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Parameter Estimator (parameter + estimator)
Selected AbstractsA covariance-adaptive approach for regularized inversion in linear modelsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2007Christopher Kotsakis SUMMARY The optimal inversion of a linear model under the presence of additive random noise in the input data is a typical problem in many geodetic and geophysical applications. Various methods have been developed and applied for the solution of this problem, ranging from the classic principle of least-squares (LS) estimation to other more complex inversion techniques such as the Tikhonov,Philips regularization, truncated singular value decomposition, generalized ridge regression, numerical iterative methods (Landweber, conjugate gradient) and others. In this paper, a new type of optimal parameter estimator for the inversion of a linear model is presented. The proposed methodology is based on a linear transformation of the classic LS estimator and it satisfies two basic criteria. First, it provides a solution for the model parameters that is optimally fitted (in an average quadratic sense) to the classic LS parameter solution. Second, it complies with an external user-dependent constraint that specifies a priori the error covariance (CV) matrix of the estimated model parameters. The formulation of this constrained estimator offers a unified framework for the description of many regularization techniques that are systematically used in geodetic inverse problems, particularly for those methods that correspond to an eigenvalue filtering of the ill-conditioned normal matrix in the underlying linear model. Our study lies on the fact that it adds an alternative perspective on the statistical properties and the regularization mechanism of many inversion techniques commonly used in geodesy and geophysics, by interpreting them as a family of ,CV-adaptive' parameter estimators that obey a common optimal criterion and differ only on the pre-selected form of their error CV matrix under a fixed model design. [source] Improved adaptive control for the discrete-time parametric-strict-feedback formINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 12 2009Graciela Adriana González Abstract Adaptive control design for a class of single-input single-output nonlinear discrete-time systems in parametric-strict-feedback form is re-visited. No growth restrictions are assumed on the nonlinearities. The control objective is to achieve tracking of a reference signal. As usual, the algorithm derives from the combination of a control law and a parameter estimator (certainty equivalence principle). The parameter estimator strongly lies on the regressor subspace identification by means of an orthogonalization process. Certain drawbacks of previous schemes are analyzed. Several modifications on them are considered to improve the algorithm complexity, control performance and numerical stability. As a result, an alternative control scheme is proposed. When applied to the proposed class of systems, global boundedness and convergence remain as achieved objectives while improving the performance issues of previous schemes. Copyright © 2009 John Wiley & Sons, Ltd. [source] Robust stabilization of a class of non-minimum-phase nonlinear systems in a generalized output feedback canonical formINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 3 2009Jun Fu Abstract In this paper, a globally robust stabilizer for a class of uncertain non-minimum-phase nonlinear systems in generalized output feedback canonical form is designed. The system contains unknown parameters multiplied by output-dependent nonlinearities and output-dependent nonlinearities enter such a system both additively and multiplicatively. The proposed method relies on a recently developed novel parameter estimator and state observer design methodology together with a combination of backstepping and small-gain approach. Our design has three distinct features. First, the parameter estimator and state observer do not necessarily follow the classical certainty-equivalent principle any more. Second, the design treats unknown parameters and unmeasured states in a unified way. Third, the technique by combining standard backstepping and small-gain theorem ensures robustness with respect to dynamic uncertainties. Finally, two numerical examples are given to show that the proposed method is effective, and that it can be applied to more general systems that do not satisfy the cascading upper diagonal dominance conditions developed in recent papers, respectively. Copyright © 2008 John Wiley & Sons, Ltd. [source] Adaptive control of Burgers' equation with unknown viscosityINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 7 2001Wei-Jiu Liu Abstract In this paper, we propose a fortified boundary control law and an adaptation law for Burgers' equation with unknown viscosity, where no a priori knowledge of a lower bound on viscosity is needed. This control law is decentralized, i.e., implementable without the need for central computer and wiring. Using the Lyapunov method, we prove that the closed-loop system, including the parameter estimator as a dynamic component, is globally H1 stable and well posed. Furthermore, we show that the state of the system is regulated to zero by developing an alternative to Barbalat's Lemma which cannot be used in the present situation. Copyright © 2001 John Wiley & Sons, Ltd. [source] Variable structure robust state and parameter estimatorINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 2 2001Alex S. Poznyak Abstract The problem of simultaneous robust state and parameters estimation for a class of SISO non-linear systems under mixed uncertainties (unmodelled dynamics as well as observation noises) is addressed. A non-linear variable structure robust ,observer,identifier' is introduced to obtain the corresponding estimates. Lie derivative technique is used to obtain the observability conditions for the equivalent extended non-linear system. It is shown that, in general, the extended system can lose the global observability property and a special procedure is needed to work well in this situation. The suggested adaptive observer has the non-linear high-gain observer structure with adjusted parameters that provides ,a good' upper bound for the identification error performance index. The van der Monde transformation is used to derive this bound which turns out to be tight. Three examples dealing with a simple pendulum, the Duffing equation and the van del Pol oscillator are considered to illustrate the effectiveness of the suggested approach. Copyright © 2001 John Wiley & Sons, Ltd. [source] Hybrid modeling of inulinase bio-production processJOURNAL OF CHEMICAL TECHNOLOGY & BIOTECHNOLOGY, Issue 4 2010Marcio A. Mazutti Abstract BACKGROUND: A potential application of inulinase in the food industry is the production of fructooligosaccharides (FOS) through transfructosilation of sucrose. Besides their ability to increase the shelf-life and flavor of many products, FOS have many interesting functional properties. The use of an industrial medium may represent a good, cost-effective alternative to produce inulinase, since the activity of the enzyme produced may be improved or at least remain the same compared with that obtained using a synthetic medium. Thus, inulinase production for use in FOS synthesis is of considerable scientific and technological appeal, as is the development of a reliable mathematical model of the process. This paper describes a hybrid neural network approach to model inulinase production in a batch bioreactor using agroindustrial residues as substrate. The hybrid modeling makes use of a series artificial neural network to estimate the kinetic parameters of the process and the mass balance as constitutive equations. RESULTS: The proposed model was shown to be capable of describing the complex behavior of inulinase production employing agroindustrial residues as substrate, so that the mathematical framework developed is a useful tool for simulation of this process. CONCLUSION: The hybrid neural network model developed was shown to be an interesting alternative to estimate model parameters since complete elucidation of the phenomena and mechanisms involved in the fermentation is not required owing to the black-box nature of the ANN used as parameter estimator. Copyright © 2010 Society of Chemical Industry [source] The structured total least-squares approach for non-linearly structured matricesNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 4 2002P. Lemmerling Abstract In this paper, an extension of the structured total least-squares (STLS) approach for non-linearly structured matrices is presented in the so-called ,Riemannian singular value decomposition' (RiSVD) framework. It is shown that this type of STLS problem can be solved by solving a set of Riemannian SVD equations. For small perturbations the problem can be reformulated into finding the smallest singular value and the corresponding right singular vector of this Riemannian SVD. A heuristic algorithm is proposed. Some examples of Vandermonde-type matrices are used to demonstrate the improved accuracy of the obtained parameter estimator when compared to other methods such as least squares (LS) or total least squares (TLS). Copyright © 2002 John Wiley & Sons, Ltd. [source] Moment based regression algorithms for drift and volatility estimation in continuous-time Markov switching modelsTHE ECONOMETRICS JOURNAL, Issue 2 2008Robert J. Elliott Summary, We consider a continuous time Markov switching model (MSM) which is widely used in mathematical finance. The aim is to estimate the parameters given observations in discrete time. Since there is no finite dimensional filter for estimating the underlying state of the MSM, it is not possible to compute numerically the maximum likelihood parameter estimate via the well known expectation maximization (EM) algorithm. Therefore in this paper, we propose a method of moments based parameter estimator. The moments of the observed process are computed explicitly as a function of the time discretization interval of the discrete time observation process. We then propose two algorithms for parameter estimation of the MSM. The first algorithm is based on a least-squares fit to the exact moments over different time lags, while the second algorithm is based on estimating the coefficients of the expansion (with respect to time) of the moments. Extensive numerical results comparing the algorithm with the EM algorithm for the discretized model are presented. [source] A covariance-adaptive approach for regularized inversion in linear modelsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2007Christopher Kotsakis SUMMARY The optimal inversion of a linear model under the presence of additive random noise in the input data is a typical problem in many geodetic and geophysical applications. Various methods have been developed and applied for the solution of this problem, ranging from the classic principle of least-squares (LS) estimation to other more complex inversion techniques such as the Tikhonov,Philips regularization, truncated singular value decomposition, generalized ridge regression, numerical iterative methods (Landweber, conjugate gradient) and others. In this paper, a new type of optimal parameter estimator for the inversion of a linear model is presented. The proposed methodology is based on a linear transformation of the classic LS estimator and it satisfies two basic criteria. First, it provides a solution for the model parameters that is optimally fitted (in an average quadratic sense) to the classic LS parameter solution. Second, it complies with an external user-dependent constraint that specifies a priori the error covariance (CV) matrix of the estimated model parameters. The formulation of this constrained estimator offers a unified framework for the description of many regularization techniques that are systematically used in geodetic inverse problems, particularly for those methods that correspond to an eigenvalue filtering of the ill-conditioned normal matrix in the underlying linear model. Our study lies on the fact that it adds an alternative perspective on the statistical properties and the regularization mechanism of many inversion techniques commonly used in geodesy and geophysics, by interpreting them as a family of ,CV-adaptive' parameter estimators that obey a common optimal criterion and differ only on the pre-selected form of their error CV matrix under a fixed model design. [source] On-line almost-sure parameter estimation for partially observed discrete-time linear systems with known noise characteristicsINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 6 2002Robert J. Elliott Abstract In this paper we discuss parameter estimators for fully and partially observed discrete-time linear stochastic systems (in state-space form) with known noise characteristics. We propose finite-dimensional parameter estimators that are based on estimates of summed functions of the state, rather than of the states themselves. We limit our investigation to estimation of the state transition matrix and the observation matrix. We establish almost-sure convergence results for our proposed parameter estimators using standard martingale convergence results, the Kronecker lemma and an ordinary differential equation approach. We also provide simulation studies which illustrate the performance of these estimators. Copyright © 2002 John Wiley & Sons, Ltd. [source] Asymptotic bias in the linear mixed effects model under non-ignorable missing data mechanismsJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 1 2005Chandan Saha Summary., In longitudinal studies, missingness of data is often an unavoidable problem. Estimators from the linear mixed effects model assume that missing data are missing at random. However, estimators are biased when this assumption is not met. In the paper, theoretical results for the asymptotic bias are established under non-ignorable drop-out, drop-in and other missing data patterns. The asymptotic bias is large when the drop-out subjects have only one or no observation, especially for slope-related parameters of the linear mixed effects model. In the drop-in case, intercept-related parameter estimators show substantial asymptotic bias when subjects enter late in the study. Eight other missing data patterns are considered and these produce asymptotic biases of a variety of magnitudes. [source] Autoregressive processes with data-driven regime switchingJOURNAL OF TIME SERIES ANALYSIS, Issue 5 2009Joseph Tadjuidje Kamgaing Abstract., We develop a switching-regime vector autoregressive model in which changes in regimes are governed by an underlying Markov process. In contrast to the typical hidden Markov approach, we allow the transition probabilities of the underlying Markov process to depend on past values of the time series and exogenous variables. Such processes have potential applications in finance and neuroscience. In the latter, the brain activity at time t (measured by electroencephalograms) will be modelled as a function of both its past values as well as exogenous variables (such as visual or somatosensory stimuli). In this article, we establish stationarity, geometric ergodicity and existence of moments for these processes under suitable conditions on the parameters of the model. Such properties are important for understanding the stability properties of the model as well as for deriving the asymptotic behaviour of various statistics and model parameter estimators. [source] On Latent-Variable Model Misspecification in Structural Measurement Error Models for Binary ResponseBIOMETRICS, Issue 3 2009Xianzheng Huang Summary We consider structural measurement error models for a binary response. We show that likelihood-based estimators obtained from fitting structural measurement error models with pooled binary responses can be far more robust to covariate measurement error in the presence of latent-variable model misspecification than the corresponding estimators from individual responses. Furthermore, despite the loss in information, pooling can provide improved parameter estimators in terms of mean-squared error. Based on these and other findings, we create a new diagnostic method to detect latent-variable model misspecification in structural measurement error models with individual binary response. We use simulation and data from the Framingham Heart Study to illustrate our methods. [source] Semiparametric Transformation Models with Random Effects for Joint Analysis of Recurrent and Terminal EventsBIOMETRICS, Issue 3 2009Donglin Zeng Summary We propose a broad class of semiparametric transformation models with random effects for the joint analysis of recurrent events and a terminal event. The transformation models include proportional hazards/intensity and proportional odds models. We estimate the model parameters by the nonparametric maximum likelihood approach. The estimators are shown to be consistent, asymptotically normal, and asymptotically efficient. Simple and stable numerical algorithms are provided to calculate the parameter estimators and to estimate their variances. Extensive simulation studies demonstrate that the proposed inference procedures perform well in realistic settings. Applications to two HIV/AIDS studies are presented. [source] | ||||||||||