A new robust Kalman filter-based subspace tracking algorithm in an impulsive noise environment

The conventional projection approximation subspace tracking (PAST) algorithm is based on the recursive least-squares algorithm, and its performance will degrade considerably when the subspace rapidly changes and the additive noise is impulsive. This brief proposes a new robust Kalman filter-based subspace tracking algorithm to overcome these two limitations of the PAST algorithm. It is based on a new extension of the adaptive Kalman filter with variable number of measurements (KFVNM) for tracking fast-varying subspace. Furthermore, M-estimation is incorporated into this KFVNM algorithm to combat the adverse effects of impulsive noise. Simulation results show that the robust KFVNM-based subspace tracking algorithm has a better performance than the PAST algorithm for tracking fast-varying subspace and in an impulsive noise environment. © 2010 IEEE.published_or_final_versio

Robust recursive bi-iteration singular value decomposition (SVD) for subspace tracking and adaptive filtering

IEEE International Symposium on Circuits and Systems Proceedings, Bangkok, Thailand, 25-28 May 2003The recursive bi-iteration singular value decomposition (Bi-SVD), proposed by Strobach, is en efficient and well-structured algorithm for performing subspace tracking. Unfortunately, its performance under impulse noise environment degrades substantially. In this paper, a new robust-statistics-based bi-iteration SVD algorithm (robust Bi-SVD) is proposed. Simulation results show that the proposed algorithm offers significantly improved robustness against impulse noise than the conventional Bi-SVD algorithm with slight increase in arithmetic complexity. For nominal Gaussian noise, the two algorithms have similar performance.published_or_final_versio

Robust Subspace Tracking Algorithms in Signal Processing: A Brief Survey

Principal component analysis (PCA) and subspace estimation (SE) are popular data analysis tools and used in a wide range of applications. The main interest in PCA/SE is for dimensionality reduction and low-rank approximation purposes. The emergence of big data streams have led to several essential issues for performing PCA/SE. Among them are (i) the size of such data streams increases over time, (ii) the underlying models may be time-dependent, and (iii) problem of dealing with the uncertainty and incompleteness in data. A robust variant of PCA/SE for such data streams, namely robust online PCA or robust subspace tracking (RST), has been introduced as a good alternative. The main goal of this paper is to provide a brief survey on recent RST algorithms in signal processing. Particularly, we begin this survey by introducing the basic ideas of the RST problem. Then, different aspects of RST are reviewed with respect to different kinds of non-Gaussian noises and sparse constraints. Our own contributions on this topic are also highlighted

A robust subspace tracking algorithm for subspace-based blind multiuser detection in impulsive noise

Subspace tracking is an efficient method to reduce the complexity in estimating the signal subspace required in subspace-based multiuser detection algorithm. Recursive least square (RLS)-based subspace tracking algorithms such as the PAST algorithm can be used to estimate the signal subspace adaptively with relatively low computational complexity. However, it is shown in this paper that subspace estimation using conventional autocorrelation matrix is very sensitive to impulse noise. A new robust correlation matrix, based on robust statistics, is proposed to overcome this problem. Moreover, a new robust PAST algorithm is developed, again using robust statistics, for robust subspace tracking. A new restoring mechanism is also proposed to handle long bursts of impulses, which sporadically occur in communications systems. Simulation results show that the proposed robust subspace tracking-based blind multiuser detector performs better than the conventional approach, especially under consecutive impulses. The adaptation of the proposed scheme in a dynamic multiple access channel, where users may enter and exit the shared mobile channel, is also found to be satisfactory.published_or_final_versio

Robust recursive eigendecomposition and subspace-based algorithms with application to fault detection in wireless sensor networks

The principal component analysis (PCA) is a valuable tool in multivariate statistics, and it is an effective method for fault detection in wireless sensor networks (WSNs) and other related applications. However, its online implementation requires the computation of eigendecomposition (ED) or singular value decomposition. To reduce the arithmetic complexity, we propose an efficient fault detection approach using the subspace tracking concept. In particular, two new robust subspace tracking algorithms are developed, namely, the robust orthonormal projection approximation subspace tracking (OPAST) with rank-1 modification and the robust OPAST with deflation. Both methods rely on robust M-estimate-based recursive covariance estimate to improve the robustness against the effect of faulty samples, and they offer different tradeoff between fault detection accuracy and arithmetic complexity. Since only the ED in the major subspace is computed, their arithmetic complexities are much lower than those of other conventional PCA-based algorithms. Furthermore, we propose new robust T 2 score and SPE detection criteria with recursive update formulas to improve the robustness over their conventional counterparts and to facilitate online implementation for the proposed robust subspace ED and tracking algorithms. Computer simulation and experimental results on WSN data show that the proposed fault detection approach, which combines the aforementioned robust subspace tracking algorithms with the robust detection criteria, is able to achieve better performance than other conventional approaches. Hence, it serves as an attractive alternative to other conventional approaches to fault detection in WSNs and other related applications because of its low complexity, efficient recursive implementation, and good performance. © 2012 IEEE.published_or_final_versio