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Book ChapterDOI

Fractional Order Extended Kalman Filter for Attitude Estimation

TL;DR: The Fractional Order Extended Kalman Filter (FKF) approach is designed for estimating attitude with the help of inertial sensors in the attitude heading and reference system architecture.
Abstract: Attitude estimation is one of the core frameworks for a vehicle navigating with the help of inertial sensors such as accelerometer, gyroscope and magnetometer. Measurements obtained by these sensors are fused together to obtain vehicle attitude in the form of roll, pitch and yaw angles. Several state estimation frameworks have been proposed in the literature of which the extended Kalman filter and the complementary filtering based schemes are most popular. In this paper, the Fractional Order Extended Kalman Filter (FKF) approach is designed for estimating attitude with the help of inertial sensors in the attitude heading and reference system architecture. The FKF scheme is applied on the sensor data captured from commercial navigation units and compared with reference attitude for analysis. The simulations are carried out for varying fractional orders of different states and the corresponding results depict the dependency of estimation accuracy on system order.
Citations
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Proceedings ArticleDOI
02 Dec 2022
TL;DR: In this paper , different configurations of analog filters are tested in order to possibly find a better solution than that offered by the algorithm, used in many low-cost applications of Unmanned Aerial Vehicle positional awareness.
Abstract: This work deals with the comparison between different analog implementations of complementary filters with a digital processing algorithm. For this purpose, different configurations of analog filters are tested in order to possibly find a better solution than that offered by the algorithm, used in many low-cost applications of Unmanned Aerial Vehicle positional awareness.
References
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Book
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

6,015 citations

Proceedings Article
01 Jan 2001

3,169 citations

Book
23 Jun 2006
TL;DR: With its expert blend of theory and practice, coupled with its presentation of recent research results, Optimal State Estimation is strongly recommended for undergraduate and graduate-level courses in optimal control and state estimation theory.
Abstract: A bottom-up approach that enables readers to master and apply the latest techniques in state estimationThis book offers the best mathematical approaches to estimating the state of a general system. The author presents state estimation theory clearly and rigorously, providing the right amount of advanced material, recent research results, and references to enable the reader to apply state estimation techniques confidently across a variety of fields in science and engineering.While there are other textbooks that treat state estimation, this one offers special features and a unique perspective and pedagogical approach that speed learning: Straightforward, bottom-up approach begins with basic concepts and then builds step by step to more advanced topics for a clear understanding of state estimation Simple examples and problems that require only paper and pen to solve lead to an intuitive understanding of how theory works in practice MATLAB(r)-based source code that corresponds to examples in the book, available on the author's Web site, enables readers to recreate results and experiment with other simulation setups and parameters Armed with a solid foundation in the basics, readers are presented with a careful treatment of advanced topics, including unscented filtering, high order nonlinear filtering, particle filtering, constrained state estimation, reduced order filtering, robust Kalman filtering, and mixed Kalman/H? filtering.Problems at the end of each chapter include both written exercises and computer exercises. Written exercises focus on improving the reader's understanding of theory and key concepts, whereas computer exercises help readers apply theory to problems similar to ones they are likely to encounter in industry. A solutions manual is available for instructors.With its expert blend of theory and practice, coupled with its presentation of recent research results, Optimal State Estimation is strongly recommended for undergraduate and graduate-level courses in optimal control and state estimation theory. It also serves as a reference for engineers and science professionals across a wide array of industries.A solutions manual is available upon request from the Wiley editorial board.

2,711 citations

Journal ArticleDOI
TL;DR: In this article, a fractional-order PI/sup/spl lambda/D/sup /spl mu/controller with fractionalorder integrator and fractional order differentiator is proposed.
Abstract: Dynamic systems of an arbitrary real order (fractional-order systems) are considered. The concept of a fractional-order PI/sup /spl lambda//D/sup /spl mu//-controller, involving fractional-order integrator and fractional-order differentiator, is proposed. The Laplace transform formula for a new function of the Mittag-Leffler-type made it possible to obtain explicit analytical expressions for the unit-step and unit-impulse response of a linear fractional-order system with fractional-order controller for both open- and closed-loops. An example demonstrating the use of the obtained formulas and the advantages of the proposed PI/sup /spl lambda//D/sup /spl mu//-controllers is given.

2,479 citations

BookDOI
01 Jan 2010

1,696 citations