Proceedings Article•

# An introduction to the Kalman filter

01 Jan 2001-

About: This article is published in International Conference on Computer Graphics and Interactive Techniques.The article was published on 2001-01-01 and is currently open access. It has received 3169 citations till now. The article focuses on the topics: Kalman filter.

##### Citations

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01 May 2007TL;DR: A survey on gesture recognition with particular emphasis on hand gestures and facial expressions is provided, and applications involving hidden Markov models, particle filtering and condensation, finite-state machines, optical flow, skin color, and connectionist models are discussed in detail.

Abstract: Gesture recognition pertains to recognizing meaningful expressions of motion by a human, involving the hands, arms, face, head, and/or body. It is of utmost importance in designing an intelligent and efficient human-computer interface. The applications of gesture recognition are manifold, ranging from sign language through medical rehabilitation to virtual reality. In this paper, we provide a survey on gesture recognition with particular emphasis on hand gestures and facial expressions. Applications involving hidden Markov models, particle filtering and condensation, finite-state machines, optical flow, skin color, and connectionist models are discussed in detail. Existing challenges and future research possibilities are also highlighted

1,797 citations

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TL;DR: It is demonstrated that trackers can be evaluated objectively by survival curves, Kaplan Meier statistics, and Grubs testing, and it is found that in the evaluation practice the F-score is as effective as the object tracking accuracy (OTA) score.

Abstract: There is a large variety of trackers, which have been proposed in the literature during the last two decades with some mixed success. Object tracking in realistic scenarios is a difficult problem, therefore, it remains a most active area of research in computer vision. A good tracker should perform well in a large number of videos involving illumination changes, occlusion, clutter, camera motion, low contrast, specularities, and at least six more aspects. However, the performance of proposed trackers have been evaluated typically on less than ten videos, or on the special purpose datasets. In this paper, we aim to evaluate trackers systematically and experimentally on 315 video fragments covering above aspects. We selected a set of nineteen trackers to include a wide variety of algorithms often cited in literature, supplemented with trackers appearing in 2010 and 2011 for which the code was publicly available. We demonstrate that trackers can be evaluated objectively by survival curves, Kaplan Meier statistics, and Grubs testing. We find that in the evaluation practice the F-score is as effective as the object tracking accuracy (OTA) score. The analysis under a large variety of circumstances provides objective insight into the strengths and weaknesses of trackers.

1,604 citations

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TL;DR: Characteristics of the process industry data which are critical for the development of data-driven Soft Sensors are discussed.

Abstract: In the last two decades Soft Sensors established themselves as a valuable alternative to the traditional means for the acquisition of critical process variables, process monitoring and other tasks which are related to process control. This paper discusses characteristics of the process industry data which are critical for the development of data-driven Soft Sensors. These characteristics are common to a large number of process industry fields, like the chemical industry, bioprocess industry, steel industry, etc. The focus of this work is put on the data-driven Soft Sensors because of their growing popularity, already demonstrated usefulness and huge, though yet not completely realised, potential. A comprehensive selection of case studies covering the three most important Soft Sensor application fields, a general introduction to the most popular Soft Sensor modelling techniques as well as a discussion of some open issues in the Soft Sensor development and maintenance and their possible solutions are the main contributions of this work.

1,399 citations

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TL;DR: The developments of the last 20 years in the area of vision for mobile robot navigation are surveyed and the cases of navigation using optical flows, using methods from the appearance-based paradigm, and by recognition of specific objects in the environment are discussed.

Abstract: Surveys the developments of the last 20 years in the area of vision for mobile robot navigation. Two major components of the paper deal with indoor navigation and outdoor navigation. For each component, we have further subdivided our treatment of the subject on the basis of structured and unstructured environments. For indoor robots in structured environments, we have dealt separately with the cases of geometrical and topological models of space. For unstructured environments, we have discussed the cases of navigation using optical flows, using methods from the appearance-based paradigm, and by recognition of specific objects in the environment.

1,386 citations

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TL;DR: This paper provides a comprehensive survey of research on computer-vision-based human motion analysis, namely human detection, tracking and activity understanding, and various methods for each issue are discussed in order to examine the state of the art.

Abstract: Visual analysis of human motion is currently one of the most active research topics in computer vision. This strong interest is driven by a wide spectrum of promising applications in many areas such as virtual reality, smart surveillance, perceptual interface, etc. Human motion analysis concerns the detection, tracking and recognition of people, and more generally, the understanding of human behaviors, from image sequences involving humans. This paper provides a comprehensive survey of research on computer-vision-based human motion analysis. The emphasis is on three major issues involved in a general human motion analysis system, namely human detection, tracking and activity understanding. Various methods for each issue are discussed in order to examine the state of the art. Finally, some research challenges and future directions are discussed.

1,106 citations

##### References

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14 Mar 1970

TL;DR: In this paper, a unified treatment of linear and nonlinear filtering theory for engineers is presented, with sufficient emphasis on applications to enable the reader to use the theory for engineering problems.

Abstract: This book presents a unified treatment of linear and nonlinear filtering theory for engineers, with sufficient emphasis on applications to enable the reader to use the theory. The need for this book is twofold. First, although linear estimation theory is relatively well known, it is largely scattered in the journal literature and has not been collected in a single source. Second, available literature on the continuous nonlinear theory is quite esoteric and controversial, and thus inaccessible to engineers uninitiated in measure theory and stochastic differential equations. Furthermore, it is not clear from the available literature whether the nonlinear theory can be applied to practical engineering problems. In attempting to fill the stated needs, the author has retained as much mathematical rigor as he felt was consistent with the prime objective" to explain the theory to engineers. Thus, the author has avoided measure theory in this book by using mean square convergence, on the premise that everyone knows how to average. As a result, the author only requires of the reader background in advanced calculus, theory of ordinary differential equations, and matrix analysis.

6,539 citations

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01 Oct 1972

TL;DR: In this article, the authors provide an excellent introduction to feedback control system design, including a theoretical approach that captures the essential issues and can be applied to a wide range of practical problems.

Abstract: Linear Optimal Control SystemsFeedback Control TheoryOptimal ControlLinear Optimal ControlOptimal Control SystemsThe Zeros of Linear Optimal Control Systems and Their Role in High Feedback Gain Stability DesignOptimal ControlLinear State-Space Control SystemsOptimal Control of Dynamic Systems Driven by Vector MeasuresApplied Linear Optimal Control Paperback with CD-ROMNonlinear and Optimal Control SystemsLinear SystemsLinear Control TheoryLinear Systems and Optimal ControlOptimal Control Methods for Linear Discrete-Time Economic SystemsOptimal Control Theory for Infinite Dimensional SystemsInfinite Dimensional Linear Control SystemsStochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop SolutionsApplications of Optimal Control Theory to Computer Controller DesignSwitching and Learning in Feedback SystemsContinuous Time Dynamical SystemsNew Trends in Optimal Filtering and Control for Polynomial and Time-Delay SystemsThe Theory and Application of Linear Optimal ControlTurnpike Theory of Continuous-Time Linear Optimal Control ProblemsLinear Optimal Control SystemsLinear Control TheoryCalculus of Variations and Optimal Control TheoryOptimal ControlNonlinear Controllability and Optimal ControlOptimal Control TheoryOptimal Control Of Singularly Perturbed Linear Systems And ApplicationsOptimal Control SystemsDesign criterion for improving the sensitivity of linear optimal control systemsLinear Stochastic Control SystemsConstrained Optimal Control of Linear and Hybrid SystemsOptimal Control Of Singularly Perturbed Linear Systems And ApplicationsPredictive Control for Linear and Hybrid SystemsOptimal ControlOptimal Control Theory with Applications in EconomicsNonlinear Optimal Control Theory Successfully classroom-tested at the graduate level, Linear Control Theory: Structure, Robustness, and Optimization covers three major areas of control engineering (PID control, robust control, and optimal control). It provides balanced coverage of elegant mathematical theory and useful engineering-oriented results. The first part of the book develops results relating to the design of PID and first-order controllers for continuous and discrete-time linear systems with possible delays. The second section deals with the robust stability and performance of systems under parametric and unstructured uncertainty. This section describes several elegant and sharp results, such as Kharitonov’s theorem and its extensions, the edge theorem, and the mapping theorem. Focusing on the optimal control of linear systems, the third part discusses the standard theories of the linear quadratic regulator, Hinfinity and l1 optimal control, and associated results. Written by recognized leaders in the field, this book explains how control theory can be applied to the design of real-world systems. It shows that the techniques of three term controllers, along with the results on robust and optimal control, are invaluable to developing and solving research problems in many areas of engineering.An excellent introduction to feedback control system design, this book offers a theoretical approach that captures the essential issues and can be applied to a wide range of practical problems. Its explorations of recent developments in the field emphasize the relationship of new procedures to classical control theory, with a focus on single input and output systems that keeps concepts accessible to students with limited backgrounds. The text is geared toward a single-semester senior course or a graduate-level class for students of electrical engineering. The opening chapters constitute a basic treatment of feedback design. Topics include a detailed formulation of the control design program, the fundamental issue of performance/stability robustness tradeoff, and the graphical design technique of loopshaping. Subsequent chapters extend the discussion of the loopshaping technique and connect it with notions of optimality. Concluding chapters examine controller design via optimization, offering a mathematical approach that is useful for multivariable systems.Upper-level undergraduate text introduces aspects of optimal control theory: dynamic programming, Pontryagin's minimum principle, and numerical techniques for trajectory optimization. Numerous figures, tables. Solution guide available upon request. 1970 edition.Infinite dimensional systems can be used to describe many phenomena in the real world. As is well known, heat conduction, properties of elastic plastic material, fluid dynamics, diffusion-reaction processes, etc., all lie within this area. The object that we are studying (temperature, displace ment, concentration, velocity, etc.) is usually referred to as the state. We are interested in the case where the state satisfies proper differential equa tions that are derived from certain physical laws, such as Newton's law, Fourier's law etc. The space in which the state exists is called the state space, and the equation that the state satisfies is called the state equation. By an infinite dimensional system we mean one whose corresponding state space is infinite dimensional. In particular, we are interested in the case where the state equation is one of the following types: partial differential equation, functional differential equation, integro-differential equation, or abstract evolution equation. The case in which the state equation is being a stochastic differential equation is also an infinite dimensional problem, but we will not discuss such a case in this book.For more than forty years, the equation y’(t) = Ay(t) + u(t) in Banach spaces has been used as model for optimal control processes described by partial differential equations, in particular heat and diffusion processes. Many of the outstanding open problems, however, have remained open until recently, and some have never been solved. This book is a survey of all results know to the author, with emphasis on very recent results (1999 to date). The book is restricted to linear equations and two particular problems (the time optimal problem, the norm optimal problem) which results in a more focused and concrete treatment. As experience shows, results on linear equations are the basis for the treatment of their semilinear counterparts, and techniques for the time and norm optimal problems can often be generalized to more general cost functionals. The main object of this book is to be a state-of-the-art monograph on the theory of the time and norm optimal controls for y’(t) = Ay(t) + u(t) that ends at the very latest frontier of research, with open problems and indications for future research. Key features: · Applications to optimal diffusion processes. · Applications to optimal heat propagation processes. · Modelling of optimal processes governed by partial differential equations. · Complete bibliography. · Includes the latest research on the subject. · Does not assume anything from the reader except basic functional analysis. · Accessible to researchers and advanced graduate students alike · Applications to optimal diffusion processes. · Applications to optimal heat propagation processes. · Modelling of optimal processes governed by partial differential equations. · Complete bibliography. · Includes the latest research on the subject. · Does not assume anything from the reader except basic functional analysis. · Accessible to researchers and advanced graduate students alikeLinear Stochastic Control Systems presents a thorough description of the mathematical theory and fundamental principles of linear stochastic control systems. Both continuous-time and discrete-time systems are thoroughly covered. Reviews of the modern probability and random processes theories and the Itô stochastic differential equations are provided. Discrete-time stochastic systems theory, optimal estimation and Kalman filtering, and optimal stochastic control theory are studied in detail. A modern treatment of these same topics for continuous-time stochastic control systems is included. The text is written in an easy-to-understand style, and the reader needs only to have a background of elementary real analysis and linear deterministic systems theory to comprehend the subject matter. This graduate textbook is also suitable for self-study, professional training, and as a handy research reference. Linear Stochastic Control Systems is self-contained and provides a step-by-step development of the theory, with many illustrative examples, exercises, and engineering applications.This outstanding reference presents current, state-of-the-art research on importantproblems of finite-dimensional nonlinear optimal control and controllability theory. Itpresents an overview of a broad variety of new techniques useful in solving classicalcontrol theory problems.Written and edited by renowned mathematicians at the forefront of research in thisevolving field, Nonlinear Controllability and Optimal Control providesdetailed coverage of the construction of solutions of differential inclusions by means ofdirectionally continuous sections Lie algebraic conditions for local controllability the use of the Campbell-Hausdorff series to derive properties of optimal trajectories the Fuller phenomenon the theory of orbits and more.Containing more than 1,300 display equations, this exemplary, instructive reference is aninvaluable source for mathematical researchers and applied mathematicians, electrical andelectronics, aerospace, mechanical, control, systems, and computer engineers, and graduatestudents in these disciplines .This book is based on lectures from a one-year course at the Far Eastern Federal University (Vladivostok, Russia) as well as on workshops on optimal control offered to students at various mathematical departments at the university level. The main themes of the theory of linear and nonlinear systems are considered, including the basic problem of establishing the necessary and sufficient conditions of optimal processes. In the

4,294 citations

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01 Sep 1993

TL;DR: Brief review of linear algebra and linear systems brief review of probability theory and statistics some basic concepts in estimation linear estimation in static systems linear dynamic systems with random inputs state estimation in discrete-timelinear dynamic systems estimation for Kinematic models.

Abstract: Brief review of linear algebra and linear systems brief review of probability theory brief review of statistics some basic concepts in estimation linear estimation in static systems linear dynamic systems with random inputs state estimation in discrete-time linear dynamic systems estimation for Kinematic models computational aspects of estimation extensions of discrete-time estimation continuous-time linear state estimation state estimation for nonlinear dynamic systems adaptive estimation and manoeuvering targets problem solutions

2,118 citations