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# Applied Optimal Estimation

01 Jan 1974-

TL;DR: This is the first book on the optimal estimation that places its major emphasis on practical applications, treating the subject more from an engineering than a mathematical orientation, and the theory and practice of optimal estimation is presented.

Abstract: This is the first book on the optimal estimation that places its major emphasis on practical applications, treating the subject more from an engineering than a mathematical orientation. Even so, theoretical and mathematical concepts are introduced and developed sufficiently to make the book a self-contained source of instruction for readers without prior knowledge of the basic principles of the field. The work is the product of the technical staff of the The Analytic Sciences Corporation (TASC), an organization whose success has resulted largely from its applications of optimal estimation techniques to a wide variety of real situations involving large-scale systemsArthur Gelb writes in the Foreword that "It is our intent throughout to provide a simple and interesting picture of the central issues underlying modern estimation theory and practice. Heuristic, rather than theoretically elegant, arguments are used extensively, with emphasis on physical insights and key questions of practical importance."Numerous illustrative examples, many based on actual applications, have been interspersed throughout the text to lead the student to a concrete understanding of the theoretical material. The inclusion of problems with "built-in" answers at the end of each of the nine chapters further enhances the self-study potential of the text.After a brief historical prelude, the book introduces the mathematics underlying random process theory and state-space characterization of linear dynamic systems. The theory and practice of optimal estimation is them presented, including filtering, smoothing, and prediction. Both linear and non-linear systems, and continuous- and discrete-time cases, are covered in considerable detail. New results are described concerning the application of covariance analysis to non-linear systems and the connection between observers and optimal estimators. The final chapters treat such practical and often pivotal issues as suboptimal structure, and computer loading considerations.This book is an outgrowth of a course given by TASC at a number of US Government facilities. Virtually all of the members of the TASC technical staff have, at one time and in one way or another, contributed to the material contained in the work

##### Citations

More filters

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TL;DR: The Condensation algorithm uses “factored sampling”, previously applied to the interpretation of static images, in which the probability distribution of possible interpretations is represented by a randomly generated set.

Abstract: The problem of tracking curves in dense visual clutter is challenging. Kalman filtering is inadequate because it is based on Gaussian densities which, being unimo dal, cannot represent simultaneous alternative hypotheses. The Condensation algorithm uses “factored sampling”, previously applied to the interpretation of static images, in which the probability distribution of possible interpretations is represented by a randomly generated set. Condensation uses learned dynamical models, together with visual observations, to propagate the random set over time. The result is highly robust tracking of agile motion. Notwithstanding the use of stochastic methods, the algorithm runs in near real-time.

5,804 citations

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01 Oct 1996

TL;DR: This article provides a tutorial introduction to visual servo control of robotic manipulators by reviewing the prerequisite topics from robotics and computer vision, including a brief review of coordinate transformations, velocity representation, and a description of the geometric aspects of the image formation process.

Abstract: This article provides a tutorial introduction to visual servo control of robotic manipulators. Since the topic spans many disciplines our goal is limited to providing a basic conceptual framework. We begin by reviewing the prerequisite topics from robotics and computer vision, including a brief review of coordinate transformations, velocity representation, and a description of the geometric aspects of the image formation process. We then present a taxonomy of visual servo control systems. The two major classes of systems, position-based and image-based systems, are then discussed in detail. Since any visual servo system must be capable of tracking image features in a sequence of images, we also include an overview of feature-based and correlation-based methods for tracking. We conclude the tutorial with a number of observations on the current directions of the research field of visual servo control.

3,619 citations

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29 Nov 1995TL;DR: The discrete Kalman filter as mentioned in this paper is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error.

Abstract: In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation. The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error. The filter is very powerful in several aspects: it supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modeled system is unknown. The purpose of this paper is to provide a practical introduction to the discrete Kalman filter. This introduction includes a description and some discussion of the basic discrete Kalman filter, a derivation, description and some discussion of the extended Kalman filter, and a relatively simple (tangible) example with real numbers & results.

2,811 citations

01 Jan 2003

TL;DR: This paper presents FastSLAM, an algorithm that recursively estimates the full posterior distribution over robot pose and landmark locations, yet scales logarithmically with the number of landmarks in the map.

Abstract: Simultaneous Localization and Mapping (SLAM) is an essential capability for mobile robots exploring unknown environments. The Extended Kalman Filter (EKF) has served as the de-facto approach to SLAM for the last fifteen years. However, EKF-based SLAM algorithms suffer from two well-known shortcomings that complicate their application to large, real-world environments: quadratic complexity and sensitivity to failures in data association. I will present an alternative approach to SLAM that specifically addresses these two areas. This approach, called FastSLAM, factors the full SLAM posterior exactly into a product of a robot path posterior, and N landmark posteriors conditioned on the robot path estimate. This factored posterior can be approximated efficiently using a particle filter. The time required to incorporate an observation into FastSLAM scales logarithmically with the number of landmarks in the map.
In addition to sampling over robot paths, FastSLAM can sample over potential data associations. Sampling over data associations enables FastSLAM to be used in environments with highly ambiguous landmark identities. This dissertation will describe the FastSLAM algorithm given both known and unknown data association. The performance of FastSLAM will be compared against the EKF on simulated and real-world data sets. Results will show that FastSLAM can produce accurate maps in extremely large environments, and in environments with substantial data association ambiguity. Finally, a convergence proof for FastSLAM in linear-Gaussian worlds will be presented.

2,358 citations

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01 Jan 1997TL;DR: This paper provides a tutorial on data fusion, introducing data fusion applications, process models, and identification of applicable techniques.

Abstract: Multisensor data fusion is an emerging technology applied to Department of Defense (DoD) areas such as automated target recognition, battlefield surveillance, and guidance and control of autonomous vehicles, and to non-DoD applications such as monitoring of complex machinery, medical diagnosis, and smart buildings. Techniques for multisensor data fusion are drawn from a wide range of areas including artificial intelligence, pattern recognition, statistical estimation and other areas. This paper provides a tutorial on data fusion, introducing data fusion applications, process models, and identification of applicable techniques. Comments are made on the state-of-the-art in data fusion.

2,356 citations