Skip to content
Free planNo credit card requiredStart writing
AI for Research home
AI for Research home
Dashboard
Sign inGet started

Search 250 million research papers

Read the abstract, see who wrote it and who cites it, and get the citation in APA, MLA, Chicago or Harvard.

About 10,000 papers for “nonlinear estimation”

Nonlinear Estimation

E. W. Kamen, J. K. Su · Advanced textbooks in control and signal processing · 1999

Cited by 0

Simultaneous Nonlinear Estimation

John J. Beauchamp, Richard G. Cornell · Technometrics · 1966

An iterative procedure is given for the estimation of a vector of parameters some of which may be common to more than one of a set of nonlinear regression equations in the model presented. The procedure is given for the situation when the covariance matrix in the model is known and is extended to include the model when the covariance matrix is unknown. The covariance matrix allows for correlation between observations made on different regression equations but for the same value of the independent vector of variables. Under certain assumptions the procedure is shown to converge to a consistent estimator of the vector of parameters with probability one. The procedure is illustrated with data from a compartmental tracer experiment.

Cited by 34

NONLINEAR ESTIMATION THEORY

John H. Seinfeld · Industrial & Engineering Chemistry · 1970

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTNONLINEAR ESTIMATION THEORYJohn H. SeinfeldCite this: Ind. Eng. Chem. 1970, 62, 1, 32–42Publication Date (Print):January 1, 1970Publication History Published online1 May 2002Published inissue 1 January 1970https://doi.org/10.1021/ie50721a006RIGHTS & PERMISSIONSArticle Views188Altmetric-Citations24LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (1 MB) Get e-Alerts

Cited by 47

Nonlinear Parameter Estimation

Martin Magnevall, Andreas Josefsson, Kjell Ahlin · KTH Publication Database DiVA (KTH Royal Institute of Technology) · 2017

The industrial demand on good dynamical simulation models is increasing. Since most structures show some form of nonlinear behavior, linear models are not good enough to predict the true dynamical behavior. Therefore nonlinear characterization, localization and parameter estimation becomes important issues when building simulation models. This paper presents identification techniques for nonlinear systems based on both random and harmonic excitation signals. The identification technique based on random excitation builds on the well known reverse-path method developed by Julius S. Bendat. This method treats the nonlinearity as a feedback forcing term acting on an underlying linear system and the parameter estimation is performed in the frequency domain by using conventional MISO/MIMO techniques. Although this method provides a straightforward and systematic way of handling nonlinearities, it has been somewhat limited in use due to the complexity of creating uncorrelated inputs to the model. As is shown in this paper, the parameter estimation will not be improved with conditioned inputs and the nonlinear parameters and the underlying linear system can still be estimated with partially correlated inputs. This paper will also describe a parameter estimation method to be used with harmonic input signals. By using the principle of harmonic balance and multi-harmonic balance it is possible to estimate an analytical frequency response function of the studied nonlinear system. This frequency response function can, in conjunction with measured nonlinear transfer functions, be used to estimate the nonlinearity present in the system. This method is also applicable on nonlinear systems with memory, e.g. systems with hysteresis effects. The above mentioned methods are applied to multi-degree-of-freedom and single-degree-of-freedom systems with different types of nonlinearities. Also, techniques for locating nonlinearities are discussed.

Cited by 34Open access

Nonlinear MEI Estimation

Kumaraswamy Virupakshan · Harvard Dataverse · 2026

This contains data for MEI curve estimation and select test results

Cited by 0Open access

Approximate nonlinear estimation.

Phaneuf, Roger Joseph. · DSpace@MIT (Massachusetts Institute of Technology) · 1968

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 1968

Cited by 4

Nonlinear Estimation and Classification

Yuhong Yang · Journal of the American Statistical Association · 2004

(2004). Nonlinear Estimation and Classification. Journal of the American Statistical Association: Vol. 99, No. 466, pp. 561-561.

Cited by 27

Nonlinear least squares estimation

John M. Lewis, S. Lakshmivarahan, Sudarshan Dhall · Cambridge University Press eBooks · 2006

In this chapter our aim is to provide an introduction to the nonlinear least squares problem. In practice many of the problems of interest are nonlinear in nature. These include several problems of interest in radar and satellite meteorology, exploration problems in geology, and tomography, to mention a few. In Section 7.1, we describe the first-order method which in many ways is a direct extension of the ideas developed in Chapters 5 and 6. This method is based on a classical idea from numerical analysis – replacing h(x) by its linear approximation at a given operating point xc, and solving a linear problem to obtain a new operating point, xnew, which is closer to the target state, x, than the original starting point. By repeatedly applying this idea, we can get as close to the target state as needed. The second-order counterpart of this idea is to replace h(x) by its quadratic approximation and, except for a few algebraic details, this method essentially follows the above iterative paradigm. This second-order method is described in Section 7.2.

Cited by 1

Nonlinear Blind Parameter Estimation

Sébastien Lagrange, Luc Jaulin, Vincent Vigneron et al. · IEEE Transactions on Automatic Control · 2008

This note deals with parameter estimation of nonlinear continuous-time models when the input signals of the corresponding system are not measured. The contribution of the note is to show that, with simple priors about the unknown input signals and using derivatives of the output signals, one can perform the estimation procedure. As an illustration, we consider situations where the simple priors, e.g., independence or Gaussianity of the unknown inputs, is assumed.

Cited by 4Open access

Exact Nonlinear State Estimation

Hristo G. Chipilski · Journal of the Atmospheric Sciences · 2025

Abstract The majority of data assimilation (DA) methods in the geosciences are based on Gaussian assumptions. While such approximations facilitate efficient algorithms, they cause analysis biases and subsequent forecast degradations. Nonparametric, particle-based DA algorithms have superior accuracy, but their application to high-dimensional models still poses operational challenges. Drawing inspiration from recent advances in the fields of measure transport and generative artificial intelligence, this paper develops a new estimation-theoretic framework which can incorporate general invertible transformations in a principled way. Specifically, a conjugate transform filter (CTF) is derived and shown to extend the celebrated Kalman filter to a much broader class of non-Gaussian distributions. The new filter has several desirable properties, such as its ability to preserve statistical relationships in the prior state and converge to highly accurate observations. An ensemble approximation of the new filtering framework is also presented and validated through idealized examples. The numerical demonstrations feature bounded quantities with non-Gaussian distributions, which is a typical challenge in Earth system models. Results suggest that the greatest benefits from the new filtering framework occur when the observation errors are small relative to the forecast uncertainty and when state variables exhibit strong nonlinear dependencies. Significance Statement Data assimilation (DA) is the science of combining numerical models and observations. Common applications include estimating the state of large geophysical systems and inferring unknown model parameters. The Kalman filter and its many variants, which played a crucial role for the success of the Apollo space missions, is still the workhorse of operational DA algorithms. However, Kalman’s theory is based on highly restrictive assumptions which often compromise the DA accuracy. To address this challenge, the present article derives a new filtering theory in which the Kalman filter emerges as a special case. The flexibility of the proposed framework and its ability to integrate powerful mathematical techniques commonly used in artificial intelligence (AI) applications opens promising new avenues for improving conventional DA algorithms.

Cited by 5

Nonlinear Least Squares Estimation

H. O. Hartley, Aaron Booker · The Annals of Mathematical Statistics · 1965

We are given a set of $N$ responses $Y_t$ which have arisen from a nonlinear regression model \begin{equation*}\tag{(1.1)}Y_t = f(x_t, \theta) + e_t; \quad t = 1, 2, \cdots, N.\end{equation*} Here $x_t$ denotes the $t$th fixed input vector of $k$ elements giving rise to $Y_t$, whilst $\theta$ is an $m$-element unknown parameter vector with elements $\theta_i$ and the $e_t$ are a set of $N$ independent error residuals from $N(0, \sigma^2)$ with $\sigma^2$ unknown. The expectations of the $Y_t$, are therefore the functions $f(x_t, \theta)$ which will be assumed to satisfy certain regularity conditions. The problem is to estimate $\theta$ notably by least squares. In this paper we shall develop an iterative method of solution of the least squares equations which has the following properties: (a) the computational procedure is convergent for finite $N$; (b) the resulting estimators are asymptotically $100{\tt\#}$ efficient as $N \rightarrow \infty$. In Sections 2-4 we give a survey of our results leaving the mathematical proofs to Sections 5-7 whilst in Section 8 we illustrate our method with an example. Although our theoretical development is oriented towards our specific goals certain results are proved in a somewhat more general form. Some of our theory will be seen to correspond to well known theorems on stochastic limits which have to be reproved because of certain modifications which we require.

Cited by 108Open access

Estimation of nonlinear dynamics.

Jane Hung, J. David Irwin · NASA Technical Reports Server (NASA) · 1967

Nonlinear dynamics discrete estimation by computational algorithm involving nonlinear algebraic equations

Cited by 0