Propagator-based methods for recursive subspace model identification

Abstract

The problem of the online identification of multi-input multi-output (MIMO) state-space models in the framework of discrete-time subspace methods is considered in this paper. Several algorithms, based on a recursive formulation of the MIMO output error state-space (MOESP) identification class, are developed. The main goals of the proposed methods are to circumvent the huge complexity of eigenvalues or singular values decomposition techniques used by the offline algorithm and to provide consistent state-space matrices estimates in a noisy framework. The underlying principle consists in using the relationship between array signal processing and subspace identification to adjust the propagator method (originally developed in array signal processing) to track the subspace spanned by the observability matrix. The problem of the (coloured) disturbances acting on the system is solved by introducing an instrumental variable in the minimised cost functions. A particular attention is paid to the algorithmic development and to the computational cost. The benefits of these algorithms in comparison with existing methods are emphasised with a simulation study in time-invariant and time-varying scenarios. matrices.

A least squares approach to the subspace identification problem

“…In contrast to most of the existing subspace techniques, our method does not require any SVD. Therefore, it can be naturally and straightforwardly extended to recursive identification [8], [13], [9]. Moreover, it allows to set up very simply the state basis of the matrices to be identified.…”

Recursive Subspace Identification Algorithm using the Propagator Based Method

“…The batch subspace identifications are not appropriate for online implementation because of the computational complexity of SVD. Hence, it is necessary to find the SVD alternatives in order to apply the subspace algorithm in a recursive framework [13]. In this paper, we will adapt a method from array signal processing which is the propagator method.…”

“…The fundamental principle of using the relationship between array signal processing and subspace identification is to apply the propagator method which initially obtained in array signal processing in order to track the subspace spanned by the extended observability matrix. In array signal processing, the considered subspace tracking problem consists in recursively determine the direction of arrival (DOA), , by online estimating the column subspace of the steering matrix, (), from the following data generation model [13]:…”

“…Furthermore, this method can be implemented for multiple inputs and multiple outputs (MIMO) system identification. There are several algorithms commonly used for subspace identification which are Canonical Variate Analysis (CVA) proposed by [1,2], Multivariable Output Error State Space (MOESP) by [3,4] and Numerical Subspace State Space System Identification (N4SID) by [5,6]. Basically, subspace identification algorithms are based on the concepts from different branches which are system theory, numerical linear algebra and statistics [7].…”

Recursive parameter and state estimation for an input nonlinear state space system using the hierarchical identification principle

“…It is easy to estimate the parameters of linear time-invariant state space systems by resorting to the subspace identification methods [8][9][10]. Favoreel et al gave an overview of the subspace identification methods and compared with the prediction error methods from the view of the cost functions [11,12].…”