In this paper we review the most peculiar and interesting information-theoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information theory of fading channels, by emphasizing capacity as the most important performance measure. Both single-user and multiuser transmission are examined. Further, we describe how the structure of fading channels impacts code design, and finally overview equalization of fading multipath channels.

The simultaneous recovery of 3D shape and motion from image sequences is one of the more difficult problems in computer vision. Classical approaches to the problem rely on using algebraic techniques to solve for these unknowns given two or more images. More recently, a batch analysis of image streams (the temporal tracks of distinguishable image features) under orthography has resulted in highly accurate reconstructions. We generalize this approach to perspective projection and partial or uncertain tracks by using a non-linear least squares technique. While our approach requires iteration, it quickly converges to the desired solution, even in the absence of a priori knowledge about the shape or motion. Important features of the algorithm include its ability to handle partial point tracks, to use line segment matches and point matches simultaneously, and to use an object-centered representation for faster and more accurate structure and motion recovery. We also show how a projective (a...

A suboptimal Kalman filter called the ensemble transform Kalman filter (ET KF) is introduced. Like other Kalman filters, it provides a framework for assimilating observations and also for estimating the effect of observations on forecast error covariance. It differs from other ensemble Kalman filters in that it uses ensemble transformation and a normalization to rapidly obtain the prediction error covariance matrix associated with a particular deployment of observational resources. This rapidity enables it to quickly assess the ability of a large number of future feasible sequences of observational networks to reduce forecast error variance. The ET KF was used by the National Centers for Environmental Prediction in the Winter Storm Reconnaissance missions of 1999 and 2000 to determine where aircraft should deploy dropwindsondes in order to improve 24-72-h forecasts over the continental United States. The ET KF may be applied to any well-constructed set of ensemble perturbations. The ET KF

this paper the extended Kalman filter is used with a nonlinear multilayer quasi-geostrophic (QG) model. This provides us with both a realistic ocean model and a very sophisticated error statistics scheme. The extended Kalman filter is an extension of the common Kalman filter and may be used when the model dynamics or the measurement equation is nonlinear. It consists of an approximative equation for the propagation of error covariances, and also approximative filter equations if the measurement equation is nonlinear. When changing from a linear system to nonlinear dynamics the possible existence of a wide variety of phenomena which are nonexistent in the linear theory is introduced. Nonlinear systems may have solutions with multiple equilibria, where the solutions sometimes abruptly undergo transitions from one equilibrium to another as parameters change (bifurcations). Also chaotic behavior occurs in many deterministic systems, where solutions exhibit an apparently random behavior. The Lorenz [1963] model is probably the best known example of chaotic systems. It has solutions which undergo "unpredictable" transitions between two different equilibria (chaos). As discussed by Miller and Ghil

The lure of using motion vision as a fundamental element in the perception of space drives this effort to use flow features as the sole cues for robot mobility.

Recovering the shape of an object from two views fails at occluding contours of smooth objects because the extremal contours are view dependent. For three or more views, shape recovery is possible, and several algorithms have recently been developed for this purpose. We present a new approach to the multiframe stereo problem which does not depend on differential measurements in the image, which may be noise sensitive. Instead, we use a linear smoother to optimally combine all of the measurements available at the contours (and other edges) in all of the images. This allows us to extract a robust and dense estimate of surface shape, and to integrate shape information from both surface markings and occluding contours. Keywords: Computer vision, image sequence analysis, motion analysis and multiframe stereo, shape and object representation, occluding contours (profiles). c flDigital Equipment Corporation 1993. All rights reserved. 1 Computer and Information Science Department, University...

Solving the SLAM problem is one way to enable a robot to explore, map, and navigate in a previously unknown environment. We investigate smoothing approaches as a viable alternative to extended Kalman filter-based solutions to the problem. In particular, we look at approaches that factorize either the associated information matrix or the measurement Jacobian into square root form. Such techniques have several significant advantages over the EKF: they are faster yet exact, they can be used in either batch or incremental mode, are better equipped to deal with non-linear process and measurement models, and yield the entire robot trajectory, at lower cost for a large class of SLAM problems. In addition, in an indirect but dramatic way, column ordering heuristics automatically exploit the locality inherent in the geographic nature of the SLAM problem. In this paper we present the theory underlying these methods, along with an interpretation of factorization in terms of the graphical model associated with the SLAM problem. We present both simulation results and actual SLAM experiments in large-scale environments that underscore the potential of these methods as an alternative to EKF-based approaches. 1

To recognize an object in an image one must have an internal model of how that object may appear. We describe a method for learning such models from training images. An object is modeled by a probability distribution describing the range of possible variation in the object's appearance. This distribution is organized on two levels. Large variations are handled by partitioning the training images into clusters that correspond to distinctly different views of the object. Within each cluster, smaller variations are represented by distributions that characterize the presence, position, and measurements of various discrete features of appearance. The learning process combines an incremental conceptual clustering algorithm for forming the clusters with a generalization algorithm for consolidating each cluster's training images into a single description. Recognition employs information about feature positions, numeric measurements, and relations in order to constrain and speed the search. Pre...

We describe how to model the appearance of a 3-D object using multiple views, learn such a model from training images, and use the model for object recognition. The model uses probability distributions to describe the range of possible variation in the object’s appearance. These distributions are organized on two levels. Large variations are handled by partitioning training images into clusters corresponding to distinctly different views of the object. Within each cluster, smaller variations are represented by distributions characterizing uncertainty in the presence, position, and measurements of various discrete features of appearance. Many types of features are used, ranging in abstraction from edge segments to perceptual groupings and regions. A matching procedure uses the feature uncertainty information to guide the search for a match between model and image. Hypothesized feature pairings are used to estimate a viewpoint transformation taking account of feature uncertainty. These methods have been implemented in an object recognition system, Oliver. Experiments show that Oliver is capable of learning to recognize complex objects in cluttered images, while acquiring models that represent those objects using relatively few views.

Ensemble data assimilation methods assimilate observations using state-space estimation methods and lowrank representations of forecast and analysis error covariances. A key element of such methods is the transformation of the forecast ensemble into an analysis ensemble with appropriate statistics. This transformation may be performed stochastically by treating observations as random variables, or deterministically by requiring that the updated analysis perturbations satisfy the Kalman filter analysis error covariance equation. Deterministic analysis ensemble updates are implementations of Kalman square root filters. The nonuniqueness of the deterministic transformation used in square root Kalman filters provides a framework to compare three recently proposed ensemble data assimilation methods.