James M. Gelb

Cold dark matter. 1: The formation of dark halos

We use numerical simulations of critically closed cold dark matter (CDM) models to study the effects of numerical resolution on observable quantities. We study simulations with up to 256(exp 3) particles using the particle-mesh (PM) method and with up to 144(exp 3) particles using the adaptive particle-particle-mesh (P3M) method. Comparisons of galaxy halo distributions are made among the various simulations. We also compare distributions with observations, and we explore methods for identifying halos, including a new algorithm that finds all particles within closed contours of the smoothed density field surrounding a peak. The simulated halos show more substructure than predicted by the Press-Schechter theory. We are able to rule out all omega = 1 CDM models for linear amplitude sigma(sub 8) greater than or approximately = 0.5 because the simulations produce too many massive halos compared with the observations. The simulations also produce too many low-mass halos. The distribution of halos characterized by their circular velocities for the P3M simulations is in reasonable agreement with the observations for 150 km/s less than or = V(sub circ) less than or = 350 km/s.

Cold dark matter. 2: Spatial and velocity statistics

We examine high-resolution gravitational N-body simulations of the omega = 1 cold dark matter (CDM) model in order to determine whether there is any normalization of the initial density fluctuation spectrum that yields acceptable results for galaxy clustering and velocities. Dense dark matter halos in the evolved mass distribution are identified with luminous galaxies; the most massive halos are also considered as sites for galaxy groups, with a range of possibilities explored for the group mass-to-light ratios. We verify the earlier conclusions of White et al. (1987) for the low-amplitude (high-bias) CDM model-the galaxy correlation function is marginally acceptable but that there are too many galaxies. We also show that the peak biasing method does not accurately reproduce the results obtained using dense halos identified in the simulations themselves. The Cosmic Background Explorer (COBE) anisotropy implies a higher normalization, resulting in problems with excessive pairwise galaxy velocity dispersion unless a strong velocity bias is present. Although we confirm the strong velocity bias of halos reported by Couchman & Carlberg (1992), we show that the galaxy motions are still too large on small scales. We find no amplitude for which the CDM model can reconcile simultaneously and galaxy correlation function, the low pairwise velocity dispersion, and the richness distribution of groups and clusters. With the normalization implied by COBE, the CDM spectrum has too much power on small scales if omega = 1.

Background and Clutter Mixture Distributions for Active Sonar Statistics

False alarms in active sonar systems arising from physical objects in the ocean (e.g., rocks, fish, or seaweed) are often called clutter. A variety of statistical models have been proposed for representing the sonar probability of false alarm (Pfa) in the presence of clutter, including the log-normal, generalized-Pareto, Weibull, and K distributions. However, owing to the potential sparseness of the clutter echoes within the analysis window, a mixture distribution comprising one of the clutter distributions and a Rayleigh-distributed envelope (i.e., an exponentially distributed intensity) to represent diffuse background scattering and noise is proposed. Parameter-estimation techniques based on the expectation-maximization (EM) algorithm are developed for mixtures containing the aforementioned clutter distributions. While the standard EM algorithm handles the mixture containing log-normal clutter, the EM-gradient algorithm, which combines the EM algorithm with a one-step Newton optimization, is necessary for the generalized-Pareto and Weibull cases. The mixture containing K -distributed clutter requires development of a variant of the EM algorithm exploiting method-of-moments parameter estimation. Evaluation of three midfrequency active-sonar data examples, spanning mildly to very heavy-tailed Pfa, illustrates that the mixture models provide a better fit than single-component models. As might be expected, inference on clutter-source scattering based on the shape parameter of the clutter distribution is shown to be less biased using the mixture model compared with a single-component distribution when the data contain both clutter echoes and diffuse background scattering or noise.

Statistics of Distinct Clutter Classes in Midfrequency Active Sonar

The empirical distributions of normalized matched-filter echoes from a midfrequency active sonar with hyperbolic frequency-modulated waveforms in a myriad of oceanic environments are studied for three broad clutter (nontarget) classes: bottom structures, diffuse compact clutter, and compact nonstationary (moving) clutter. The distributions are characterized using the K -distribution (KD) and the generalized Pare to distribution (GPD). Methods of parameter estimation are discussed, and parameters are computed for small subregions of the clutter fields. A plot of the Kolmogorov-Smirnov (KS) goodness-of-fit statistic of individual subregions is presented for each model and class to highlight the versatility of the models when applied to large quantities of data. Cumulants are computed from the data and are utilized as features in a classifier to demonstrate separability between the classes. An important aspect of this work is the use of distinct clutter classes as opposed to collectively characterizing all clutter as reverberation. Environmental effects are not considered, as the goal of this work is to determine the utility of local clutter estimation models in practical sonar processing systems where accurate environmental data are unavailable.

Searching for the Mikheyev-Smirnov-Wolfenstein Enhancement

We point out that the length scale associated with the MSW effect is the radius of the Earth. Therefore to verify matter enhancement of neutrino oscillations, it will be necessary to study neutrinos passing through the Earth. For the parameters of MSW solutions to the solar neutrino problem, the only detectable effects occur in a narrow band of energies from 5 to 10 MeV. We propose that serious consideration be given to mounting an experiment at a location within 9.5 degrees of the equator.

K-Rayleigh mixture model for sparse active sonar clutter

The mixture of a Rayleigh probability density function (PDF) and a K PDF is proposed for representing active sonar data comprising clutter sparsely observed in a Rayleigh-distributed background. While both the Rayleigh and K distributions have been shown to accurately represent the statistics of certain types of active sonar data, it is common to observe data containing both echoes from distinct clutter objects and more diffuse, Rayleigh-distributed reverberation. While the K distribution can often still capture the behavior of such data, the K-Rayleigh mixture is seen to provide improved PDF fits and inference on the clutter statistics. A parameter estimation algorithm for the K-Rayleigh mixture PDF based on the expectation-maximization (EM) technique is proposed and shown to provide adequate performance in representing the PDF of very heavy tailed real sonar data.

Interpreting Echo Statistics of Three Distinct Clutter Classes Measured With a Midfrequency Active Sonar: Accounting for Number of Scatterers, Scattering Statistics, and Beampattern Effects

A recently developed published approach to predict echo statistics is applied to clutter data that were collected with a midfrequency sonar and published in a separate independent study. This method explicitly accounts for the (finite) number of unresolved scatterers, the statistics associated with the arbitrary scattering properties of the individual scatterers [but assumed to have identical echo probability density functions (pdfs) in this application], and beampattern effects which significantly affect the echo statistics due to each scatterer being randomly located in the sonar beam. The data had been categorized according to whether they were associated with bottom structures, diffuse compact clutter, and compact nonstationary (moving) clutter. In this paper, the recently developed method is incorporated in a two-component mixed pdf (mixed with a Rayleigh distribution to account for the diffuse background) to model the statistics of the three classes of clutter. This is the first such application of the model which had principally been validated only numerically. The degree to which the data are non-Rayleigh (heavy tailed) is reasonably predicted by the model and the number of scatterers per resolution cell is inferred for each type of clutter.

Active sonar clutter classification using higher order moments.

The statistics of normalized matched‐filter echoes from an active sonar system operating in a myriad of oceanic environments has been studied extensively for three broad clutter classes including using low‐order cumulants to classify subregions of the data [Gelb et al., Proceedings of the ISURC (2008) and references therein]. That work compared empirical distributions to parametric models (e.g., the K distribution and the generalized Pareto distribution). A report on extensions of this work is presented including studies of the accuracy of analytic parameter estimation methods and the efficacy of using higher order moments in the classification process. For each class, with increasingly heavy non‐Rayleigh distributed tails, comparisons are made of brute force parameter estimation with the use of analytic estimators. Additionally, comparisons of higher order moments (including skew and kurtosis) computed from the data are made with analytic fits to the data. Using a feature‐based classifier, the gains of u...

Classification of Clutter Types in Active Sonar Using Spatial Image Processing Techniques

Clutter (e.g., reverberation and bottom structures) can lead to excessive false alarm rates (identifying clutter as submarines) in antisubmarine warfare (ASW) active sonar systems. False alarm reduction is an important marine challenge in an era where ASW has shifted from noisy submarines in deep waters to quiet submarines in highly cluttered littoral regions. In this paper, physically motivated image processing features have been developed and are extracted from digitized clutter images for the purpose of classifying these images. The ability to automatically classify these images can ultimately be applied in situ to tactical systems to improve automated tracking and classification. The clutter images are generated by averaging mid-frequency active sonar acoustic returns, which have been convolved with an appropriate measurement error kernel, from sea trial archives over several pings of history. Match filtered, normalized mid-frequency data from the full two-dimensional tactical field are considered, which provides contextual information and avoids analyzing the complicated time series data directly. Marginal probability distributions of features extracted from each class and multi-class classification results using log-likelihood techniques are presented.

Hybrid joint PDF estimation and classification for sparse systems

We developed methods for estimating joint probability density functions (PDFs) of statistically dependent features from sparse data with the main focus on computing likelihood functions for classification. We limited methods to those that use marginal probabilities as building blocks. The estimators studied are (1) semiparametric models, i.e., combinations of nonparametric and parametric components of the form /spl Pi//sub i/p/sub i/(f/sub i/)[M/sub n/(f)//spl Pi//sub i/m/sub i/(f/sub i/)], where f represents a set of n features p/sub i/(f/sub i/) are the marginal probabilities and M/sub n/(f) is a model for the n-dimensional multivariate PDF with model marginals m/sub i/(f/sub i/); and (2) nonparametric expansion models: the PDF is expanded in terms of its excess probabilities, /spl Pi//sub l/p/sub l/(f/sub l/)[1+/spl Sigma//sub i<j//spl xi//sub ij/+/spl Sigma//sub i<j<k/+....], with, for example, the 2-point functions defined as /spl xi//sub ij/=p/sub ij/(f/sub i/, f/sub j//p/sub i/(f/sub i/)p/sub j/(f/sub j/)-1. We studied a particular semiparametric model with multivariate Gaussian (MVG) for M/sub n/ (pseudogauss). We found that the expansion model was practical only for the inclusion of 2-point terms, yet it often captured much of the effect of the full distribution. The nonparametric models were made robust for classification by smoothly mixing in the marginals in poorly sampled regions. Because the models considered have multiple components, we collectively refer to them as hybrid models.