A least squares interpretation of sub-space methods for system identification (original) (raw)

Performance of subspace based state-space system identification methods

1993

Traditional prediction-error techniques for multivariable system identi cation require canonical descriptions using a large number of parameters. This problem can be avoided using subspace based methods, since these estimate a state-space model directly from the data. The main computations consist of a QR-decomposition and a singular-value decomposition. Herein, a subspace based technique for identifying general nite-dimensional linear systems is presented and analyzed. The technique applies to general noise covariance structures. Explicit formulas for the asymptotic pole estimation error variances are given. The proposed method is found to perform comparable to a prediction error method in a simple example.

Analysis of state space system identification methods based on instrumental variables and subspace fitting

Automatica, 1997

Subspace-based State Space System IDenti cation (4SID) methods have recently been proposed as an alternative to more traditional techniques for multivariable system identi cation. The advantages are that the user has simple and few design variables, and that the methods have robust numerical properties and relatively low computational complexities. Though subspace techniques have been demonstrated to perform well in a number of cases, the performance of these methods is neither fully understood nor analyzed. Our principal objective is to undertake a statistical investigation of subspace based system identi cation techniques. The studied methods consist of two steps. The subspace spanned by the extended observability matrix is rst estimated. The asymptotic properties of this subspace estimate are derived herein. In the second step, the structure of the extended observability matrix is used to nd a system model estimate. Two possible methods are considered. The simplest one only uses a certain shift-invariance property, while in the other method a parametric representation of the null-space of the observability matrix is exploited. Explicit expressions for the asymptotic estimation error variances of the corresponding pole estimates are given.

A Subspace Based Instrumental Variable Method For State-Space System Identification

1994

Traditional prediction-error techniques for multivariable system identi cation require canonical descriptions using a large number of parameters. This problem may b e avoided using subspace based methods, since these estimate a state-space model directly from the data. In this paper, a subspace based technique for identifying general nite-dimensional linear systems is presented and analyzed. Similar to subspace based identi cation schemes, the space spanned by the extended observability matrix is rst estimated. The system parameters are then extracted by reparametrizing the nullspace of the subspace estimate in terms of the coe cients of the characteristic polynomial. A quadratic problem is obtain and based on a statistical analysis, an optimal weighting derived.

Subspace algorithms for system identification and stochastic realization

1991

The subspace approach for linear realization and identi cation problems is a promising alternative for the 'classical' identi cation methods. It has advantages with respect to structure determination and parametrization of linear models, is computationally simple and numerically robust. A summary is given of existing techniques based upon the singular value and qr decomposition. Algebraic, geometric, statistical and numerical points are emphasized. A new idea is outlined for the joint stochastic realization -deterministic identi cation problem. Several examples are given.

On subspace system identification methods

Modeling Identification and Control, 2022

An open and closed loop subspace system identification algorithm DSR e is compared to competitive open loop algorithms, DSR, and N4SID. Additionally, DSR e is compared vs the optimal Prediction Error Method (PEM). Monte Carlo simulations with discrete random state space models are used for testing the subspace identification algorithms in the numerical simulation section.

A hybrid subspace projection method for system identification

Acoustics, Speech, and …, 2003

A HYBRID SUBSPACE PROJECTION METHOD FOR SYSTEM IDENTIFICATION Sung-Phil Kim, Yadunandana N. Rao, Reniz Erdogmus, Jose C. Principe ... In this paper, we first propose a hybrid subspace projection method that finds optimal projections in the joint space. ...

Computing the Oblique Projection in Subspace-Based Multivariable System Identification

IFAC Proceedings Volumes, 1997

Recently proposed algorithms for mult.ivariable syst.em identification by subspace techniques involve the computation of the so-called "oblique projection" to estimat.e t.he system order and system matrices. The paper shows that this comput a-!.ion can be performed without. (lctually solving any least-squ(lre problems. and that ort.hogonal transformations only should be applied to the original input.-out.put dat.a sequences. Both det.erministic and combined deterministic-stochastic identification problems can be dealt with. Copyright© 1998 IFAC

Subspace state space system identification for industrial processes

Journal of Process Control, 2000

We give a general overview of the state-of-the-art in subspace system identi®cation methods. We have restricted ourselves to the most important ideas and developments since the methods appeared in the late eighties. First, the basics of linear subspace identi-®cation are summarized. Dierent algorithms one ®nds in literature (such as N4SID, IV-4SID, MOESP, CVA) are discussed and put into a unifying framework. Further, a comparison between subspace identi®cation and prediction error methods is made on the basis of computational complexity and precision of the methods by applying them on 10 industrial data sets. #

Subspace identification by data orthogonalization and model decoupling

Automatica, 2004

It has been observed that identiÿcation of state-space models with inputs may lead to unreliable results in certain experimental conditions even when the input signal excites well within the bandwidth of the system. This may be due to ill-conditioning of the identiÿcation problem, which occurs when the state space and the future input space are nearly parallel.