An Unscented Kalman Filter Approach to the Estimation of Nonlinear Dynamical Systems Models

• Published in: Multivariate behavioral research Vol. 42; no. 2; pp. 283 - 321
• Main Authors: Chow, Sy-Miin, Ferrer, Emilio, Nesselroade, John R.
• Format: Journal Article
• Language: English
• Published: United States Taylor & Francis Group 01.04.2007; Lawrence Erlbaum; Taylor & Francis Ltd
• Subjects: Behavioral sciences; Estimating techniques; Item Response Theory; Latent Variables; Multivariate analysis; Research methodology; Statistical methods
• ISSN: 0027-3171; 1532-7906
• DOI: 10.1080/00273170701360423

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.