Estimating the instantaneous velocity of randomly moving target swarms in a stratified ocean waveguide by Doppler analysis.

Doppler analysis has been extensively used in active radar and sonar sensing to estimate the speed and direction of a single target within an imaging system resolution cell following deterministic theory. For target swarms, such as fish and plankton in the ocean, and raindrops, birds and bats in the atmosphere, multiple randomly moving targets typically occupy a single resolution cell, making single-target theory inadequate. Here, a method is developed for simultaneously estimating the instantaneous mean velocity and position of a group of randomly moving targets within a resolution cell, as well as the respective standard deviations across the group by Doppler analysis in free-space and in a stratified ocean waveguide. While the variance of the field scattered from the swarm is shown to typically dominate over the mean in the range-velocity ambiguity function, cross-spectral coherence remains and maintains high Doppler velocity and position resolution even for coherent signal processing algorithms such as the matched filter. For pseudo-random signals, the mean and variance of the swarms' velocity and position can be expressed in terms of the first two moments of the measured range-velocity ambiguity function. This is shown analytically for free-space and with Monte-Carlo simulations for an ocean waveguide.

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.

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.

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.