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Author: Yury A. Kutoyants
Publisher:
ISBN: 9789401110211
Category :
Languages : en
Pages : 314
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Book Description
Author: Yury A. Kutoyants
Publisher:
ISBN: 9789401110211
Category :
Languages : en
Pages : 314
Get Book Here
Book Description
Author: Yury A. Kutoyants
Publisher: Springer Science & Business Media
ISBN: 9401110204
Category : Mathematics
Languages : en
Pages : 308
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Book Description
Small noise is a good noise. In this work, we are interested in the problems of estimation theory concerned with observations of the diffusion-type process Xo = Xo, 0 ~ t ~ T, (0. 1) where W is a standard Wiener process and St(') is some nonanticipative smooth t function. By the observations X = {X , 0 ~ t ~ T} of this process, we will solve some t of the problems of identification, both parametric and nonparametric. If the trend S(-) is known up to the value of some finite-dimensional parameter St(X) = St((}, X), where (} E e c Rd , then we have a parametric case. The nonparametric problems arise if we know only the degree of smoothness of the function St(X), 0 ~ t ~ T with respect to time t. It is supposed that the diffusion coefficient c is always known. In the parametric case, we describe the asymptotical properties of maximum likelihood (MLE), Bayes (BE) and minimum distance (MDE) estimators as c --+ 0 and in the nonparametric situation, we investigate some kernel-type estimators of unknown functions (say, StO,O ~ t ~ T). The asymptotic in such problems of estimation for this scheme of observations was usually considered as T --+ 00 , because this limit is a direct analog to the traditional limit (n --+ 00) in the classical mathematical statistics of i. i. d. observations. The limit c --+ 0 in (0. 1) is interesting for the following reasons.
Author: Nils Berglund
Publisher: Springer Science & Business Media
ISBN: 1846281865
Category : Mathematics
Languages : en
Pages : 283
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Book Description
Stochastic Differential Equations have become increasingly important in modelling complex systems in physics, chemistry, biology, climatology and other fields. This book examines and provides systems for practitioners to use, and provides a number of case studies to show how they can work in practice.
Author: Rolf Isermann
Publisher: Springer
ISBN: 9783540871552
Category : Technology & Engineering
Languages : en
Pages : 705
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Book Description
Precise dynamic models of processes are required for many applications, ranging from control engineering to the natural sciences and economics. Frequently, such precise models cannot be derived using theoretical considerations alone. Therefore, they must be determined experimentally. This book treats the determination of dynamic models based on measurements taken at the process, which is known as system identification or process identification. Both offline and online methods are presented, i.e. methods that post-process the measured data as well as methods that provide models during the measurement. The book is theory-oriented and application-oriented and most methods covered have been used successfully in practical applications for many different processes. Illustrative examples in this book with real measured data range from hydraulic and electric actuators up to combustion engines. Real experimental data is also provided on the Springer webpage, allowing readers to gather their first experience with the methods presented in this book. Among others, the book covers the following subjects: determination of the non-parametric frequency response, (fast) Fourier transform, correlation analysis, parameter estimation with a focus on the method of Least Squares and modifications, identification of time-variant processes, identification in closed-loop, identification of continuous time processes, and subspace methods. Some methods for nonlinear system identification are also considered, such as the Extended Kalman filter and neural networks. The different methods are compared by using a real three-mass oscillator process, a model of a drive train. For many identification methods, hints for the practical implementation and application are provided. The book is intended to meet the needs of students and practicing engineers working in research and development, design and manufacturing.
Author: Arunabha Bagchi
Publisher:
ISBN:
Category : Electronic noise
Languages : en
Pages : 82
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Book Description
The present dissertation is a study of identifying parameters of a continuous-time dynamical system with noisy observation and with or without noise in the state of the system. In identifying parameters of a continuous-time dynamical system, the difficulty arises when the observation noise covariance is unknown. The present paper solves this problem in the case of a linear time invariant system with white noise affecting additively both the state and the observation. Likelihood functional cannot be obtained when the observation noise covariance is unknown. A similar procedure, however, works and the estimates are obtained by finding roots of an appropriate functional. It is shown that the estimates obtained are weakly consistent. In the special case of no noise in the state, it is further shown that similar procedure yields estimates that are strongly consistent. Consistency is proved under certain sufficient condition called the 'Identifiability Condition'. This condition is studied in detail and computational algorithm for determining the estimates is discussed.
Author: Frank Moss
Publisher: Cambridge University Press
ISBN: 0521352290
Category : Mathematics
Languages : en
Pages : 410
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Book Description
A specially written review of all areas of noise and nonlinear in natural environments.
Author: Odell R. Reynolds
Publisher:
ISBN: 9781423573463
Category : Differentiable dynamical systems
Languages : en
Pages : 155
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Book Description
Sensor noise is an unavoidable fact of life when it comes to measurements on physical systems, as is the case in feedback control. Therefore, it must be properly addressed during dynamic system identification. In this work, a novel approach is developed toward the treatment of measurement noise in dynamical systems. This approach hinges on proper stochastic modeling, and it can be adapted easily to many different scenarios, where it yields consistently good parameter estimates. The Generalized Minimum Variance algorithm developed and used in this work is based on the theory behind the minimum variance identification process, and the estimate produced is a fixed point of a mapping based on the minimum variance solution. Additionally, the algorithm yields an accurate prediction of the estimation error. This algorithm is applied to many different noise models associated with three basic identification problems. First, continuous-time systems are identified using frequency domain measurements. Next, a discrete-time plant is identified using discrete-time measurements. Finally, the physical parameters of a continuous-time plant are identified using sampled measurements of the continuous-time input and output. Validation of the estimates is performed correctly, and the results are compared with other, more common, identification algorithms.
Author: Yu KUTOYANTS
Publisher:
ISBN:
Category :
Languages : en
Pages : 298
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Book Description
Auxiliary results, asymptotic properties of estimators in standard and nonstandard situations, expansions, nonparametric estimation, the disorder problem, partially observed systems, minimum distance estimation.
Author: D. C. Saha
Publisher:
ISBN: 9783662199008
Category :
Languages : en
Pages : 176
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Book Description
Author: Yasumichi Hasegawa
Publisher: Springer Science & Business Media
ISBN: 3540794336
Category : Technology & Engineering
Languages : en
Pages : 249
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Book Description
This monograph deals with approximation and noise cancellation of dynamical systems which include linear and nonlinear input/output relations. It will be of special interest to researchers, engineers and graduate students who have specialized in ?ltering theory and system theory. From noisy or noiseless data, reductionwillbemade.Anewmethodwhichreducesnoiseormodelsinformation will be proposed. Using this method will allow model description to be treated as noise reduction or model reduction. As proof of the e?cacy, this monograph provides new results and their extensions which can also be applied to nonlinear dynamical systems. To present the e?ectiveness of our method, many actual examples of noise and model information reduction will also be provided. Using the analysis of state space approach, the model reduction problem may have become a major theme of technology after 1966 for emphasizing e?ciency in the ?elds of control, economy, numerical analysis, and others. Noise reduction problems in the analysis of noisy dynamical systems may havebecomeamajorthemeoftechnologyafter1974foremphasizinge?ciencyin control.However,thesubjectsoftheseresearcheshavebeenmainlyconcentrated in linear systems. In common model reduction of linear systems in use today, a singular value decompositionofaHankelmatrixisusedto?ndareducedordermodel.However, the existence of the conditions of the reduced order model are derived without evaluationoftheresultantmodel.Inthecommontypicalnoisereductionoflinear systems in use today, the order and parameters of the systems are determined by minimizing information criterion. Approximate and noisy realization problems for input/output relations can be roughly stated as follows: A. The approximate realization problem. For any input/output map, ?nd one mathematical model such that it is similar totheinput/outputmapandhasalowerdimensionthanthegivenminimalstate spaceofadynamicalsystemwhichhasthesamebehaviortotheinput/outputmap. B. The noisy realization problem.
