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Author: Stuart Charles Kramer Publisher: ISBN: Category : Bayesian statistical decision theory Languages : en Pages : 268
Book Description
In Bayesian estimation, the objective is to calculate the complete density function for an unknown quantity conditioned on noisy observations of that quantity. This work considers recursive estimation of a nonlinear discrete-time system state using successive observations. The formal recursion for the density function is easily written, but generally there is no closed form solution. The numerical solution proposed here is obtained by modifying the recursion and using a simple piece-wise constant approximation to the density functions. The critical part of the algorithm then becomes a discrete linear convolution that can be realized using FFT's. Keywords: error analysis; and parameter estimation.
Author: Stuart Charles Kramer Publisher: ISBN: Category : Bayesian statistical decision theory Languages : en Pages : 268
Book Description
In Bayesian estimation, the objective is to calculate the complete density function for an unknown quantity conditioned on noisy observations of that quantity. This work considers recursive estimation of a nonlinear discrete-time system state using successive observations. The formal recursion for the density function is easily written, but generally there is no closed form solution. The numerical solution proposed here is obtained by modifying the recursion and using a simple piece-wise constant approximation to the density functions. The critical part of the algorithm then becomes a discrete linear convolution that can be realized using FFT's. Keywords: error analysis; and parameter estimation.
Author: Simo Särkkä Publisher: Cambridge University Press ISBN: 110703065X Category : Computers Languages : en Pages : 255
Book Description
A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.
Author: Andrew H. Jazwinski Publisher: Courier Corporation ISBN: 0486318192 Category : Science Languages : en Pages : 404
Book Description
This unified treatment of linear and nonlinear filtering theory presents material previously available only in journals, and in terms accessible to engineering students. Its sole prerequisites are advanced calculus, the theory of ordinary differential equations, and matrix analysis. Although theory is emphasized, the text discusses numerous practical applications as well. Taking the state-space approach to filtering, this text models dynamical systems by finite-dimensional Markov processes, outputs of stochastic difference, and differential equations. Starting with background material on probability theory and stochastic processes, the author introduces and defines the problems of filtering, prediction, and smoothing. He presents the mathematical solutions to nonlinear filtering problems, and he specializes the nonlinear theory to linear problems. The final chapters deal with applications, addressing the development of approximate nonlinear filters, and presenting a critical analysis of their performance.
Author: Timothy D. Barfoot Publisher: Cambridge University Press ISBN: 1107159393 Category : Computers Languages : en Pages : 381
Book Description
A modern look at state estimation, targeted at students and practitioners of robotics, with emphasis on three-dimensional applications.
Author: Lawrence D. Stone Publisher: Artech House ISBN: 1608075532 Category : Technology & Engineering Languages : en Pages : 315
Book Description
This second edition has undergone substantial revision from the 1999 first edition, recognizing that a lot has changed in the multiple target tracking field. One of the most dramatic changes is in the widespread use of particle filters to implement nonlinear, non-Gaussian Bayesian trackers. This book views multiple target tracking as a Bayesian inference problem. Within this framework it develops the theory of single target tracking, multiple target tracking, and likelihood ratio detection and tracking. In addition to providing a detailed description of a basic particle filter that implements the Bayesian single target recursion, this resource provides numerous examples that involve the use of particle filters. With these examples illustrating the developed concepts, algorithms, and approaches -- the book helps radar engineers develop tracking solutions when observations are non-linear functions of target state, when the target state distributions or measurement error distributions are not Gaussian, in low data rate and low signal to noise ratio situations, and when notions of contact and association are merged or unresolved among more than one target.
Author: Yuriy S. Shmaliy Publisher: John Wiley & Sons ISBN: 1119863074 Category : Technology & Engineering Languages : en Pages : 484
Book Description
A unified and systematic theoretical framework for solving problems related to finite impulse response (FIR) estimate Optimal and Robust State Estimation: Finite Impulse Response (FIR) and Kalman Approaches is a comprehensive investigation into batch state estimators and recursive forms. The work begins by introducing the reader to the state estimation approach and provides a brief historical overview. Next, the work discusses the specific properties of finite impulse response (FIR) state estimators. Further chapters give the basics of probability and stochastic processes, discuss the available linear and nonlinear state estimators, deal with optimal FIR filtering, and consider a limited memory batch and recursive algorithms. Other topics covered include solving the q-lag FIR smoothing problem, introducing the receding horizon (RH) FIR state estimation approach, and developing the theory of FIR state estimation under disturbances. The book closes by discussing the theory of FIR state estimation for uncertain systems and providing several applications where the FIR state estimators are used effectively. Key concepts covered in the work include: A holistic overview of the state estimation approach, which arose from the need to know the internal state of a real system, given that the input and output are both known Optimal, optimal unbiased, maximum likelihood, and unbiased and robust finite impulse response (FIR) structures FIR state estimation approach along with the infinite impulse response (IIR) and Kalman approaches Cost functions and the most critical properties of FIR and IIR state estimates Optimal and Robust State Estimation: Finite Impulse Response (FIR) and Kalman Approaches was written for professionals in the fields of microwave engineering, system engineering, and robotics who wish to move towards solving finite impulse response (FIR) estimate issues in both theoretical and practical applications. Graduate and senior undergraduate students with coursework dealing with state estimation will also be able to use the book to gain a valuable foundation of knowledge and become more adept in their chosen fields of study.
Author: Ch. Venkateswarlu Publisher: Elsevier ISBN: 0323900682 Category : Technology & Engineering Languages : en Pages : 400
Book Description
Optimal State Estimation for Process Monitoring, Fault Diagnosis and Control presents various mechanistic model based state estimators and data-driven model based state estimators with a special emphasis on their development and applications to process monitoring, fault diagnosis and control. The design and analysis of different state estimators are highlighted with a number of applications and case studies concerning to various real chemical and biochemical processes. The book starts with the introduction of basic concepts, extending to classical methods and successively leading to advances in this field. Design and implementation of various classical and advanced state estimation methods to solve a wide variety of problems makes this book immensely useful for the audience working in different disciplines in academics, research and industry in areas concerning to process monitoring, fault diagnosis, control and related disciplines. - Describes various classical and advanced versions of mechanistic model based state estimation algorithms - Describes various data-driven model based state estimation techniques - Highlights a number of real applications of mechanistic model based and data-driven model based state estimators/soft sensors - Beneficial to those associated with process monitoring, fault diagnosis, online optimization, control and related areas
Author: Harry L. Van Trees Publisher: Wiley-IEEE Press ISBN: 9780470120958 Category : Technology & Engineering Languages : en Pages : 951
Book Description
The first comprehensive development of Bayesian Bounds for parameter estimation and nonlinear filtering/tracking Bayesian estimation plays a central role in many signal processing problems encountered in radar, sonar, communications, seismology, and medical diagnosis. There are often highly nonlinear problems for which analytic evaluation of the exact performance is intractable. A widely used technique is to find bounds on the performance of any estimator and compare the performance of various estimators to these bounds. This book provides a comprehensive overview of the state of the art in Bayesian Bounds. It addresses two related problems: the estimation of multiple parameters based on noisy measurements and the estimation of random processes, either continuous or discrete, based on noisy measurements. An extensive introductory chapter provides an overview of Bayesian estimation and the interrelationship and applicability of the various Bayesian Bounds for both static parameters and random processes. It provides the context for the collection of papers that are included. This book will serve as a comprehensive reference for engineers and statisticians interested in both theory and application. It is also suitable as a text for a graduate seminar or as a supplementary reference for an estimation theory course.
Author: Stuart Charles Kramer
Author: Stuart Charles Kramer
Author: Simo Särkkä
Author: Andrew H. Jazwinski
Author: Timothy D. Barfoot
Author: 
Author: Lawrence D. Stone
Author: Yuriy S. Shmaliy
Author: Timothy D. Barfoot
Author: Ch. Venkateswarlu
Author: Harry L. Van Trees