Subspace algorithms for the stochastic identification problem
Automatica (Journal of IFAC)
Automatica (Journal of IFAC) - Special issue on statistical signal processing and control
N4SID: subspace algorithms for the identification of combined deterministic-stochastic systems
Automatica (Journal of IFAC) - Special issue on statistical signal processing and control
Automatica (Journal of IFAC)
Stochastic realization with exogenous inputs and “subspace-methods” identification
Signal Processing - Special issue: subspace methods, part II: system identification
Statistical analysis of novel subspace identification methods
Signal Processing - Special issue: subspace methods, part II: system identification
Realization of stochastic systems with exogenous inputs and subspace identification methods
Automatica (Journal of IFAC)
On Consistency of Subspace Methods for System Identification
Automatica (Journal of IFAC)
Some facts about the choice of the weighting matrices in Larimore type of subspace algorithms
Automatica (Journal of IFAC)
Analysis of the asymptotic properties of the MOESP type of subspace algorithms
Automatica (Journal of IFAC)
Numerical conditioning and asymptotic variance of subspace estimates
Automatica (Journal of IFAC)
The role of vector autoregressive modeling in predictor-based subspace identification
Automatica (Journal of IFAC)
Subspace identification of MIMO LPV systems using a periodic scheduling sequence
Automatica (Journal of IFAC)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Brief paper: Fast computation of smoothing splines subject to equality constraints
Automatica (Journal of IFAC)
Brief paper: Consistency of subspace methods for signals with almost-periodic components
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Subspace identification by data orthogonalization and model decoupling
Automatica (Journal of IFAC)
Asymptotic properties of subspace estimators
Automatica (Journal of IFAC)
Consistency analysis of some closed-loop subspace identification methods
Automatica (Journal of IFAC)
Numerical conditioning and asymptotic variance of subspace estimates
Automatica (Journal of IFAC)
Subspace-based fault detection robust to changes in the noise covariances
Automatica (Journal of IFAC)
N4SID and MOESP algorithms to highlight the ill-conditioning into subspace identification
International Journal of Automation and Computing
Hi-index | 22.17 |
There is experimental evidence that the performance of standard subspace algorithms from the literature (e.g. the N4SID method) may be surprisingly poor in certain experimental conditions. This happens typically when the past signals (past inputs and outputs) and future input spaces are nearly parallel. In this paper we argue that the poor behavior may be attributed to a form of ill-conditioning of the underlying multiple regression problem, which may occur for nearly parallel regressors. An elementary error analysis of the subspace identification problem, shows that there are two main possible causes of ill-conditioning. The first has to do with near collinearity of the state and future input subspaces. The second has to do with the dynamical structure of the input signal and may roughly be attributed to ''lack of excitation''. Stochastic realization theory constitutes a natural setting for analyzing subspace identification methods. In this setting, we undertake a comparative study of three widely used subspace methods (N4SID, Robust N4SID and PO-MOESP). The last two methods are proven to be essentially equivalent and the relative accuracy, regarding the estimation of the (A,C) parameters, is shown to be the same.