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recursive parameter estimation for Hammerstein-Wiener systems using modified EKF algorithm

ISA TRANSACTIONS 2017年 70卷 104-115页

作者： Yu, Feng Mao, Zhizhong Yuan, Ping He, Dakuo Jia, Mingxing Northeastern Univ Dept Control Theory & Control Engn 11Lane 3WenHua Rd Shenyang Liaoning Peoples R China

This paper focuses on the recursive parameter estimation for the single input single output Hammerstein-Wiener system model, and the study is then extended to a rarely mentioned multiple input single output Hammerstein-Wiener system. Inspired by the extended Kalman filter algorithm, two basic recursive algorithms are derived from the first and the second order Taylor approximation. Based on the form of the first order approximation algorithm, a modified algorithm with larger parameter convergence domain is proposed to cope with the problem of small parameter convergence domain of the first order one and the application limit of the second order one. The validity of the modification on the expansion of convergence domain is shown from the convergence analysis and is demonstrated with two simulation cases. (C) 2017 ISA. Published by Elsevier Ltd. All rights reserved.

关键词： Hammerstein-Wiener system recursive parameter estimation Extended Kalman filter algorithm Multiple input single output Uniform convergence

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recursive parameter estimation and its convergence for bilinear systems

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IET CONTROL THEORY AND APPLICATIONS 2020年第5期14卷 677-688页

作者： Zhang, Xiao Ding, Feng Jiangnan Univ Sch Internet Things Engn Key Lab Adv Proc Control Light Ind Minist Educ Wuxi 214122 Jiangsu Peoples R China Qingdao Univ Sci & Technol Coll Automat & Elect Engn Qingdao 266061 Peoples R China

This study develops an adaptive filtering-based recursive identification algorithm for joint estimation of states and parameters of bilinear state-space systems with an autoregressive moving average noise. In order to handle the correlated noise and unmeasurable states in parameter estimation, an adaptive filter is established to whiten the coloured noise and a bilinear state observer is constructed to update the unavailable states recursively. Then a hierarchical generalised extended least squares (HGELS) algorithm and an adaptive filtering-based HGELS algorithm are developed for simultaneously estimating the unknown states and parameters. The convergence analysis indicates that the parameter estimates can converge to their true values. A numerical example illustrates the convergence results.

关键词： least squares approximations adaptive filters estimation theory parameter estimation bilinear systems autoregressive moving average processes filtering theory state-space methods observers recursive estimation approximation theory convergence of numerical methods recursive parameter estimation bilinear systems adaptive filtering-based recursive identification algorithm joint estimation bilinear state-space systems autoregressive moving average noise correlated noise unmeasurable states adaptive filter coloured noise bilinear state observer hierarchical generalised extended least squares algorithm adaptive filtering-based HGELS algorithm unknown states convergence analysis

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recursive parameter estimation of thermostatically controlled loads via unscented Kalman filter

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SUSTAINABLE ENERGY GRIDS & NETWORKS 2016年 8卷 12-25页

作者： Burger, Eric M. Moura, Scott J. Univ Calif Berkeley Energy Control & Applicat Lab Berkeley CA 94720 USA

For thermostatically controlled loads (TCLs) to perform demand response services in real-time markets, online methods for parameter estimation are needed. As the physical characteristics of a TCL change (e.g. the contents of a refrigerator or the occupancy of a conditioned room), it is necessary to update the parameters of the TCL model. Otherwise, the TCL will be incapable of accurately predicting its potential energy demand, thereby decreasing the reliability of a TCL aggregation to perform demand response. In this paper, we investigate the potential of various unscented Kalman filter (UKF) algorithm variations to recursively identify a TCL model that is non-linear in the parameters. Experimental results demonstrate the parameter estimation of two residential refrigerators. Finally, simulation results demonstrate the incorporation of the recursive parameter estimation methods into a model predictive controller for demand response. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Smart grid Unscented Kalman filter Online system identification recursive parameter estimation Thermostatically controlled loads (TCL) Demand response

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recursive parameter estimation for Continuous-time Bivariate Markov Chains

Recursive Parameter Estimation for Continuous-time Bivariate...

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作者： Li, Zhuxuan George Mason University

学位级别：master

A continuous-time bivariate Markov chain comprises a pair of continuous-time randomprocesses which are jointly Markov. One of the two processes is an underlying process whilethe other is assumed observable. An important special bivariate Markov chain is given bythe continuous-time Markov modulated Poisson process (MMPP). The underlying process ofan MMPP is a Markov chain, and the observable process is conditionally Poisson. Discretetimebivariate Markov chains may also be de ned, but they shall not be studied in thisthesis. Bivariate Markov chains are useful in modeling ion-channel currents in living cells,Internet tra c, and in other problems in queuing theory. In this thesis we focus on recursiveestimation of the parameter of a bivariate Markov chain which comprises its in nitesimalgenerator. We study a stochastic approximation approach using a newly developed recursionfor the gradient of the log-likelihood function of the observed signal. The recursive algorithmis compared with a batch expectation-maximization (EM) algorithm developed earlier. Thebias and mean squared error obtained in estimating each component of the parameter usingeach algorithm are evaluated and compared. The recursive algorithm requires far moredata to provide an estimate comparable to that obtained by the EM algorithm, but theEM algorithm iterates over the entire data multiple times. The main advantage of the recursive estimator is its ability to adapt to slow changes in the underlying statistics of themodel. The EM algorithm is a batch approach which must be re-applied whenever newdata becomes available or there is a change in the underlying statistics of the model

关键词： Bivariate Markov chain Markov modulated Poisson process recursive parameter estimation EM algorithm

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Batch scheme recursive parameter estimation of continuous-time systems using the modulating functions method

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AUTOMATICA 1997年第6期33卷 1185-1191页

作者： Co, TB Ungarala, S Department of Chemical Engineering Michigan Technological University Houghton MI 49931 United States

The modulating functions method is a very effective method for parameter estimation of continuous-time systems that are linear in their parameters. One efficient implementation developed by Pearson and Lee involves the use of trigonometric functions and fast computations offered by FPT techniques. In this paper, a recursive implementation of the method is developed for on-line parameter estimation of a continuous-time system by shifting a fixed window of time series data one step forward at each sampling instant. The resulting recursion algorithms are fast, and use the identities of discrete Fourier transforms along with some inherent commutative properties. A simulation example with a Van der Pol oscillator is included to investigate the performance of the proposed estimation method. (C) 1997 Elsevier Science Ltd.

关键词： recursive parameter estimation modulating functions method Pearson-Lee method discrete Fourier transform

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Sensitivity models for nonlinear filters with application to recursive parameter estimation for nonlinear state-space models

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IEE PROCEEDINGS-CONTROL THEORY AND APPLICATIONS 2001年第2期148卷 137-145页

作者： Bohn, C Unbehauen, H Continental AG Strateg Technol Dept D-30419 Hannover Germany Ruhr Univ Bochum Dept Elect Elect & Informat Sci Control Engn Lab D-44780 Bochum Germany

If a recursive prediction error method is applied for the parameter estimation of state-space models, a filter must be used as the predictor, resulting in an adaptive filtering problem. Whereas for linear systems the optimal linear filter, the Kalman filter, can be used, approximate nonlinear filters have to be employed for nonlinear systems. For the parameter estimation, the gradient of the prediction error, and maybe the gradient of its covariance matrix as well, are required. These can be obtained from a sensitivity model;however, the derivation of such a sensitivity model is tedious and has only been done for the extended Kalman filter. Sensitivity models for four common continuous-discrete nonlinear filters are derived: the extended Kalman filter, the first-order bias-corrected filter, the truncated second-order filter, and the modified Gaussian second-order filter. The derivation of these sensitivity models relies heavily on the use of matrix differential calculus, and utilises a reformulation of the approximate nonlinear filters derived earlier. Elementwise derivatives and bookkeeping over indices are thus entirely avoided. An adaptive filter is applied for real-time parameter identification and tracking for a laboratory three-tank process.

关键词： adaptive filtering problem first-order bias-corrected filter recursive estimation Simulation, modelling and identification truncated second-order filter recursive parameter estimation state-space methods continuous-discrete nonlinear filter nonlinear control systems Nonlinear control systems Kalman filters recursive prediction error method approximate nonlinear filters modified Gaussian second-order filter Other topics in statistics Control system analysis and synthesis methods flow control matrix differential calculus nonlinear filters laboratory three-tank process extended Kalman filter nonlinear state-space models Level, flow and volume control Signal processing theory sensitivity models

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recursive parameter estimation for counting processes with linear intensity

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Stochastics 1986年第3-4期18卷 277-312页

recursive estimation algorithms are presented for counting processes that have an intensity process which is linear in the parameter. Strong consistency and asymptotic normality of the estimators generated by the algo... 详细信息

关键词： Counting process recursive parameter estimation linear intensity

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A multistart weight-adaptive recursive parameter estimation method

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WATER RESOURCES RESEARCH 2008年第4期44卷

作者： Pauwels, Valentijn R. N. Univ Ghent Lab Hydrol & Water Management B-9000 Ghent Belgium

The determination of the parameters for hydrologic models has been the subject of a large number of studies during the last 3 decades. A multitude of methods have been developed for this purpose. Generally, the mismatch between the model simulations and the observations is lumped into an objective function, which is then is optimized by these methods. This can lead to parameter values that result in a good model performance under certain (e. g., low flow) conditions but not under other (e. g., high flow) conditions. The objective of this paper is to demonstrate a calibration algorithm which leads to a good model performance under all boundary conditions. This algorithm is referred to as Multistart Weight-Adaptive recursive parameter estimation (MWARPE). For this purpose the equations of the Extended Kalman Filter (EKF) have been used recursively in a Monte-Carlo approach, strongly increasing the chance that a globally optimal parameter set is obtained instead of a local optimum. The method has been applied to a rainfall-runoff model for the Zwalm catchment in Belgium, using a 1-year, a 2-year, and a 3-year calibration period. The results have been compared to the Shuffled Complex Evolution (SCE)-UA method. A synthetic study revealed that for narrow parameter limits the SCE-UA algorithm outperformed MWARPE, while for broad parameter limits the opposite occurred. For the test case using in situ observed data, the SCE-UA method resulted in slightly lower RMSE values than MWARPE, but MWARPE performed better outside the calibration period. It has been found that MWARPE can bypass local optima in the determination of the final parameter set. Also, the best initial parameter sets (with the lowest RMSE) do not lead to the best final parameter values. To apply the method only four parameters need to be specified, more specifically the number of starting points, the number of iterations per starting point, one parameter used to initialize the model error covariance matrix, an

关键词： model calibration Extended Kalman Filter recursive parameter estimation

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CONSTRAINED recursive parameter estimation FOR ADAPTIVE CONTROL

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IFAC Proceedings Volumes 2007年第5期40卷 279-284页

作者： Angadh Singh Abhijit S. Badwe Sachin C. Patwardhan Department of Chemical Engineering Indian Institute of Technology Bombay Powai Mumbai 400076 India

In adaptive control of systems with poles close to the unit circle, application of recursive estimation techniques can lead to excursions of poles outside the unit circle even when the process has no unstable poles. In this work, we propose a novel constrained formulation for recursive estimation of parameters using pseudo linear regression approach. The Jury's stability criterion is used to impose constraints in the parameter space. The proposed strategy has considerable computational advantage when compared to moving window constrained estimation . We demonstrate the efficacy of the proposed method using experimental data collected from a laboratory heater-mixer setup.

关键词： recursive parameter estimation Constrained estimation Dynamic Data Reconciliation Jury's stability criterion Pseudo linear regression

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Gauss, Kalman and Advances in recursive parameter estimation

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JOURNAL OF FORECASTING 2011年第1期30卷 104-146页

作者： Young, Peter C. Univ Lancaster Lancaster Environm Ctr Lancaster LA1 England Australian Natl Univ Fenner Sch Environm & Soc Canberra ACT Australia Univ New S Wales Sch Elect Engn & Telecommun Sydney NSW Australia

The paper considers how the Kalman filter has influenced the development of recursive parameter estimation since the publication of Rudolf Kalman's seminal article in 1960. It will present a partial review of developments over the past half century and provide a tutorial introduction to the refined instrumental variable approach to the optimal recursive estimation of parameters in both discrete and continuous-time transfer function models. The paper concludes with a case study that shows how recursive parameter estimation and the Kalman filter can be combined in the design and development of a real-time adaptive forecasting and data assimilation system for flow in river systems. Copyright (C) 2010 John Wiley & Sons, Ltd.

关键词： Kalman filter recursive parameter estimation adaptive forecasting

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