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parameters. The results showed that, for slowly varying
environments, all filters performed similarly. However, when abrupt changes such as a rapid transition to a different sedi- mentary rock formation occurred, the PF outperformed the KF variants. The trade-off for better track quality is the increased computational cost of the PF compared to the KF variants.
Sequential geoacoustic tracking was demonstrated on
25
Because the source parameters were also unknown, the state vector included the unknown source parameters (source depth, range, and speed) together with the geoacoustic parameters, effectively tracking the source in an unknown and changing environment. A constant velocity model was adopted in that problem. The algorithm was test- ed in a region with bathymetry ranging from 100 to 250 m and a range-dependent sedimentary layer given by the Bachman profile43 as shown in Fig. 10(a). It was conducted in May 1996, off the coast of San Diego, CA, near Point Loma. A 118 m long, 21-element VLA was deployed from R/P Flip at 216.5 m deep water north of Loma Canyon. The source was towed at 2.6 m/s at a depth of 55 m. The source was a comb signal composed of 13 frequencies from 49 to 388 Hz. A PF with 200 particles was able to track the moving source array and the environmental parameters that included array tilt, water depth, sediment thickness, sediment top and bot- tom sound speed values. The posterior PDFs for four of these parameters, shown in Fig. 10(b), are in agreement with the true values obtained from the Bachman database. Note that the PF allows the PDFs to be non-Gaussian as is the case for
SWellEx-96 data.
the sediment thickness and upper sound speed.
The ocean shelfbreak region is characterized by rapid change in bathymetry and large variations in geoacoustic parameters. The ocean sound speed can be evolving rapidly both temporally and spatially due to the interplay between deep and shallow water. The capabilities of sequential Bayesian geoacoustic and source tracking were also tested in the shelfbreak regions with strong spatial and temporal vari- ability44 using the data from the SW06 experiment. The PF was able to track the source and bottom parameters as well as the sound speed profile in terms of empirical orthogonal
functions. AT
References
1 S. M. Kay, Fundamentals of Statistical Signal Processing—Volume I: Estimation Theory (Prentice-Hall, Englewood Cliffs, NJ, 1993).
2 L. L. Scharf, Statistical Signal Processing: Detection, Estimation, and Time Series Analysis (Prentice Hall, Englewood Cliffs, NJ,
1993).
3 J. V. Candy, Signal Processing: The Model Based Approach
(McGraw-Hill, New York, 1985).
4 J. V. Candy, Model Based Signal Processing: Detection, Estimation,
and Time Series Analysis (Wiley, New York, 2005).
5 M. J. Hinich, “Maximum-likelihood signal processing for a ver-
tical array,” J. Acoust. Soc. Am. 54, 499–503 (1973).
6 H. P. Bucker, “Use of calculated sound fields and matched-field detection to locate sound sources in shallow water,” J. Acoust.
Soc. Am. 59, 368–373 (1976).
7 Special Issue of IEEE Journal of Oceanic Engineering on
 Detection and Estimation in Matched Field Processing, R. D. Doolittle, A. Tolstoy, and E. J. Sullivan, Eds. (Institute of Electrical and Electronic Engineers, New York, 1993).
8 A. M. Richardson and L. W. Nolte, “A posteriori probability source localization in an uncertain sound speed, deep ocean environment,” J. Acoust. Soc. Am. 89, 2280–2284 (1991).
9 E. Livingston and O. Diachok, “Estimation of average under-ice reflection amplitudes and phases using matched-field process- ing,” J. Acoust. Soc. Am. 86, 1909–1919 (1989).
10 M. D. Collins, W. A. Kuperman, and H. Schmidt, “Nonlinear inversion for ocean-bottom properties,” J. Acoust. Soc. Am. 92, 2770–2783 (1992).
11 P. Gerstoft, “Inversion of seismoacoustic data using genetic algo- rithms and a posteriori probability distributions,” J. Acoust. Soc. Am. 95, 770–782 (1994).
12 S. E. Dosso, “Quantifying uncertainty in geoacoustic inversion I. A fast Gibbs sampler approach,” J. Acoust. Soc. Am. 111, 129–142 (2002).
13 M. Siderius, P. L. Nielsen, and P. Gerstoft, “Range-dependent seabed characterization by inversion of acoustic data from a towed receiver array,” J. Acoust. Soc. Am. 112, 1523–1535 (2002).
14 N. R. Chapman, S. Chin-Bing, D. King, and R. B. Evans, “Benchmarking geoacoustic inversion methods for range-depend- ent waveguides,” IEEE J. Oceanic Eng. 28, 320–330 (2003).
15 R. A. Koch and D. P. Knobles, “Geoacoustic inversion with ships as sources,” J. Acoust. Soc. Am. 117, 626–637 (2005).
16 Y.-M. Jiang, N. R. Chapman, and M. Badiey, “Quantifying the uncertainty of geoacoustic parameter estimates for the New Jersey Shelf by inverting air gun data,” J. Acoust. Soc. Am. 121, 1879–1894 (2007).
17 J. V. Candy and E. J. Sullivan, “Ocean acoustic signal processing: A model-based approach,” J. Acoust. Soc. Am. 92, 3185–3201 (1992).
18 A. H. Jazwinski, Stochastic Processes and Filtering Theory. (Academic Press, New York, 1970).
19 E. A. Wan and R. van der Merve, “The unscented Kalman filter,” in S. Haykin, Kalman Filtering and Neural Networks. (John Wiley & Sons, New York, 2001).
20 B. Ristic, S. Arulampalam, and N. Gordon, Beyond the Kalman Filter: Particle Filters for Tracking Applications. (Artech House, Boston, 2004).
21 J. V. Candy and S. J. Godsill, “Bayesian space-time processing for acoustic array source estimation using a towed array,” J. Acoust. Soc. Am. 120, 3179 (2006).
22 J. V. Candy, “Particle filtering for signal enhancement in a noisy shallow ocean environment,” in OCEANS 2010, 1–6 (2010).
23 I. Zorych and Z.-H. Michalopoulou, “Particle filtering for dis-
persion curve tracking in ocean acoustics,” J. Acoust. Soc. Am.
124, EL45–EL50 (2008).
24 C. Yardim, P. Gerstoft, and W. S. Hodgkiss, “Tracking of geoa-
coustic parameters using Kalman and particle filters,” J. Acoust.
Soc. Am. 125, 746–760 (2009).
25 C. Yardim, P. Gerstoft, and W. S. Hodgkiss, “Geoacoustic and
source tracking using particle filtering: Experimental results,” J.
Acoust. Soc. Am. 128, 75–87 (2010).
26 R. Jain and Z.-H. Michalopoulou, “A particle filtering approach
for spatial arrival time tracking in ocean acoustics,” J. Acoust.
Soc. Am. 129, EL236–EL241 (2011).
27 C. Yardim, Z.-H. Michalopoulou, and P. Gerstoft, “An overview
of sequential Bayesian filtering in ocean acoustics,” IEEE J. Oceanic Eng. 36, 73–91 (2011).
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