Structure identification of nonlinear dynamic systems—a survey on input/output approaches
Automatica (Journal of IFAC)
Nonlinear black-box modeling in system identification: a unified overview
Automatica (Journal of IFAC) - Special issue on trends in system identification
Stochastic Complexity in Statistical Inquiry Theory
Stochastic Complexity in Statistical Inquiry Theory
On sequential Monte Carlo sampling methods for Bayesian filtering
Statistics and Computing
Modelling and identification of non-linear deterministic systems in the delta-domain
Automatica (Journal of IFAC)
A stable estimator of the information matrix under EM for dependent data
Statistics and Computing
System identification of nonlinear state-space models
Automatica (Journal of IFAC)
An EM Algorithm for Nonlinear State Estimation With Model Uncertainties
IEEE Transactions on Signal Processing
Asymptotic MAP criteria for model selection
IEEE Transactions on Signal Processing
A tutorial on particle filters for online nonlinear/non-GaussianBayesian tracking
IEEE Transactions on Signal Processing
Maximum-Likelihood Estimation of Delta-Domain Model Parameters From Noisy Output Signals
IEEE Transactions on Signal Processing - Part I
Robust maximum-likelihood estimation of multivariable dynamic systems
Automatica (Journal of IFAC)
A two-stage algorithm for identification of nonlinear dynamic systems
Automatica (Journal of IFAC)
Computational system identification for Bayesian NARMAX modelling
Automatica (Journal of IFAC)
| Hi-index | 22.15 |
In this paper, we consider structure detection and parameter estimation of the nonlinear auto-regressive with exogenous inputs (NARX) model, using the EM (expectation-maximisation) algorithm. The parameter estimation step uses particle smoothing to obtain the necessary expectations in the E-step and the parameters are then estimated in closed form in the M-step. The model structure detection is performed using an F-test, which makes use of the parameter information matrix (inverse of the covariance matrix), obtained from an augmentation of the EM algorithm. The steps for obtaining the information matrix are robust, guaranteeing a positive semi-definite information matrix to use in the structure detection step. For the case of unknown model orders, a method is proposed using the stochastic complexity (SC) information criterion for selecting between candidate models. The SC is composed of the information matrix (representing model complexity) and a likelihood estimate (representing model accuracy), which are both generated as byproducts of the augmented EM algorithm. Numerical results demonstrate that the EM approach performs well in comparison to a standard alternative based on orthogonal least squares, and also avoids the need to estimate a noise model for the case of measurement noise corrupted output signals.