the whale.
B. Prior information
- This latter definition of T uses 3n+5 parameters, that is to say redundant information.
- Indeed, the coordinates of the last summit E n+1 can be calculated given the coordinates of the first summit E 1 and using the values of speeds and change of heading in the n segments.
- Sperm whales usually keep a constant vertical speed while descending to reach their prey and while ascending to reach the sea surface Miller et al., 2004a .
- Relative to the research vessel, between the fluking and the resurfacing points.
- Such uncertainties are modeled in the following section using random variables.
E. Probability distribution of the prior
- The author will give a more accurate description of the prior distributions appearing in Eq. 13 .
- By choosing such a prior, the author indicates that the underwater movement of the whale is not erratic, and that it is likely that the whale tends to swim in a given direction.
- The probability density functions have a maximum at the most likely prior value of the parameters, and its width illustrates the confidence the authors grant to this most likely prior value.
- One could choose for instance gamma probability distributions.
- For practical reasons, the author has chosen truncated normal distributions.
G. MCMC algorithm
- One can use a Markov Chain Monte Carlo MCMC algorithm to draw samples of the posterior.
- One can use the Metropolis-Hastings algorithm Robert and Casella, 2004 to draw such samples.
- Calculate the acceptance ratio of this sample to determine if the new sample Instead of drawing a whole new trajectory at each iteration i, draw the summits one by one.
- In practice, the second method requires a lower total amount of samples, as it requires less than I /C samples per subchain to lead to a correct estimate T̂. The author has used the subchain method.
H. Data set
- The author has run simulations using the free software SBPLASH implemented in MATLAB.
- The efficiency of the algorithm is illustrated using synthetic data.
- The depth, range, vertical speed, and horizontal speed of the whale when following this trajectory are given in Figs. 3–6, respectively.
- The initial value of the trajectory is in the author’s simulations the rectilinear, constant speed trajectory linking the prior locations of the points E 1 and E n+1 Figs.
- These parameters here are constants which are empirically chosen.
A. Convergence
- The algorithm generates trajectories with values close to the data after I0=100 iterations.
- The acceptance orithm left, circles of the depth z of the sperm whale throughout the dive.
- Draws of the first s=1 and last s=n+1 summits are more often accepted than the others 2 s n , given the different constraints and priors they are bound to.
B. Depth, range, and speeds
- The vertical and horizontal speeds of the whale are estimated using Eq. 19 .
- The estimate of the depth and the range of the whale are calculated using these values.
- Results of vz, vr, z, and r are plotted plus/minus twice their standard deviation.
IV. DISCUSSION AND CONCLUSION
- The algorithm correctly estimates the depth and the range of the whale throughout the dive Figs. 3 and 4 .
- The author is, however, confident regarding the choice of I1 for the given data set.
- The parameters used in the probability distributions of the priors have been fixed and empirically chosen.
- As stated regarding the standard deviation of the prior speed, an optimal value of could be estimated while sampling and estimating the trajectory parameters.
- Not requiring seafloor echoes, the method could be used to estimate the depth and the range of foraging sperm whales using a single hydrophone in any location no matter what the depth, the relief, or the constitution of the seafloor might be.
Did you find this useful? Give us your feedback
Citations
25 citations
17 citations
Cites methods from "A Bayesian method to estimate the d..."
...Markov-chain Monte-Carlo localization algorithms, such as that described by Laplanche (2007), or state-space algorithms, such as those employed by Jonsen et al. (2003, 2005) or Tremblay et al. (2009) may be able to take advantage of these additional data, thus such algorithms should be considered…...
[...]
11 citations
8 citations
Cites background or methods from "A Bayesian method to estimate the d..."
...(2012) The Journal of the Acoustical Society of America, vol. 132 (n°5). pp. 3225-3233....
[...]
...Visual methods use photo-identification to differentiate individuals, map their surface movements, and catalogue their clustering preferences (Whitehead, 2003, pp. 206–285)....
[...]
...Electronic mail: laplanche@gmail.com procedure (Davis and Pitre, 1995; Laplanche, 2007; Tiemann et al., 2006)....
[...]
7 citations
References
31 citations
"A Bayesian method to estimate the d..." refers background or methods in this paper
...It does not seem possible, without making stronger and speculative hy- potheses regarding the behavior of the whale Laplanche et al., 2005 , or without using additional information Tiemann et al., 2006 , to reconstruct a three-dimensional trajectory using a single hydrophone....
[...]
...One noteworthy passive acoustic localization technique requires a single hydrophone see for instance Thode et al. 2002 or Laplanche et al. 2005 ....
[...]
...In low sea state conditions, using a hydrophone close to the sea surface, one can however clearly detect surface echoes during the whole dive see for instance Thode 2004 or Laplanche et al. 2005 ....
[...]
23 citations
"A Bayesian method to estimate the d..." refers methods in this paper
...The Bayesian approach has already proven to be efficient to locate sound sources using TOADs Spiesberger, 2005 ....
[...]
...In this case the hyperboloid sheets defined by the TOADs intersect into a circle....
[...]
...By measuring the TOADs of the echoes later referred to as echo delays relative to the nonreflected transmitted signal, one can calculate the depth and the range of the sound source....
[...]
...By repeating this localization process using different TOADs, one can, using the required amount of hydrophones Spiesberger, 2001 , geometrically or ana- a Electronic mail: laplanche@gmail.com lytically compute the intersection of the hyperboloid sheets and therefore be able to more accurately identify the location of the source....
[...]