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Author: Harry L. Van Trees
Publisher: Wiley-IEEE Press
ISBN: 9780470120958
Category : Technology & Engineering
Languages : en
Pages : 951
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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: Harry L. Van Trees
Publisher: Wiley-IEEE Press
ISBN: 9780470120958
Category : Technology & Engineering
Languages : en
Pages : 951
Get Book
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: Simo Särkkä
Publisher: Cambridge University Press
ISBN: 1108912303
Category : Mathematics
Languages : en
Pages : 438
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Book Description
Now in its second edition, this accessible text presents a unified Bayesian treatment of state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models. The book focuses on discrete-time state space models and carefully introduces fundamental aspects related to optimal filtering and smoothing. In particular, it covers a range of efficient non-linear Gaussian filtering and smoothing algorithms, as well as Monte Carlo-based algorithms. This updated edition features new chapters on constructing state space models of practical systems, the discretization of continuous-time state space models, Gaussian filtering by enabling approximations, posterior linearization filtering, and the corresponding smoothers. Coverage of key topics is expanded, including extended Kalman filtering and smoothing, and parameter estimation. The book's practical, algorithmic approach assumes only modest mathematical prerequisites, suitable for graduate and advanced undergraduate students. Many examples are included, with Matlab and Python code available online, enabling readers to implement algorithms in their own projects.
Author: Peyman Setoodeh
Publisher: John Wiley & Sons
ISBN: 1118835816
Category : Technology & Engineering
Languages : en
Pages : 308
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Book Description
NONLINEAR FILTERS Discover the utility of using deep learning and (deep) reinforcement learning in deriving filtering algorithms with this insightful and powerful new resource Nonlinear Filters: Theory and Applications delivers an insightful view on state and parameter estimation by merging ideas from control theory, statistical signal processing, and machine learning. Taking an algorithmic approach, the book covers both classic and machine learning-based filtering algorithms. Readers of Nonlinear Filters will greatly benefit from the wide spectrum of presented topics including stability, robustness, computability, and algorithmic sufficiency. Readers will also enjoy: Organization that allows the book to act as a stand-alone, self-contained reference A thorough exploration of the notion of observability, nonlinear observers, and the theory of optimal nonlinear filtering that bridges the gap between different science and engineering disciplines A profound account of Bayesian filters including Kalman filter and its variants as well as particle filter A rigorous derivation of the smooth variable structure filter as a predictor-corrector estimator formulated based on a stability theorem, used to confine the estimated states within a neighborhood of their true values A concise tutorial on deep learning and reinforcement learning A detailed presentation of the expectation maximization algorithm and its machine learning-based variants, used for joint state and parameter estimation Guidelines for constructing nonparametric Bayesian models from parametric ones Perfect for researchers, professors, and graduate students in engineering, computer science, applied mathematics, and artificial intelligence, Nonlinear Filters: Theory and Applications will also earn a place in the libraries of those studying or practicing in fields involving pandemic diseases, cybersecurity, information fusion, augmented reality, autonomous driving, urban traffic network, navigation and tracking, robotics, power systems, hybrid technologies, and finance.
Author: Anton J. Haug
Publisher: John Wiley & Sons
ISBN: 1118287800
Category : Mathematics
Languages : en
Pages : 400
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Book Description
A practical approach to estimating and tracking dynamicsystems in real-worl applications Much of the literature on performing estimation for non-Gaussiansystems is short on practical methodology, while Gaussian methodsoften lack a cohesive derivation. Bayesian Estimation andTracking addresses the gap in the field on both accounts,providing readers with a comprehensive overview of methods forestimating both linear and nonlinear dynamic systems driven byGaussian and non-Gaussian noices. Featuring a unified approach to Bayesian estimation andtracking, the book emphasizes the derivation of all trackingalgorithms within a Bayesian framework and describes effectivenumerical methods for evaluating density-weighted integrals,including linear and nonlinear Kalman filters for Gaussian-weightedintegrals and particle filters for non-Gaussian cases. The authorfirst emphasizes detailed derivations from first principles ofeeach estimation method and goes on to use illustrative anddetailed step-by-step instructions for each method that makescoding of the tracking filter simple and easy to understand. Case studies are employed to showcase applications of thediscussed topics. In addition, the book supplies block diagrams foreach algorithm, allowing readers to develop their own MATLAB®toolbox of estimation methods. Bayesian Estimation and Tracking is an excellent book forcourses on estimation and tracking methods at the graduate level.The book also serves as a valuable reference for researchscientists, mathematicians, and engineers seeking a deeperunderstanding of the topics.
Author: Mahendra Mallick
Publisher: John Wiley & Sons
ISBN: 1118450566
Category : Technology & Engineering
Languages : en
Pages : 569
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Book Description
A unique guide to the state of the art of tracking, classification, and sensor management This book addresses the tremendous progress made over the last few decades in algorithm development and mathematical analysis for filtering, multi-target multi-sensor tracking, sensor management and control, and target classification. It provides for the first time an integrated treatment of these advanced topics, complete with careful mathematical formulation, clear description of the theory, and real-world applications. Written by experts in the field, Integrated Tracking, Classification, and Sensor Management provides readers with easy access to key Bayesian modeling and filtering methods, multi-target tracking approaches, target classification procedures, and large scale sensor management problem-solving techniques. Features include: An accessible coverage of random finite set based multi-target filtering algorithms such as the Probability Hypothesis Density filters and multi-Bernoulli filters with focus on problem solving A succinct overview of the track-oriented MHT that comprehensively collates all significant developments in filtering and tracking A state-of-the-art algorithm for hybrid Bayesian network (BN) inference that is efficient and scalable for complex classification models New structural results in stochastic sensor scheduling and algorithms for dynamic sensor scheduling and management Coverage of the posterior Cramer-Rao lower bound (PCRLB) for target tracking and sensor management Insight into cutting-edge military and civilian applications, including intelligence, surveillance, and reconnaissance (ISR) With its emphasis on the latest research results, Integrated Tracking, Classification, and Sensor Management is an invaluable guide for researchers and practitioners in statistical signal processing, radar systems, operations research, and control theory.
Author: Lawrence D. Stone
Publisher: Artech House
ISBN: 1608075532
Category : Technology & Engineering
Languages : en
Pages : 315
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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: Peyman Setoodeh
Publisher: John Wiley & Sons
ISBN: 1119078156
Category : Technology & Engineering
Languages : en
Pages : 308
Get Book
Book Description
NONLINEAR FILTERS Discover the utility of using deep learning and (deep) reinforcement learning in deriving filtering algorithms with this insightful and powerful new resource Nonlinear Filters: Theory and Applications delivers an insightful view on state and parameter estimation by merging ideas from control theory, statistical signal processing, and machine learning. Taking an algorithmic approach, the book covers both classic and machine learning-based filtering algorithms. Readers of Nonlinear Filters will greatly benefit from the wide spectrum of presented topics including stability, robustness, computability, and algorithmic sufficiency. Readers will also enjoy: Organization that allows the book to act as a stand-alone, self-contained reference A thorough exploration of the notion of observability, nonlinear observers, and the theory of optimal nonlinear filtering that bridges the gap between different science and engineering disciplines A profound account of Bayesian filters including Kalman filter and its variants as well as particle filter A rigorous derivation of the smooth variable structure filter as a predictor-corrector estimator formulated based on a stability theorem, used to confine the estimated states within a neighborhood of their true values A concise tutorial on deep learning and reinforcement learning A detailed presentation of the expectation maximization algorithm and its machine learning-based variants, used for joint state and parameter estimation Guidelines for constructing nonparametric Bayesian models from parametric ones Perfect for researchers, professors, and graduate students in engineering, computer science, applied mathematics, and artificial intelligence, Nonlinear Filters: Theory and Applications will also earn a place in the libraries of those studying or practicing in fields involving pandemic diseases, cybersecurity, information fusion, augmented reality, autonomous driving, urban traffic network, navigation and tracking, robotics, power systems, hybrid technologies, and finance.
Author: Roy L. Streit
Publisher: Springer Science & Business Media
ISBN: 1441969233
Category : Technology & Engineering
Languages : en
Pages : 274
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Book Description
"Poisson Point Processes provides an overview of non-homogeneous and multidimensional Poisson point processes and their numerous applications. Readers will find constructive mathematical tools and applications ranging from emission and transmission computed tomography to multiple target tracking and distributed sensor detection, written from an engineering perspective. A valuable discussion of the basic properties of finite random sets is included. Maximum likelihood estimation techniques are discussed for several parametric forms of the intensity function, including Gaussian sums, together with their Cramer-Rao bounds. These methods are then used to investigate: -Several medical imaging techniques, including positron emission tomography (PET), single photon emission computed tomography (SPECT), and transmission tomography (CT scans) -Various multi-target and multi-sensor tracking applications, -Practical applications in areas like distributed sensing and detection, -Related finite point processes such as marked processes, hard core processes, cluster processes, and doubly stochastic processes, Perfect for researchers, engineers and graduate students working in electrical engineering and computer science, Poisson Point Processes will prove to be an extremely valuable volume for those seeking insight into the nature of these processes and their diverse applications.
Author: Marcelo G. S. Bruno
Publisher: Morgan & Claypool Publishers
ISBN: 1627051201
Category : Technology & Engineering
Languages : en
Pages : 101
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Book Description
In these notes, we introduce particle filtering as a recursive importance sampling method that approximates the minimum-mean-square-error (MMSE) estimate of a sequence of hidden state vectors in scenarios where the joint probability distribution of the states and the observations is non-Gaussian and, therefore, closed-form analytical expressions for the MMSE estimate are generally unavailable. We begin the notes with a review of Bayesian approaches to static (i.e., time-invariant) parameter estimation. In the sequel, we describe the solution to the problem of sequential state estimation in linear, Gaussian dynamic models, which corresponds to the well-known Kalman (or Kalman-Bucy) filter. Finally, we move to the general nonlinear, non-Gaussian stochastic filtering problem and present particle filtering as a sequential Monte Carlo approach to solve that problem in a statistically optimal way. We review several techniques to improve the performance of particle filters, including importance function optimization, particle resampling, Markov Chain Monte Carlo move steps, auxiliary particle filtering, and regularized particle filtering. We also discuss Rao-Blackwellized particle filtering as a technique that is particularly well-suited for many relevant applications such as fault detection and inertial navigation. Finally, we conclude the notes with a discussion on the emerging topic of distributed particle filtering using multiple processors located at remote nodes in a sensor network. Throughout the notes, we often assume a more general framework than in most introductory textbooks by allowing either the observation model or the hidden state dynamic model to include unknown parameters. In a fully Bayesian fashion, we treat those unknown parameters also as random variables. Using suitable dynamic conjugate priors, that approach can be applied then to perform joint state and parameter estimation. Table of Contents: Introduction / Bayesian Estimation of Static Vectors / The Stochastic Filtering Problem / Sequential Monte Carlo Methods / Sampling/Importance Resampling (SIR) Filter / Importance Function Selection / Markov Chain Monte Carlo Move Step / Rao-Blackwellized Particle Filters / Auxiliary Particle Filter / Regularized Particle Filters / Cooperative Filtering with Multiple Observers / Application Examples / Summary
Author: Peter J. Schreier
Publisher: Cambridge University Press
ISBN: 1139487620
Category : Technology & Engineering
Languages : en
Pages : 331
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Book Description
Complex-valued random signals are embedded in the very fabric of science and engineering, yet the usual assumptions made about their statistical behavior are often a poor representation of the underlying physics. This book deals with improper and noncircular complex signals, which do not conform to classical assumptions, and it demonstrates how correct treatment of these signals can have significant payoffs. The book begins with detailed coverage of the fundamental theory and presents a variety of tools and algorithms for dealing with improper and noncircular signals. It provides a comprehensive account of the main applications, covering detection, estimation, and signal analysis of stationary, nonstationary, and cyclostationary processes. Providing a systematic development from the origin of complex signals to their probabilistic description makes the theory accessible to newcomers. This book is ideal for graduate students and researchers working with complex data in a range of research areas from communications to oceanography.
