Fast Subspace Tracking Algorithm Research Articles

Real-time low-frequency oscillations monitoring.

A major concern for interconnected power grid systems is low-frequency oscillation, which limits the scalability and transmission capacity of power systems. Undamped or poorly damped oscillations will lead to undesirable conditions or even a catastrophic system blackout. Real-time synchrophasor data can be used to reliably detect and control these low-frequency oscillations in order to mitigate their catastrophic impact. In this paper, two low complexity tracking algorithms are proposed to identify and monitor low-frequency oscillations; namely, a fast subspace tracking algorithm and a gradient descent based fast recursive algorithm. Initially, both methods perform a one-time matrix pencil method on the power spectrum matrix of real-time Phasor Measurement Unit (PMU) data to detect low-frequency oscillations. This is then followed by two different low-complexity algorithms to fast track the low-frequency oscillations. While the first method uses a recursive fast data projection method-based algorithm, the latter runs a gradient-descent based fast recursive algorithm on every PMU to track and monitor low-frequency oscillations. Both methods have been compared to other state-of-the-art techniques, such as matrix pencil method, frequency domain decomposition, and TLS-ESPRIT. We have shown that the proposed approaches are capable of achieving performance with high accuracy, especially in terms of computational complexity for a large system with many PMUs.

Fast Identification Algorithm of Time-varying Modal Parameter Based on Two-layer Linear Neural Network Learning

The key of fast identification algorithm of time-varying modal parameter based on subspace tracking is to find efficient and fast subspace-tracking algorithm. This paper presents a new version of NIC(Novel Information Criterion) using two-layer linear neural network learning for subspace tracking. Comparing with the original algorithm, there is no need to set a key control parameter in advance. Simulation experiments show that new algorithm has a faster convergence in the initial period.

Fast Time-varying modal parameter identification algorithm based on two-layer linear neural network learning for subspace tracking

The key of fast identification algorithm of time-varying modal parameter based on subspace tracking is to find efficient and fast subspace-tracking algorithm. This paper presents a modified version of NIC(Novel Information Criterion) adopted in two-layer linear neural network learning for subspace tracking, which is applied in time-varying modal parameter identification algorithm based on subspace tracking and get a new time-varying modal parameter identification algorithm. Comparing with the original subspace-tracking algorithm, there is no need to set a key control parameter in advance. Simulation experiments show that new time-varying modal parameter identification algorithm has a faster convergence in the initial period and a real experiment under laboratory conditions confirms further its validity of the time-varying modal identification algorithm presented in this paper.

Fast Subspace Tracking Algorithm Based on the Constrained Projection Approximation

We present a new algorithm for tracking the signal subspace recursively. It is based on an interpretation of the signal subspace as the solution of a constrained minimization task. This algorithm, referred to as the constrained projection approximation subspace tracking (CPAST) algorithm, guarantees the orthonormality of the estimated signal subspace basis at each iteration. Thus, the proposed algorithm avoids orthonormalization process after each update for postprocessing algorithms which need an orthonormal basis for the signal subspace. To reduce the computational complexity, the fast CPAST algorithm is introduced which has complexity. In addition, for tracking the signal sources with abrupt change in their parameters, an alternative implementation of the algorithm with truncated window is proposed. Furthermore, a signal subspace rank estimator is employed to track the number of sources. Various simulation results show good performance of the proposed algorithms.

Performance Analysis of Blind Adaptive MOE Multiuser Receivers Using Inverse QRD-RLS Algorithm

The inverse QR (IQRD) recursive least-squares (RLS) algorithm (IQRD-RLS) is very popular because it has good numerical stability and can be mapped onto COordinate Rotation DIgital Computer (CORDIC) processor-based systolic arrays, which are suitable for very large-scale integrated circuits (VLSI) architecture and real-time applications. In this paper, the blind optimal minimum output energy (MOE) detector which is developed for multiuser detection (MUD) in direct-sequence code-division multiple-access (DS-CDMA) systems is implemented using the linearly constrained IQRD-RLS algorithm. Specifically, the max/min approach is combined with subspace tracking for producing the optimal MOE multiuser detector. A new fast subspace tracking algorithm based on Lagrange multiplier methodology and the IQRD-RLS algorithm is developed. A comparative analysis among the recently emerged channel-estimation techniques is conducted using the IQRD-RLS algorithm. The corresponding robust MOE receivers at low SNR are implemented using the IQRD method, and their performances are assessed in terms of SINR, BER, and computational complexity. A robust multiuser receiver is developed by adding a quadratic inequality constraint to the optimal max/min MOE detector. The feasibility of systolic array implementation of the IQRD-based optimal MOE detector is explored. Several simulation experiments are conducted in a severe near-far environment to analyze the IQRD-based receivers and the subspace tracking algorithms.

Performance Analysis of Blind Adaptive MOE Multiuser Receivers Using Inverse QRD-RLS Algorithm

The inverse QR (IQRD) recursive least-squares (RLS) algorithm (IQRD-RLS) is very popular because it has good numerical stability and can be mapped onto COordinate Rotation DIgital Computer (CORDIC) processor-based systolic arrays, which are suitable for very large-scale integrated circuits (VLSI) architecture and real-time applications. In this paper, the blind optimal minimum output energy (MOE) detector which is developed for multiuser detection (MUD) in direct-sequence code-division multiple-access (DS-CDMA) systems is implemented using the linearly constrained IQRD-RLS algorithm. Specifically, the max/min approach is combined with subspace tracking for producing the optimal MOE multiuser detector. A new fast subspace tracking algorithm based on Lagrange multiplier methodology and the IQRD-RLS algorithm is developed. A comparative analysis among the recently emerged channel-estimation techniques is conducted using the IQRD-RLS algorithm. The corresponding robust MOE receivers at low SNR are implemented using the IQRD method, and their performances are assessed in terms of SINR, BER, and computational complexity. A robust multiuser receiver is developed by adding a quadratic inequality constraint to the optimal max/min MOE detector. The feasibility of systolic array implementation of the IQRD-based optimal MOE detector is explored. Several simulation experiments are conducted in a severe near-far environment to analyze the IQRD-based receivers and the subspace tracking algorithms.

Global convergence analysis for the NIC flow

Previously, a family of fast subspace tracking algorithms based on a novel information criterion (NIC) has been proposed and investigated. It is known that these new algorithms are associated with a new kind of flow, which is called the NIC flow in this paper as in the case of the conventional Oja subspace algorithms with the Oja flow. In this paper, some fundamental questions about this new NIC flow such as its solution existence and convergence, are investigated. In addition, the convergence domain is characterized. Some important results on these issues are obtained via manifold theory.

Bi-iteration SVD subspace tracking algorithms

We present a class of fast subspace tracking algorithms that arise from a straightforward extension of Bauer's (1957) classical bi-iteration to the sequential processing case. The bi-iteration concept has an unexpected potential in subspace tracking. Our new bi-SVD subspace trackers are well structured and show excellent convergence properties. They outperform the TQR-SVD subspace tracking algorithm. Detailed comparisons confirm our claims. An application to rank and data adaptive signal reconstruction is also discussed.

Fast, rank adaptive subspace tracking and applications

High computational complexity and inadequate parallelism have deterred the use of subspace-based algorithms in real-time systems. We proposed a new class of fast subspace tracking (FST) algorithms that overcome these problems by exploiting the matrix structure inherent in multisensor processing. These algorithms simultaneously track an orthonormal basis for the signal subspace and preserve signal eigenstructure information while requiring only O(Nr) operations per update (where N is the number of channels, and r is the effective rank). Because of their low computational complexity, these algorithms have applications in both recursive and block data processing. Because they preserve the signal eigenstructure as well as compute an orthonormal basis for the signal subspace, these algorithms may be used in a wide range of sensor array applications including bearing estimation, beamforming, and recursive least squares. We present a detailed description of the FST algorithm and its rank adaptive variation (RA-FST) as well as a number of enhancements. We also demonstrate the FST's rapid convergence properties in a number of application scenarios.