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This work is directed toward approximating the evolution of forecast error covariances for data assimilation. We study the performance of different algorithms based on simplification of the standard Kalman filter (KF). These are suboptimal schemes (SOS's) when compared to the KF, which is optimal for linear problems with known statistics. The SOS's considered here are several versions of optimal interpolation (OI), a scheme for height error variance advection, and a simplified KF in which the full height error covariance is advected. In order to employ a methodology for exact comparison among these schemes we maintain a linear environment, choosing a beta--plane shallow water model linearized about a constant zonal flow for the testbed dynamics. Our results show that constructing dynamically--balanced forecast error covariances, rather than using conventional geostrophically--balanced ones, is essential for successful performance of any SOS. A posteriori initialization of SOS's to comp...

This correspondence presents a new technique for calibrating a camera mounted on a controllable head/eye platform. It uses the trajectories of an arbitrary number of tracked corner features to improve the calibration parameter estimates over time, utilising a novel variable state dimension form of recursive filter. No special visual stimuli are required and no assumptions are made about the structure of the scene, other than that it is stationary relative to the head. The algorithm runs at 4 frames per second on a single Inmos T805 transputer, and is fully integrated into a real-time active vision system. Updated calibration parameters are regularly passed to the vision modules that require them. Although the algorithm requires an initial estimate of camera focal length, results are presented from real experiments demonstrating that convergence is achieved for initial errors up to 50%. I. Introduction Scene reconstruction and object recognition are areas of computer vision which have ...

How does the visual system learn an internal model of the external environment? How is this internal model used during visual perception? How are occlusions and background clutter so effortlessly discounted for when recognizing a familiar object? How is a particular object of interest attended to and recognized in the presence of other objects in the field of view? In this paper, we attempt to address these questions from the perspective of Bayesian optimal estimation theory. Using the concept of generative models and the statistical theory of Kalman filtering, we show how static and dynamic events occurring in the visual environment may be learned and recognized given only the input images. We also describe an extension of the Kalman filter model that can handle multiple objects in the field of view. The resulting robust Kalman filter model demonstrates how certain forms of attention can be viewed as an emergent property of the interaction between top–down expectations and bottom–up signals. Experimental results are provided to help demonstrate the ability of such a model to perform robust segmentation and recognition of objects and image sequences in the presence of occlusions and clutter.

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.

3D Shape modeling has received enormous attention in computer graphics and computer vision over the past decade. Several shape modeling techniques have been proposed in literature, some are local (distributed parameter) while others are global (lumped parameter) in terms of the parameters required to describe the shape. Hybrid models that combine both ends of this parameter spectrum have been in vogue only recently. However, they do not allow a smooth transition between the two extremes of this parameter spectrum. In this paper, we introduce a new shape modeling scheme that can transform smoothly from local to global models or vice-versa. The modeling scheme utilizes a hybrid primitive called the deformable superquadric constructed in an orthonormal wavelet basis. The multiresolution wavelet basis provides the power to continuously transform from local to global shape deformations and thereby allow for a continuum of shape models -- from those with local to those with global shape desc...

This tutorial provides an introduction to Simultaneous Localisation and Mapping (SLAM) and the extensive research on SLAM that has been undertaken over the past decade. SLAM is the process by which a mobile robot can build a map of an environment and at the same time use this map to compute it’s own location. The past decade has seen rapid and exciting progress in solving the SLAM problem together with many compelling implementations of SLAM methods. Part I of this tutorial (this paper), describes the probabilistic form of the SLAM problem, essential solution methods and significant implementations. Part II of this tutorial will be concerned with recent advances in computational methods and new formulations of the SLAM problem for large scale and complex environments.

The Kalman Filter is a well-known recursive state estimator for linear systems. In practice the algorithm is often used for nonlinear systems by linearizing the system's process and measurement functions. Different Kalman Filter variants linearize the functions in different ways. This paper explains how the best known Kalman Filter variants -- i.e. the Extended Kalman Filter (EKF), Iterated Extended Kalman Filter (IEKF), the Central Difference Filter (CDF), the first order Divided Difference Filter (DD1) and the Unscented Kalman Filter (UKF) -- (i) linearize the process and measurement functions; (ii) take the linearization errors into account; and (iii) how the quality of the state estimates depends on the previous two choices. Besides some

In this paper, we present a car tracking system which provides quantitative and qualitative motion estimates of the tracked car simultaneously from a moving observer. First, we construct three motion models (constant velocity, constant acceleration, and turning) to describe the qualitative motion of a moving car. Then the models are incorporated into the Extended Kalman Filters to perform quantitative tracking. Finally, we develop an Extended Interacting Multiple Model (EIMM) algorithm to manage the switching between models and to output both qualitative and quantitative motion estimates of the tracked car. Accurate motion modeling and efficient model management result in a high performance tracking system. The experimental results on simulated and real data demonstrate that our tracking system is reliable and robust, and runs in real-time. The multiple motion representations make the system useful in various autonomous driving tasks. 1 Introduction Vehicle tracking is an important a...

In this paper, we propose a framework for multi-camera video surveillance. Our framework addresses the detection, represenation, and recognition of motion events. The detection phase handles spatiotemporal data fusion for efficiently and reliably extracting motion trajectories from video. The representation phase summarizes raw trajectory data to construct a hierarchical, invariant, and content-rich representation of the motion events. Finally, the recognition phase deals with learning using imbalanced training datasets and infinitedimensional data that also exhibit temporal ordering. Due to space limit, only the following two components are discussed in the paper: fusing spatio-temporal information from multiple camera sources and characterizing and detecting suspicious surveillance events.