An Unscented Kalman Filter Approach to the Estimation of Nonlinear Dynamical Systems Models
In the past several decades, methodologies used to estimate nonlinear relationships among latent variables have been developed almost exclusively to fit cross-sectional models. We present a relatively new estimation approach, the unscented Kalman filter (UKF), and illustrate its potential as a tool...
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| Published in | Multivariate behavioral research Vol. 42; no. 2; pp. 283 - 321 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
United States
Taylor & Francis Group
01.04.2007
Lawrence Erlbaum Taylor & Francis Ltd |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0027-3171 1532-7906 |
| DOI | 10.1080/00273170701360423 |
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| Abstract | In the past several decades, methodologies used to estimate nonlinear relationships among latent variables have been developed almost exclusively to fit cross-sectional models. We present a relatively new estimation approach, the unscented Kalman filter (UKF), and illustrate its potential as a tool for fitting nonlinear dynamic models in two ways: (1) as a building block for approximating the log-likelihood of nonlinear state-space models and (2) to fit time-varying dynamic models wherein parameters are represented and estimated online as other latent variables. Furthermore, the substantive utility of the UKF is demonstrated using simulated examples of (1) the classical predator-prey model with time series and multiple-subject data, (2) the chaotic Lorenz system and (3) an empirical example of dyadic interaction. |
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| AbstractList | In the past several decades, methodologies used to estimate nonlinear relationships among latent variables have been developed almost exclusively to fit cross-sectional models. We present a relatively new estimation approach, the unscented Kalman filter (UKF), and illustrate its potential as a tool for fitting nonlinear dynamic models in two ways: (1) as a building block for approximating the log-likelihood of nonlinear state-space models and (2) to fit time-varying dynamic models wherein parameters are represented and estimated online as other latent variables. Furthermore, the substantive utility of the UKF is demonstrated using simulated examples of (1) the classical predator-prey model with time series and multiple-subject data, (2) the chaotic Lorenz system and (3) an empirical example of dyadic interaction. In the past several decades, methodologies used to estimate nonlinear relationships among latent variables have been developed almost exclusively to fit cross-sectional models. We present a relatively new estimation approach, the unscented Kalman filter (UKF), and illustrate its potential as a tool for fitting nonlinear dynamic models in two ways: (1) as a building block for approximating the log--likelihood of nonlinear state--space models and (2) to fit time-varying dynamic models wherein parameters are represented and estimated online as other latent variables. Furthermore, the substantive utility of the UKF is demonstrated using simulated examples of (1) the classical predator-prey model with time series and multiple-subject data, (2) the chaotic Lorenz system and (3) an empirical example of dyadic interaction. [PUBLICATION ABSTRACT] |
| Author | Nesselroade, John R. Ferrer, Emilio Chow, Sy-Miin |
| Author_xml | – sequence: 1 givenname: Sy-Miin surname: Chow fullname: Chow, Sy-Miin organization: Department of Psychology , University of Notre Dame – sequence: 2 givenname: Emilio surname: Ferrer fullname: Ferrer, Emilio organization: Department of Psychology , University of California – sequence: 3 givenname: John R. surname: Nesselroade fullname: Nesselroade, John R. organization: Department of Psychology , University of Virginia |
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| Title | An Unscented Kalman Filter Approach to the Estimation of Nonlinear Dynamical Systems Models |
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