Ioannis Bertsatos

Critical population density triggers rapid formation of vast oceanic fish shoals.

Similarities in the behavior of diverse animal species that form large groups have motivated attempts to establish general principles governing animal group behavior. It has been difficult, however, to make quantitative measurements of the temporal and spatial behavior of extensive animal groups in the wild, such as bird flocks, fish shoals, and locust swarms. By quantifying the formation processes of vast oceanic fish shoals during spawning, we show that (i) a rapid transition from disordered to highly synchronized behavior occurs as population density reaches a critical value; (ii) organized group migration occurs after this transition; and (iii) small sets of leaders significantly influence the actions of much larger groups. Each of these findings confirms general theoretical predictions believed to apply in nature irrespective of animal species.

General second-order covariance of Gaussian maximum likelihood estimates applied to passive source localization in fluctuating waveguides

A method is provided for determining necessary conditions on sample size or signal to noise ratio (SNR) to obtain accurate parameter estimates from remote sensing measurements in fluctuating environments. These conditions are derived by expanding the bias and covariance of maximum likelihood estimates (MLEs) in inverse orders of sample size or SNR, where the first-order covariance term is the Cramer-Rao lower bound (CRLB). Necessary sample sizes or SNRs are determined by requiring that (i) the first-order bias and the second-order covariance are much smaller than the true parameter value and the CRLB, respectively, and (ii) the CRLB falls within desired error thresholds. An analytical expression is provided for the second-order covariance of MLEs obtained from general complex Gaussian data vectors, which can be used in many practical problems since (i) data distributions can often be assumed to be Gaussian by virtue of the central limit theorem, and (ii) it allows for both the mean and variance of the measurement to be functions of the estimation parameters. Here, conditions are derived to obtain accurate source localization estimates in a fluctuating ocean waveguide containing random internal waves, and the consequences of the loss of coherence on their accuracy are quantified.

Optimal passive source localization in a fluctuating ocean waveguide based on an analytic model for the mean field and covariance

The ocean acts as an enormously complex channel for signal transmission. It is characterized by temporal fluctuations and spatial variabilities that often lead to significant randomization of the measured field. Signal processing techniques must be derived from fundamental physical models to attain statistical optimality in such an environment. Here we present such an analysis with a new analytic model [Ratilal and Makris, J. Acoust. Soc. Am. 114, 2428 (2003)] for the mean field and its covariance after propagation through a fluctuating ocean waveguide based on the first principles of waveguide scattering theory. The model is advantageous because it includes the primary physical effects of attenuation, dispersion, and coupling of modal energy due to multiple forward scattering in a convenient and intuitive form that is well suited to analytic manipulations. An example will be presented for passive source localization in range and depth in a fluctuating ocean waveguide by nonlinear matched field inversion....

Obtaining optimal time‐delay, source localization and tracking estimates in free space and in an ocean waveguide

Asymptotic methods for obtaining optimal time‐delay, source position and track estimates are derived for measurements in free‐space and in an ocean waveguide using nonlinear statistical inference theory. The methods are useful for determining necessary conditions on controllable variables such as signal‐to‐noise ratio and sample size to attain desired design error thresholds. For free‐space time‐delay estimation, it will be shown both analytically and intuitively that the matched filter cannot be unbiased and attain minimum variance unless the kurtosis of the signal’s energy spectrum exceeds the signal‐to‐noise ratio [Naftali and Makris, J. Acoust. Soc. Am. 110, 1917–1930 (2001)]. In an ocean waveguide, it will be shown that signal‐to‐noise ratios and sample sizes necessary to attain practical localization error thresholds can become prohibitively large when random waveguide inhomogeneities such as internal waves degrade intermodal coherence.

Resolving Lambertian surface orientation from fluctuating radiance

A maximum likelihood method for estimating remote surface orientation from multi-static acoustic, optical, radar, or laser images is presented. It is assumed that the images are corrupted by signal-dependent noise, known as speckle, arising from complex Gaussian field fluctuations, and that the surface properties are effectively Lambertian. Surface orientation estimates for a single sample are shown to have biases and errors that vary dramatically depending on illumination direction. This is due to the signal-dependent nature of speckle noise and the nonlinear relationship between surface orientation, illumination direction, and fluctuating radiance. The minimum number of independent samples necessary for maximum likelihood estimates to become asymptotically unbiased and to attain the lower bound on resolution of classical estimation theory are derived, as are practical design thresholds.

Population density imagery of migrating herring shoals by ocean acoustic waveguide remote sensing.

Ocean acoustic waveguide remote sensing (OAWRS) is a bistatic multibeam wide area sonar system that enables unaliased monitoring of fish populations over ecosystem scales. This allows us to quantify the formation processes of vast shoals of Atlantic herring (Clupea harengus) containing hundreds of millions of individuals, imaged during the Autumn 2006 spawning season. Areal population density estimation requires calibration of the low‐frequency target strength of an individual shoaling herring. This is estimated from experimental data acquired simultaneously at multiple frequencies in the 300–1200‐Hz range using (1) the OAWRS system, (2) areal population density calibration with several conventional fish finding sonar systems (CFFS), (3) fish length distributions obtained from trawl samples, and (4) local low‐frequency transmission loss measurements. High spatial‐temporal co‐registration was found between shoals imaged by OAWRS and concurrent CFFS line transects, which also provided fish depth distributio...

Atlantic herring low‐frequency target strength and abundance estimation: Ocean acoustic waveguide remote sensing (OAWRS) 2006 Experiment in the Gulf of Maine.

The mean low‐frequency target strength (TS) of spawning Atlantic herring populations in the Gulf of Maine is estimated from the experimental data acquired during September–October 2006 near the northern flank of Georges Bank. A low‐frequency OAWRS system with an instantaneous imaging diameter of 100 km was deployed to provide spatially unaliased imaging of fish populations over wide areas. The OAWRS system’s scattering strength measurements are calibrated with areal fish population density estimates obtained from concurrent localized line‐transect measurements with several conventional fish finding sonars (CFFSs). Trawl sampling at selected locations enables the identification of the imaged species. The mean TS estimates of herring individuals exhibits significant variation over OAWRS operating frequency range, in accordance with the results from a resonant scattering model for swimbladder‐bearing fish. The neutral buoyancy depth of herring and the species composition in the imaged population is inferred ...

Depth‐dependent resonant target strength analysis of a dense Atlantic Herring school from wide‐area OAWRS and localized 3D morphology sensing

The depth‐dependent target strength of Atlantic Herring is estimated at several distinct bandwidths close to their resonance frequency for a localized, highly dense school observed during the NOPP‐sponsored Gulf of Maine Experiment on September 22, 2006. An ocean acoustics waveguide remote sensing (OAWRS) system was deployed near Georges Bank to investigate the migration and spawning behavior of fish over wide areas. In conjunction with OAWRS, a Simrad EK60 conventional fish‐finding echosounder (CFFS) and a Reson Seabat 7125 multibeam sonar system were deployed to provide local depth extent and 3D volume morphology of the dense herring school. The calibration of low‐frequency target strength derived from OAWRS data using localized CFFS density and multibeam 3D volume estimates as inputs is discussed. The correlation between the mean depth of the vertically migrating herring school and its resonance frequency is investigated. The results are compared with a theoretical model for 3D resonance scattering fr...

Expected Doppler shift and spread in long range scattering from fish schools on the continental shelf

A stochastic model for the velocities of individual fish in a school, consistent with continous wide area observations [Symonds et al., J. Acoust. Soc. Am. 115, 2618 (2004)], is developed. This is combined with the model for scattering from a moving target submerged in a stratified ocean waveguide [Lai and Makris, J. Acoust. Soc. Am. 113, 223–244 (2003)] to estimate the Doppler shift and spread expected in long‐range scattering from fish schools on the continental shelf. The spectral characteristics expected for randomly swarming and migrating fish schools are then compared with those for stationary seafloor features and other moving targets such as underwater vehicles.

Optimally resolving Lambertian surface orientation

Sonar images of remote surfaces are typically corrupted by signal‐dependent noise known as speckle. Relative motion between source, surface, and receiver causes the received field to fluctuate over time with circular complex Gaussian random (CCGR) statistics. In many cases of practical importance, Lambert’s law is appropriate to model radiant intensity from the surface. In a previous paper, maximum likelihood estimators (MLE) for Lambertian surface orientation have been derived based on CCGR measurements [N. C. Makris, SACLANT Conference Proceedings Series CP‐45, 1997, pp. 339–346]. A Lambertian surface needs to be observed from more than one illumination direction for its orientation to be properly constrained. It is found, however, that MLE performance varies significantly with illumination direction due to the inherently nonlinear nature of this problem. It is shown that a large number of samples is often required to optimally resolve surface orientation using the optimality criteria of the MLE derived...