Recursive Subspace Research Articles

An algorithm for the fast solution of symmetric linear complementarity problems

This paper studies algorithms for the solution of mixed symmetric linear complementarity problems. The goal is to compute fast and approximate solutions of medium to large sized problems, such as those arising in computer game simulations and American options pricing. The paper proposes an improvement of a method described by Kocvara and Zowe (Numer Math 68:95–106, 1994) that combines projected Gauss–Seidel iterations with subspace minimization steps. The proposed algorithm employs a recursive subspace minimization designed to handle severely ill-conditioned problems. Numerical tests indicate that the approach is more efficient than interior-point and gradient projection methods on some physical simulation problems that arise in computer game scenarios.

Recursive Subspace Model Identification Based On Vector Autoregressive Modelling

Recursive subspace model identification (RSMI) has been developed for a decade. Most of RSMIs are only applied for open loop data. In this paper, we propose a new recursive subspace model identification which can be applied under open loop and closed loop data. The key technique of this derivation of the proposed algorithm is to bring the Vector Auto Regressive with eXogenous input (VARX) models into RSMI. Numerical studies on a closed loop identification problem show the effectiveness of the proposed algorithm.

A Novel RSMI based on Regression and Natural Power Method

In this paper, we propose a new recursive subspace model identification (RSMI) based on regression and natural power method (NP) which is an array signal processing algorithm with excellent convergence properties. We call this new algorithm as ‘R-NP'. The basic idea of the algorithm is to utilize an unstructured least squares linear regression approach at the updating observation vector step and the close relationship between RSMI with NP. This algorithm has simpler procedures than other RSMI algorithms. A numerical example illustrates that R-NP method is efficient and have a better performance in terms of transient behavior with respect to EIVPAST. In this paper, we consider the case where the order of system to be identified is a priori known.

Convergence analysis of instrumental variable recursive subspace identification algorithms

The convergence properties of recently developed recursive subspace identification methods are investigated in this paper. The algorithms operate on the basis of instrumental variable (IV) versions of the propagator method for signal subspace estimation. It is proved that, under suitable conditions on the input signal and the system, the considered recursive subspace identification algorithms converge to a consistent estimate of the propagator and, by extension, to the state-space system matrices.

Blind Linear MMSE Receivers for MC-CDMA Systems

This paper studies blind constrained minimum output energy (CMOE)-based and subspace-based linear minimum mean-squared-error (LMMSE) detectors for multi-carrier code division multiple access (MC-CDMA) systems. By imposing quadratic weight constraint, the CMOE detector is made more robust against signature waveform mismatch, and a better performance over the standard CMOE detector is obtained. Because of separation of signal and noise subspaces, the more complicated subspace-based LMMSE detector has better performance than the CMOE detector. The recursive subspace tracking algorithms are also investigated for the subspace-based MMSE receiver. Numerical results show that the steady-state performance of the robust CMOE detector is close to the subspace-based MMSE method. The blind mode decision-directed LMMSE detection is studied where the blind detectors are used for initial adaptation. Numerical simulations illustrate that the blind mode decision-directed MMSE detection substantially improves the system performance when the frequency-selective channel is slowly-varying

Reconstruction of Fetal Cardiac Vectors From Multichannel fMCG Data Using Recursively Applied and Projected Multiple Signal Classification

Previous attempts at unequivocal specification of signal strength in fetal magnetocardiographic (fMCG) recordings have used an equivalent current dipole (ECD) to estimate the cardiac vector at the peak of the averaged QRS complex. However, even though the magnitude of fetal cardiac currents are anticipated to be relatively stable, ECD-based estimates of signal strength show substantial and unrealistic variation when comparing results from different time windows of the same recording session. The present study highlights the limitations of the ECD model, and proposes a new methodology for fetal cardiac source reconstruction. The proposed strategy relies on recursive subspace projections to estimate multiple dipoles that account for the distributed myocardial currents. The dipoles are reconstructed from spatio-temporal fMCG data, and are subsequently used to derive estimators of the cardiac vector over the entire QRS. The new method is evaluated with respect to simulated data derived from a model of ventricular depolarization, which was designed to account for the complexity of the fetal cardiac source configuration on the QRS interval. The results show that the present methodology overcomes the drawbacks of conventional ECD fitting, by providing robust estimators of the cardiac vector. Additional evaluation with real fMCG data show fetal cardiac vectors whose morphology closely resembles that obtained in adult MCG.

Multivariable Adaptive Control of Synchronous Machines in a Multimachine Power System

A multivariable self-tuning adaptive control scheme used to enhance power system stability in a multimachine environment is presented. The controller is implemented locally for individual generators with supplementary stabilizing signals through the AVR and governor. A discrete multivariable state space model is developed to represent the generator. The recursive subspace identification method based on the projection approximation subspace tracking approach is employed to update generator model parameters online. A generalized predictive control strategy with constraints on the control signals is used. Simulations studies carried out on a five-machine power system without infinite bus show that the proposed multivariable adaptive controller is effective in damping both local and interarea mode oscillations under small as well as large disturbances. The self-coordinating ability of the adaptive controller with the existing conventional controllers is also demonstrated.

Real-Time Optimal Control of Flexible Structures Using Subspace Techniques

In this paper, a novel real-time optimal control is designed for a class of embedded flexible structures such as a cantilever beam. The proposed strategy is based on a new recursive subspace identification and receeding horizon optimal control. The proposed recursive strategy can be parameterized in terms of recursive approximation of subspace intersections and adaptive estimation of state sequences. The proposed integrated modeling-control strategy can be implemented, in real-time, with minimum knowledge of the controlled system. Actual hardware experiments using a DSP have been carried out in order to verify the performance of the proposed methodology

RECURSIVE UPDATING OF ERROR COVARIANCE MATRIX IN SUBSPACE METHODS

Using a unified approach, recursive algorithms of the error covariance matrices in subspace methods are derived for the MOESP type of subspace methods. The proposed approach is based on the fact that the subspace extraction amounts to computing singular value decomposition of the Schur complement (SC) of the input submatrix in data product moments and the SC can be interpreted as the least squares residuals. The recursion of the error covariance matrix can be applied to derive recursive subspace identification algorithms.

CONVERGENCE ANALYSIS OF INSTRUMENTAL VARIABLE RECURSIVE SUBSPACE IDENTIFICATION ALGORITHMS

The convergence properties of a recently developed recursive subspace identification algorithm of the MOESP class are investigated in this paper. The algorithm operates on the basis of an extended instrumental variable (EIV) version of the propagator method for signal subspace estimation. It is proved that, under weak conditions on the input signal and the identified system, the considered recursive subspace identification algorithm converges to a consistent estimate of the propagator and, by extension, of the state space system matrices.

MODELLING OF NON STATIONARY SYSTEMS BASED ON A DYNAMICAL DECISION SPACE

A new approach based on pattern recognition techniques and dedicated to the monitoring of non stationary systems is presented in this paper. More precisely, it consists of a recursive subspace identification algorithm combined with an adaptive classifier set for non stationary environment. The system identification method which provides a recursive estimation of a linear state space model is firstly described. Then, a feature vector representing the system functioning state is extracted from this estimated model. Next, the dynamical clustering algorithm which online learns the functioning modes and continuously determines the current mode of the system is introduced. Its auto adaptive and unsupervised abilities to take into account system modes evolutions are finally emphasized on simulation examples.

IDENTIFICATION OF A STATE SPACE MODEL FOR A SYNCHRONOUS MACHINE

Application of a recursive subspace identification method to derive a state space model for a synchronous machine is described in this paper. Simulation studies show the effectiveness of such an algorithm to identify on-line a synchronous machine model over a wide range of operating conditions and disturbances. The model provides a foundation for further study on a MIMO adaptive power system stabilizer.

Recursive subspace identification based on instrumental variable unconstrained quadratic optimization

AbstractThe problem of the recursive formulation of the MOESP class of subspace identification algorithms is considered and two novel instrumental variable approaches are introduced. The first one leads to an RLS‐like implementation, the second to a gradient type iteration. The relative merits of both approaches are analysed and discussed, while simulation results are used to compare their performance with one of the existing techniques. Copyright © 2004 John Wiley & Sons, Ltd.

A Numerical Aspect of Recursive Subspace Algorithm for Time-varying Systems

A Numerical Aspect of Recursive Subspace Algorithm for Time-varying Systems

逐次部分空間同定を使った変化検出法

This paper presents a new change detection method with the aid of subspace identification. The proposed method is based on monitoring a change in variance of a statistic generated by a recursive subspace identification algorithm. An asymptotic property of the statistic is presented. Without changes during sampling, it is shown that, under relevant assumptions, the statistic converges in probability to a stack of noise vectors multiplied from the left side by a Toeplitz matrix. A numerical example illustrates that the proposed method can detect changes in the dynamics of a system, without being disturbed by changes in the spectral density function of an input signal which is not our concern.

Recursive Subspace Identification with Fixed Data Size and Its Comparison with Other Recursive Algorithms

Recursive Subspace Identification with Fixed Data Size and Its Comparison with Other Recursive Algorithms

Recursive Subspace Identification Based on Projector Tracking

The problem of MIMO state space recursive identification is considered and analyzed using subspace model identification (SMI) techniques. In this paper the use of projection tracking techniques for the update of the observability subspace is proposed: existing results are used for the output error case and a novel instrumental variable (IV) projection tracking approach is proposed, to accommodate for arbitrary correlation of the disturbances. Simulation results show the performance achievable with the given algorithms.

Application of a recursive subspace identification algorithm to change detection

This paper presents a new change detection method with the aid of subspace identification. The proposed method is based on monitoring a change in variance of a statistic generated by a recursive subspace identification algorithm. An asymptotic property of the statistic is presented. Without changes during sampling, it is shown that, under relevant assumptions. the statistic converges in probability to a stack of noise vectors multiplied from the left side by a Toeplitz matrix. A numerical example illustrates that the proposed method can detect changes in the dynamics of a system, without being disturbed by changes in the dynamics of an input signal which are not our concern.

Subspace identification of switching model

Subspace identification of switching model is considered in this paper. Here the switching model is supposed to be a sum of weighted linear models. The method established uses recursive subspace identification to estimate the switching function and least squares method for local model Markov parameters estimation. To perform the computation of the weighting functions a two-steps algorithm (switching times determination and model merging) is given. Finally the local model parameter estimation is based on the estimation of the Markov parameters.

Recursive subspace identification for continuous-/discrete-time stochastic systems

A recursive algorithm is derived for subspace system identification which is flexible and applicable to continuous/discrete-time, time-invariant/varying stochastic systems. Efficacy of the algorithm is demonstrated by simulations.