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 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

A robust past algorithm for subspace tracking in impulsive noise

The PAST algorithm is an effective and low complexity method for adaptive subspace tracking. However, due to the use of the recursive least squares (RLS) algorithm in estimating the conventional correlation matrix, like other RLS algorithms, it is very sensitive to impulsive noise and the performance can be degraded substantially. To overcome this problem, a new robust correlation matrix estimate, based on robust statistics concept, is proposed in this paper. It is derived from the maximum-likelihood (ML) estimate of a multivariate Gaussian process in contaminated Gaussian noise (CG) similar to the M-estimates in robust statistics. This new estimator is incorporated into the PAST algorithm for robust subspace tracking in impulsive noise. Furthermore, a new restoring mechanism is proposed to combat the hostile effect of long burst of impulses, which sporadically occur in communications systems. The convergence of this new algorithm is analyzed by extending a previous ordinary differential equation (ODE)-based method for PAST. Both theoretical and simulation results show that the proposed algorithm offers improved robustness against impulsive noise over the PAST algorithm. The performance of the new algorithm in nominal Gaussian noise is very close to that of the PAST algorithm. © 2006 IEEE.published_or_final_versio