Download or read book Nonlinear Filtering and Approximation Techniques written by E. Pardoux and published by . This book was released on 1988 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research concerned the theory of nonlinear filtering and numerical approximation in nonlinear filtering. The following results were obtained: 1) Under very general conditions it is shown that the conditional density in nonlinear filtering is the unique solution, within an appropriate class of functions, of the Zakai equation. The main conditions is that all coefficients are bounded and smooth. These coefficients are allowed to depend on the history of the observed process; 2) Developed a Lie algebraic criterion for the non-existence of finite dimensional filters; 3) Studied numerical methods for the approximate solution of Zakai's stochastic partial differential equations; 4) Developed approximate finite dimensional filters for high signal to noise ratio problems; and 5) Compared two algorithms for maximizing the likelihood function associated with parameter estimation in partially observed diffusion processes. (KR).
Download or read book Nonlinear Filters written by Sueo Sugimoto and published by Ohmsha, Ltd.. This book was released on 2020-12-10 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers a broad range of filter theories, algorithms, and numerical examples. The representative linear and nonlinear filters such as the Kalman filter, the steady-state Kalman filter, the H infinity filter, the extended Kalman filter, the Gaussian sum filter, the statistically linearized Kalman filter, the unscented Kalman filter, the Gaussian filter, the cubature Kalman filter are first visited. Then, the non-Gaussian filters such as the ensemble Kalman filter and the particle filters based on the sequential Bayesian filter and the sequential importance resampling are described, together with their recent advances. Moreover, the information matrix in the nonlinear filtering, the nonlinear smoother based on the Markov Chain Monte Carlo, the continuous-discrete filters, factorized filters, and nonlinear filters based on stochastic approximation method are detailed. 1 Review of the Kalman Filter and Related Filters 2 Information Matrix in Nonlinear Filtering 3 Extended Kalman Filter and Gaussian Sum Filter 4 Statistically Linearized Kalman Filter 5 The Unscented Kalman Filter 6 General Gaussian Filters and Applications 7 The Ensemble Kalman Filter 8 Particle Filter 9 Nonlinear Smoother with Markov Chain Monte Carlo 10 Continuous-Discrete Filters 11 Factorized Filters 12 Nonlinear Filters Based on Stochastic Approximation Method
Download or read book Nonlinear Filtering written by Jitendra R. Raol and published by CRC Press. This book was released on 2017-07-12 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Filtering covers linear and nonlinear filtering in a comprehensive manner, with appropriate theoretic and practical development. Aspects of modeling, estimation, recursive filtering, linear filtering, and nonlinear filtering are presented with appropriate and sufficient mathematics. A modeling-control-system approach is used when applicable, and detailed practical applications are presented to elucidate the analysis and filtering concepts. MATLAB routines are included, and examples from a wide range of engineering applications - including aerospace, automated manufacturing, robotics, and advanced control systems - are referenced throughout the text.
Download or read book An Optimal Approximation for a Certain Class of Nonlinear Filtering Problems written by Talal Umar Halawani and published by . This book was released on 1983 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approximation technique to a certain class of nonlinear filtering problems is considered. The method is based on an approximation of nonlinear, partially observable systems by a stochastic control problem with fully observable state. The filter development proceeds from the assumption that the unobservables are conditionally Gaussian with respect to the observations initially. The concepts of both conditionally Gaussian processes and an optimal-control approach to filtering are utilized in the filter development. A two-step, nonlinear, recursive estimation procedure (TNF), compatible with the logical structure of the optimal mean-square estimator, generates a finite-dimensional, nonlinear filter with improved characteristics over most of the traditional methods. Moreover, a close (in the mean-square sense) approximation for the original system will be generated as well. In general the nonlinear filtering problem does not have a finite-dimensional recursive synthesis. Thus, the proposed technique may expand the range of practical problems that can be handled by nonlinear filtering. Application of the derived multi-dimensional filtering algorithm to two low-order, nonlinear tracking problems according to a global criterion and a local-time criterion respectively are presented.
Download or read book Nonlinear Filters written by Hisashi Tanizaki and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a nonlinear filtering problem, the most heuristic and easiest approximation is to use the Taylor series expansion and apply the conventional linear recursive Kalman filter algorithm directly to the linearized nonlinear measurement and transition equations. First, it is discussed that the Taylor series expansion approach gives us the biased estimators. Next, a Monte-Carlo simulation filter is proposed, where each expectation of the nonlinear functions is evaluated generating random draws. It is shown from Monte-Carlo experiments that the Monte-Carlo simulation filter yields the unbiased but inefficient estimator. Anotherapproach to the nonlinear filtering problem is to approximate the underlyingdensity functions of the state vector. In this monograph, a nonlinear and nonnormal filter is proposed by utilizing Monte-Carlo integration, in which a recursive algorithm of the weighting functions is derived. The densityapproximation approach gives us an asymptotically unbiased estimator. Moreover, in terms of programming and computational time, the nonlinear filter using Monte-Carlo integration can be easily extended to higher dimensional cases, compared with Kitagawa's nonlinear filter using numericalintegration.
Download or read book Grid based Nonlinear Estimation and Its Applications written by Bin Jia and published by CRC Press. This book was released on 2019-04-25 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Grid-based Nonlinear Estimation and its Applications presents new Bayesian nonlinear estimation techniques developed in the last two decades. Grid-based estimation techniques are based on efficient and precise numerical integration rules to improve performance of the traditional Kalman filtering based estimation for nonlinear and uncertainty dynamic systems. The unscented Kalman filter, Gauss-Hermite quadrature filter, cubature Kalman filter, sparse-grid quadrature filter, and many other numerical grid-based filtering techniques have been introduced and compared in this book. Theoretical analysis and numerical simulations are provided to show the relationships and distinct features of different estimation techniques. To assist the exposition of the filtering concept, preliminary mathematical review is provided. In addition, rather than merely considering the single sensor estimation, multiple sensor estimation, including the centralized and decentralized estimation, is included. Different decentralized estimation strategies, including consensus, diffusion, and covariance intersection, are investigated. Diverse engineering applications, such as uncertainty propagation, target tracking, guidance, navigation, and control, are presented to illustrate the performance of different grid-based estimation techniques.
Download or read book An Optimal Control Approximation for a Certain Class of Nonlinear Filtering Problems written by Talal Umar Halawani and published by . This book was released on 1983 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approximation technique to a certain class of nonlinear filtering problems is considered in this dissertation. The method is based on an approximation of nonlinear, partially-observable systems by a stochastic control problem with fully observable state. The filter development proceeds from the assumption that the unobservables are conditionally Gaussian with respect to the observations initially. The concepts of both conditionally Gaussian processes and an optimal-control approach to filtering are utilized in the filter development. A two-step, nonlinear, recursive estimation procedure (TNF), compatible with the logical structure of the optimal mean-square estimator, generates a finite-dimensional, nonlinear filter with improved characteristics over most of the traditional methods. Moreover, a "close" (in the mean-square sense) approximation model for the original system will be generated as well. In general the nonlinear filtering problem does not have a finite-dimensional recursive synthesis. Thus, the proposed technique may expand the range of practical problems that can be handled by nonlinear filtering. A detailed derivation for the filter with global property is presented. Extension of the results to largescale nonlinear systems is accomplished by incorporating a novel decomposition scheme in the filter design. Application of the developed filter to a scalar nonlinear system which lacks model "smoothness" is presented in [K2]. Application of the derived multi-dimensional filtering algorithm to two low-order, nonlinear tracking problems according to a global criterion and a local-time criterion respectively are presented. Also, a comparison with traditional methods, such as the popular Extended-Kalman Filter (EKE), are given via digital-computer simulation to demonstrate the effectiveness of the obtained results.
Download or read book Nonlinear Filters written by Peyman Setoodeh and published by John Wiley & Sons. This book was released on 2022-03-04 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Linear and Nonlinear Filtering for Scientists and Engineers written by Nasir Uddin Ahmed and published by World Scientific. This book was released on 1998 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: "many new results, especially on nonlinear filtering problems and their numerical techniques, are included in book form for the first time it will serve as a useful reference book on the recent progress in this field. The book can be used for teaching graduate courses to students in mathematics, probability, statistics, and engineering. And finally, doctoral students and young researchers in the area of filtering theory and its applications can find inspiring ideas and techniques".Journal of Applied Mathematics and Stochastic Analysis, 2000
Download or read book A Two Step Bilinear Filtering Approximation written by T. U. Halawani and published by . This book was released on 1984 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approximation technique to a certain class of nonlinear filtering (signal processing) problems is considered here. The method is based on an approximation of a nonlinear, partially observable system by a bilinear model with fully observable states. The filter development proceeds from the assumption that the unobservable states are conditionally Gaussian with respect to the observation initially. The method is shown to be promising for real-time communication and sonar applications as demonstrated by computer simulations. Moreover, some of the traditional techniques evolve as special cases of this methodology. (Author).
Download or read book Nonlinear Filtering written by Kumar Pakki Bharani Chan and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives readers in-depth know-how on methods of state estimation for nonlinear control systems. It starts with an introduction to dynamic control systems and system states and a brief description of the Kalman filter. In the following chapters, various state estimation techniques for nonlinear systems are discussed, including the extended, unscented and cubature Kalman filters, etc. The cubature Kalman filter and its variants are introduced in particular detail because of their efficiency and their ability to deal with systems with Gaussian and/or non-Gaussian noise. The book also discusses information-filter and square-root-filtering algorithms, useful for state estimation in some real-time control system design problems. A number of case studies are included in the book to illustrate the application of various nonlinear filtering algorithms. Nonlinear Filtering is written for academic and industrial researchers, engineers and research students who are interested in nonlinear control systems analysis and design. The chief features of the book include: dedicated coverage of recently developed nonlinear, Jacobian-free, filtering algorithms; examples illustrating the use of nonlinear filtering algorithms in real-world applications; detailed derivation and complete algorithms for nonlinear filtering methods help readers to a fundamental understanding and easier coding of those algorithms; and MATLAB codes associated with case-study applications can be downloaded from the Springer Extra Materials website.
Download or read book Numerical Studies in Nonlinear Filtering written by Yaakov Yavin and published by Springer. This book was released on 1985 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Efficient Nonlinear Adaptive Filters written by Haiquan Zhao and published by Springer Nature. This book was released on 2023-02-10 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the design, analysis, and application of nonlinear adaptive filters with the goal of improving efficient performance (ie the convergence speed, steady-state error, and computational complexity). The authors present a nonlinear adaptive filter, which is an important part of nonlinear system and digital signal processing and can be applied to diverse fields such as communications, control power system, radar sonar, etc. The authors also present an efficient nonlinear filter model and robust adaptive filtering algorithm based on the local cost function of optimal criterion to overcome non-Gaussian noise interference. The authors show how these achievements provide new theories and methods for robust adaptive filtering of nonlinear and non-Gaussian systems. The book is written for the scientist and engineer who are not necessarily an expert in the specific nonlinear filtering field but who want to learn about the current research and application. The book is also written to accompany a graduate/PhD course in the area of nonlinear system and adaptive signal processing.
Download or read book Approximate Solution for Nonlinear Filtering and Identification Problems written by Saleh M. Radaideh and published by . This book was released on 1995 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Filtering and identification problems of partially observable stochastic dynamical systems has been considered. A modification of the extended Kalman filter (EKF) called a modified extended Kalman filter (MEKF) and a theoretical justification for this modification have been investigated. A simple but powerful numerical method for the approximation of the unnormalized conditional (probability) density of filtered diffusion process which satisfies Zakai equation arises from diffusion processes observed in correlated (or uncorrelated) noises and solves the nonlinear filtering problem has been presented. Using Galerkin technique the solution of Zakai equation has been approximated by means of a sequence of nonstandard basis functions given by a parameterized family of Gaussian densities. The spatial domain for the solution of Zakai equation and the completeness of the Gaussian densities have been also investigated. The methods are illustrated by some numerical examples. Techniques of optimal control theory as well as linear filter theory have been utilized in identifying the parameters of linear (partially observable) stochastic differential systems. Using the method of simulated annealing a computational algorithm for identifying the unknown parameters from the available observation has been derived. The results are illustrated by some examples.
Download or read book Construction of Nonlinear Filter Algorithms Using the Saddlepoint Approximation written by Esosa O. Amayo and published by . This book was released on 2006 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we propose the use of the saddlepoint method to construct nonlinear filtering algorithms. To our knowledge, while the saddlepoint approximation has been used very successfully in the statistics literature (as an example the saddlepoint method provides a simple, highly accurate approximation to the density of the maximum likelihood estimator of a non-random parameter given a set of measurements), its potential for use in the dynamic setting of the nonlinear filtering problem has yet to be realized. This is probably because the assumptions on the form of the integrand that is typical in the asymptotic analysis literature do not necessarily hold in the filtering context. We show that the assumptions typical in asymptotic analysis (and which are directly applicable in statistical inference since the statistics applications usually involve estimating the density of a function of a sequence of random variables) can be modified in a way that is still relevant in the nonlinear filtering context while still preserving a property of the saddlepoint approximation that has made it very useful in statistical inference, namely, that the shape of the desired density is accurately approximated. As a result, the approximation can be used to calculate estimates of the mean and confidence intervals and also serves as an excellent choice of proposal density for particle filtering. We will show how to construct filtering algorithms based on the saddle point approximation.
Download or read book Nonlinear Estimation written by Shovan Bhaumik and published by CRC Press. This book was released on 2019-07-24 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Estimation: Methods and Applications with Deterministic Sample Points focusses on a comprehensive treatment of deterministic sample point filters (also called Gaussian filters) and their variants for nonlinear estimation problems, for which no closed-form solution is available in general. Gaussian filters are becoming popular with the designers due to their ease of implementation and real time execution even on inexpensive or legacy hardware. The main purpose of the book is to educate the reader about a variety of available nonlinear estimation methods so that the reader can choose the right method for a real life problem, adapt or modify it where necessary and implement it. The book can also serve as a core graduate text for a course on state estimation. The book starts from the basic conceptual solution of a nonlinear estimation problem and provides an in depth coverage of (i) various Gaussian filters such as the unscented Kalman filter, cubature and quadrature based filters, Gauss-Hermite filter and their variants and (ii) Gaussian sum filter, in both discrete and continuous-discrete domain. Further, a brief description of filters for randomly delayed measurement and two case-studies are also included. Features: The book covers all the important Gaussian filters, including filters with randomly delayed measurements. Numerical simulation examples with detailed matlab code are provided for most algorithms so that beginners can verify their understanding. Two real world case studies are included: (i) underwater passive target tracking, (ii) ballistic target tracking. The style of writing is suitable for engineers and scientists. The material of the book is presented with the emphasis on key ideas, underlying assumptions, algorithms, and properties. The book combines rigorous mathematical treatment with matlab code, algorithm listings, flow charts and detailed case studies to deepen understanding.
Download or read book Nonlinear Filtering and Stochastic Control written by S.K. Mitter and published by Springer. This book was released on 2006-11-15 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt:
