A Kalman Filter Primer
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| Author | : Randall L. Eubank |
| Publisher | : CRC Press |
| Total Pages | : 208 |
| Release | : 2005-11-29 |
| Genre | : Mathematics |
| ISBN | : 9780824723651 |
System state estimation in the presence of noise is critical for control systems, signal processing, and many other applications in a variety of fields. Developed decades ago, the Kalman filter remains an important, powerful tool for estimating the variables in a system in the presence of noise. However, when inundated with theory and vast notations, learning just how the Kalman filter works can be a daunting task. With its mathematically rigorous, “no frills” approach to the basic discrete-time Kalman filter, A Kalman Filter Primer builds a thorough understanding of the inner workings and basic concepts of Kalman filter recursions from first principles. Instead of the typical Bayesian perspective, the author develops the topic via least-squares and classical matrix methods using the Cholesky decomposition to distill the essence of the Kalman filter and reveal the motivations behind the choice of the initializing state vector. He supplies pseudo-code algorithms for the various recursions, enabling code development to implement the filter in practice. The book thoroughly studies the development of modern smoothing algorithms and methods for determining initial states, along with a comprehensive development of the “diffuse” Kalman filter. Using a tiered presentation that builds on simple discussions to more complex and thorough treatments, A Kalman Filter Primer is the perfect introduction to quickly and effectively using the Kalman filter in practice.
| Author | : Randall L. Eubank |
| Publisher | : CRC Press |
| Total Pages | : 199 |
| Release | : 2005-11-29 |
| Genre | : Mathematics |
| ISBN | : 1420028677 |
System state estimation in the presence of noise is critical for control systems, signal processing, and many other applications in a variety of fields. Developed decades ago, the Kalman filter remains an important, powerful tool for estimating the variables in a system in the presence of noise. However, when inundated with theory and vast notation
| Author | : Dan Simon |
| Publisher | : John Wiley & Sons |
| Total Pages | : 554 |
| Release | : 2006-06-19 |
| Genre | : Technology & Engineering |
| ISBN | : 0470045337 |
A bottom-up approach that enables readers to master and apply the latest techniques in state estimation This 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. 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.
| Author | : Narayan Kovvali |
| Publisher | : Springer Nature |
| Total Pages | : 71 |
| Release | : 2022-06-01 |
| Genre | : Technology & Engineering |
| ISBN | : 3031025369 |
The Kalman filter is the Bayesian optimum solution to the problem of sequentially estimating the states of a dynamical system in which the state evolution and measurement processes are both linear and Gaussian. Given the ubiquity of such systems, the Kalman filter finds use in a variety of applications, e.g., target tracking, guidance and navigation, and communications systems. The purpose of this book is to present a brief introduction to Kalman filtering. The theoretical framework of the Kalman filter is first presented, followed by examples showing its use in practical applications. Extensions of the method to nonlinear problems and distributed applications are discussed. A software implementation of the algorithm in the MATLAB programming language is provided, as well as MATLAB code for several example applications discussed in the manuscript.
| Author | : Víctor M. Moreno |
| Publisher | : BoD – Books on Demand |
| Total Pages | : 608 |
| Release | : 2009-04-01 |
| Genre | : Computers |
| ISBN | : 9533070005 |
The aim of this book is to provide an overview of recent developments in Kalman filter theory and their applications in engineering and scientific fields. The book is divided into 24 chapters and organized in five blocks corresponding to recent advances in Kalman filtering theory, applications in medical and biological sciences, tracking and positioning systems, electrical engineering and, finally, industrial processes and communication networks.
| Author | : Prasad A. Naik |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2015 |
| Genre | : Business & Economics |
| ISBN | : 9781680830668 |
Marketing Dynamics: A Primer on Estimation and Control provides an introduction to the estimation and control of dynamic marketing models. It introduces dynamic models in discrete- and continuous-time, scalar and multivariate settings, with observed outcomes and unobserved states, as well as random and/or time-varying parameters. It exemplifies how various dynamic models can be cast into the unifying state space framework, the benefit of which is to use one common algorithm to estimate all dynamic models. Marketing Dynamics: A Primer on Estimation and Control then focuses on the estimation part, answering questions about the sales elasticity of advertising, sales lift due to price promotion, and short-term sales forecasting. The estimation relies on two principles - Kalman filtering and the likelihood principle. Next, the primer elucidates the control part answering questions about how much managers should spend on advertising over time and across regions, best promotional timing and depth, and optimally responding to competing brands' actions. The control part relies on the maximum principle and the optimality principle. Finally, the primer presents three examples on the application of optimal control, differential games, and stochastic control theory to marketing problems, and illustrates how to discover novel insights into managerial decision-making.
| Author | : Kostas Triantafyllopoulos |
| Publisher | : Springer Nature |
| Total Pages | : 503 |
| Release | : 2021-11-12 |
| Genre | : Mathematics |
| ISBN | : 303076124X |
Bayesian Inference of State Space Models: Kalman Filtering and Beyond offers a comprehensive introduction to Bayesian estimation and forecasting for state space models. The celebrated Kalman filter, with its numerous extensions, takes centre stage in the book. Univariate and multivariate models, linear Gaussian, non-linear and non-Gaussian models are discussed with applications to signal processing, environmetrics, economics and systems engineering. Over the past years there has been a growing literature on Bayesian inference of state space models, focusing on multivariate models as well as on non-linear and non-Gaussian models. The availability of time series data in many fields of science and industry on the one hand, and the development of low-cost computational capabilities on the other, have resulted in a wealth of statistical methods aimed at parameter estimation and forecasting. This book brings together many of these methods, presenting an accessible and comprehensive introduction to state space models. A number of data sets from different disciplines are used to illustrate the methods and show how they are applied in practice. The R package BTSA, created for the book, includes many of the algorithms and examples presented. The book is essentially self-contained and includes a chapter summarising the prerequisites in undergraduate linear algebra, probability and statistics. An up-to-date and complete account of state space methods, illustrated by real-life data sets and R code, this textbook will appeal to a wide range of students and scientists, notably in the disciplines of statistics, systems engineering, signal processing, data science, finance and econometrics. With numerous exercises in each chapter, and prerequisite knowledge conveniently recalled, it is suitable for upper undergraduate and graduate courses.
| Author | : Timothy D. Barfoot |
| Publisher | : Cambridge University Press |
| Total Pages | : 381 |
| Release | : 2017-07-31 |
| Genre | : Computers |
| ISBN | : 1107159393 |
A modern look at state estimation, targeted at students and practitioners of robotics, with emphasis on three-dimensional applications.
| Author | : Brigitte d'Andréa-Novel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 299 |
| Release | : 2013-05-09 |
| Genre | : Technology & Engineering |
| ISBN | : 3642343244 |
Control Theory is at the heart of information and communication technologies of complex systems. It can contribute to meeting the energy and environmental challenges we are facing. The textbook is organized in the way an engineer classically proceeds to solve a control problem, that is, elaboration of a mathematical model capturing the process behavior, analysis of this model and design of a control to achieve the desired objectives. It is divided into three Parts. The first part of the text addresses modeling aspects through state space and input-output representations. The notion of the internal state of a system (for example mechanical, thermal or electrical), as well as its description using a finite number of variables, is also emphasized. The second part is devoted to the stability analysis of an equilibrium point. The authors present classical tools for stability analysis, such as linearization techniques and Lyapunov functions. Central to Control Theory are the notions of feedback and of closed-loop, and the third part of the textbook describes the linear control synthesis in a continuous and discrete-time framework and also in a probabilistic context. Quadratic optimization and Kalman filtering are presented, as well as the polynomial representation, a convenient approach to reject perturbations on the system without making the control law more complex. Throughout the text, different examples are developed, both in the chapters and in the exercises.
| Author | : Michael C. Dietze |
| Publisher | : Princeton University Press |
| Total Pages | : 285 |
| Release | : 2017-05-30 |
| Genre | : Science |
| ISBN | : 1400885450 |
An authoritative and accessible introduction to the concepts and tools needed to make ecology a more predictive science Ecologists are being asked to respond to unprecedented environmental challenges. How can they provide the best available scientific information about what will happen in the future? Ecological Forecasting is the first book to bring together the concepts and tools needed to make ecology a more predictive science. Ecological Forecasting presents a new way of doing ecology. A closer connection between data and models can help us to project our current understanding of ecological processes into new places and times. This accessible and comprehensive book covers a wealth of topics, including Bayesian calibration and the complexities of real-world data; uncertainty quantification, partitioning, propagation, and analysis; feedbacks from models to measurements; state-space models and data fusion; iterative forecasting and the forecast cycle; and decision support. Features case studies that highlight the advances and opportunities in forecasting across a range of ecological subdisciplines, such as epidemiology, fisheries, endangered species, biodiversity, and the carbon cycle Presents a probabilistic approach to prediction and iteratively updating forecasts based on new data Describes statistical and informatics tools for bringing models and data together, with emphasis on: Quantifying and partitioning uncertainties Dealing with the complexities of real-world data Feedbacks to identifying data needs, improving models, and decision support Numerous hands-on activities in R available online
