MMSE-Based Filtering for Linear and Nonlinear Systems in the Presence of Non-Gaussian System and Measurement Noise PDF Download
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Author: I. Bilik
Publisher:
ISBN: 9789533070001
Category :
Languages : en
Pages :
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Book Description
Two new recursive filters, named as GMKF and NL-GMKF, for linear and nonlinear, nonGaussian problems were presented in this chapter. The GMKF algorithm consists of the GSF followed by an efficient model order reduction method. The GSF provides a rigorous solution for state vector estimation in a linear DSS model with GMM-distributed system and measurement noises and it generalizes the original KF to GMMs. Practical implementation of the optimal GSF is limited due to the exponential model order growth. The GMKF solves this problem via an efficient model order reduction method. The problem of exponential growth of the model order was solved via the mixture PDF estimation at each step using the greedy EM algorithm. It was shown that greedy EM-based order reduction scheme does not.
Author: I. Bilik
Publisher:
ISBN: 9789533070001
Category :
Languages : en
Pages :
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Book Description
Two new recursive filters, named as GMKF and NL-GMKF, for linear and nonlinear, nonGaussian problems were presented in this chapter. The GMKF algorithm consists of the GSF followed by an efficient model order reduction method. The GSF provides a rigorous solution for state vector estimation in a linear DSS model with GMM-distributed system and measurement noises and it generalizes the original KF to GMMs. Practical implementation of the optimal GSF is limited due to the exponential model order growth. The GMKF solves this problem via an efficient model order reduction method. The problem of exponential growth of the model order was solved via the mixture PDF estimation at each step using the greedy EM algorithm. It was shown that greedy EM-based order reduction scheme does not.
Author: Víctor M. Moreno
Publisher: BoD – Books on Demand
ISBN: 9533070005
Category : Computers
Languages : en
Pages : 608
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Book Description
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: Kumar Pakki Bharani Chandra
Publisher: Springer
ISBN: 3030017974
Category : Technology & Engineering
Languages : en
Pages : 184
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Book Description
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. 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, which help readers to a fundamental understanding and easier coding of those algorithms; and MATLAB® codes associated with case-study applications, which can be downloaded from the Springer Extra Materials website.
Author: Jitendra R. Raol
Publisher: CRC Press
ISBN: 1498745180
Category : Technology & Engineering
Languages : en
Pages : 581
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Book Description
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.
Author: Richard Bucher Sowers
Publisher:
ISBN:
Category :
Languages : en
Pages : 218
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Book Description
We consider a discrete-time linear system with correlated Gaussian plant and observation noises and non-Gaussian initial condition independent of the plant and observation noises. We firstly find a solution for the filtering problem; we find a representation for the conditional distribution of the state at time t given the observations up to time t - 1. This representation is in terms of a finite collection of easily-computable statistics. With this solution to the filtering problem, we then find representations for the MMSE and LLSE estimates of the state given the previous observations, and the mean-square error between the two. (Of course the MMSE estimate will in general be a nonlinear function of the observations, whereas the LLSE estimate is by definition linear and is given by the KJman filtering equations.) We then consider the asymptotic behavior of the mean-square error between the MMSE and LLSE estimates as time tends to infinity. We find conditions on the system dynamics under which the effects of the initial condition die out; under these conditions the non-Gaussian nature of the initial condition becomes unimportant as t becomes large. The practical value of this result is dear-under these conditions, the LLSE estimate, which is usually less costly to generate than the MMSE estimate, is asymptotically as good as the MMSE estimate (i.e., asymptotically optimal) in the mean-square sense.
Author: Haiquan Zhao
Publisher: Springer Nature
ISBN: 3031208188
Category : Technology & Engineering
Languages : en
Pages : 271
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Book Description
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.
Author: Sumathi Prabhakaran Jeyakumari
Publisher:
ISBN:
Category :
Languages : en
Pages : 76
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Book Description
Filtering and estimation are two important tools of engineering. Whenever the state of the system needs to be estimated from the noisy sensor measurements, some kind of state estimator is used. If the dynamics of the system and observation model are linear under Gaussian conditions, the root mean squared error can be computed using the Kalman Filter. But practically, noise frequently enters the system as not strictly Gaussian. Therefore, the Kalman Filter does not necessarily provide the better estimate. Hence the estimation of the nonlinear system under non-Gaussian or quasi-Gaussian noise is of an acute interest. There are many versions of the Kalman filter such as the Extended Kalman filter, the Unscented Kalman filter, the Ensemble Kalman filter, the Particle filter, etc., each having their own disadvantages. In this thesis work I used a bridging strategy between the Ensemble Kalman filter and Particle filter called an Ensemble Kalman Particle filter. This filter works well in nonlinear system and non-Gaussian measurements as well. I analyzed this filter using MATLAB simulation and also applied Gaussian Noise, non-zero mean Gaussian Noise, quasi-Gaussian noise (with drift), random walk and Laplacian Noise. I applied these noises and compared the performances of the Particle filter and the Ensemble Kalman Particle filter in the presence of linear and nonlinear observations which leads to the conclusion that the Ensemble Kalman Particle filter yields the minimum error estimate. I also found the optimum value for the tuning parameter which is used to bridge the two filters using Monte Carlo Simulation.
Author: A. H. Haddad
Publisher:
ISBN:
Category :
Languages : en
Pages : 158
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Book Description
The study is concerned with the minimum-mean-squared error (MMSE) nonlinear filtering of signals in additive noise. Methods of analysis, representation, and classification of non-linear systems are treated. Integral representations and their applicability to random inputs and MMSE filtering are emphasized. The general MMSE nonlinear filtering problem is discussed briefly; the restriction of the filter to general classes of systems or input processes is considered. Usually the general solutions to the problem are difficult and in many cases are impractical; therefore restriction to special classes of systems and special classes of input processes is investigated. (Author).
Author: Robert Henry Richard
Publisher:
ISBN:
Category : Electric filters
Languages : en
Pages : 1
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Book Description
A nonlinear filter is investigated and its effectiveness in improving signal detectability in the presence of certain types of non-Gaussian noise is determined. The filter consists of a zero-memory nonlinear device followed by a lowpass filter, the nonlinear device being designed on the basis of only the first-order statistics of the interfering noise and of the sum of signal and noise. The class of noise used in the study is that obtained by passing Gaussian noise through a zero-memory nonlinear element. Because of this the non-Gaussian process can still be characterized by relatively few parameters. The results of the study indicate that, when the noise probability density function is sufficiently different from Gaussian, a considerable improvement in detection reliability can be obtained. When the noise is Gaussian the filter reduces to a linear one. (Author).
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 756
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Book Description
