Mathematics of Kalman-Bucy Filtering

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Author: Peter A. Ruymgaart,Tsu T. Soong

Publisher: Springer Science & Business Media

ISBN: 3642733417

Category: Mathematics

Page: 170

View: 6876

The second edition has not deviated significantly from the first. The printing of this edition, however, has allowed us to make a number of corrections which escaped our scrutiny at the time of the first printing, and to generally improve and tighten our presentation of the material. Many of these changes were suggested to us by colleagues and readers and their kindness in doing so is greatly appreciated. Delft, The Netherlands and P. A. Ruymgaart Buffalo, New York, December, 1987 T. T. Soong Preface to the First Edition Since their introduction in the mid 1950s, the filtering techniques developed by Kalman, and by Kalman and Bucy have been widely known and widely used in all areas of applied sciences. Starting with applications in aerospace engineering, their impact has been felt not only in all areas of engineering but as all also in the social sciences, biological sciences, medical sciences, as well other physical sciences. Despite all the good that has come out of this devel opment, however, there have been misuses because the theory has been used mainly as a tool or a procedure by many applied workers without fully understanding its underlying mathematical workings. This book addresses a mathematical approach to Kalman-Bucy filtering and is an outgrowth of lectures given at our institutions since 1971 in a sequence of courses devoted to Kalman-Bucy filters.

Mathematics of Kalman-Bucy Filtering

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Author: P.A. Ruymgaart,Tsu T. Soong

Publisher: Springer Science & Business Media

ISBN: 3642968422

Category: Computers

Page: 170

View: 5541

Since their introduction in the mid 1950s, the filtering techniques developed by Kalman, and by Kalman and Bucy have been widely known and widely used in all areas of applied sciences. Starting with applications in aerospace engineering, their impact has been felt not only in all areas of engineering but also in the social sciences, biological sciences, medical sciences, as well as all other physical sciences. Despite all the good that has come out of this devel opment, however, there have been misuses because the theory has been used mainly as a tool or a procedure by many applied workers without them fully understanding its underlying mathematical workings. This book addresses a mathematical approach to Kalman-Bucy filtering and is an outgrowth of lectures given at our institutions since 1971 in a sequence of courses devoted to Kalman-Bucy filters. The material is meant to be a theoretical complement to courses dealing with applications and is designed for students who are well versed in the techniques of Kalman-Bucy filtering but who are also interested in the mathematics on which these may be based. The main topic addressed in this book is continuous-time Kalman-Bucy filtering. Although the discrete-time Kalman filter results were obtained first, the continuous-time results are important when dealing with systems developing in time continuously, which are hence more appropriately mod eled by differential equations than by difference equations. On the other hand, observations from the former can be obtained in a discrete fashion.

Kalman-Bucy Filters

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Author: Karl Brammer,Gerhard Siffling

Publisher: Artech House on Demand

ISBN: 9780890062944

Category: Mathematics

Page: 391

View: 7206

Kalman Filtering Techniques for Radar Tracking

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Author: K.V. Ramachandra

Publisher: CRC Press

ISBN: 9780824793227

Category: Technology & Engineering

Page: 256

View: 7815

A review of effective radar tracking filter methods and their associated digital filtering algorithms. It examines newly developed systems for eliminating the real-time execution of complete recursive Kalman filtering matrix equations that reduce tracking and update time. It also focuses on the role of tracking filters in operations of radar data processors for satellites, missiles, aircraft, ships, submarines and RPVs.

Kalman Filtering

Theory and Practice with MATLAB

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Author: Mohinder S. Grewal,Angus P. Andrews

Publisher: John Wiley & Sons

ISBN: 111898496X

Category: Technology & Engineering

Page: 640

View: 9376

The definitive textbook and professional reference on KalmanFiltering – fully updated, revised, and expanded This book contains the latest developments in the implementationand application of Kalman filtering. Authors Grewal and Andrewsdraw upon their decades of experience to offer an in-depthexamination of the subtleties, common pitfalls, and limitations ofestimation theory as it applies to real-world situations. Theypresent many illustrative examples including adaptations fornonlinear filtering, global navigation satellite systems, the errormodeling of gyros and accelerometers, inertial navigation systems,and freeway traffic control. Kalman Filtering: Theory and Practice Using MATLAB, FourthEdition is an ideal textbook in advanced undergraduate andbeginning graduate courses in stochastic processes and Kalmanfiltering. It is also appropriate for self-instruction or review bypracticing engineers and scientists who want to learn more aboutthis important topic.

Numerical Solution of Stochastic Differential Equations with Jumps in Finance

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Author: Eckhard Platen,Nicola Bruti-Liberati

Publisher: Springer Science & Business Media

ISBN: 364213694X

Category: Mathematics

Page: 856

View: 1756

In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.

Advanced Financial Modelling

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Author: Hansjörg Albrecher,Wolfgang J. Runggaldier,Walter Schachermayer

Publisher: Walter de Gruyter

ISBN: 3110213133

Category: Mathematics

Page: 453

View: 8986

This book is a collection of state-of-the-art surveys on various topics in mathematical finance, with an emphasis on recent modelling and computational approaches. The volume is related to a Special Semester on Stochastics with Emphasis on Finance that took place from September to December 2008 at the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences in Linz, Austria. "

Methods and Algorithms in Navigation

Marine Navigation and Safety of Sea Transportation

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Author: Adam Weintrit,Tomasz Neumann

Publisher: CRC Press

ISBN: 0203157338

Category: Computers

Page: 218

View: 8155

The TransNav 2011 Symposium held at the Gdynia Maritime University, Poland in June 2011 has brought together a wide range of participants from all over the world. The program has offered a variety of contributions, allowing to look at many aspects of the navigational safety from various different points of view. Topics presented and discussed at the Symposium were: navigation, safety at sea, sea transportation, education of navigators and simulator-based training, sea traffic engineering, ship's manoeuvrability, integrated systems, electronic charts systems, satellite, radio-navigation and anti-collision systems and many others. This book is part of a series of six volumes and provides an overview of Methods and Algorithms in Navigation and is addressed to scientists and professionals involved in research and development of navigation, safety of navigation and sea transportation.