On the Performance Analysis of the Least Mean M-Estimate and Normalized Least Mean M-Estimate Algorithms with Gaussian Inputs and Additive Gaussian and Contaminated Gaussian Noises

Chan, S. C.; Zhou, Yi

doi:10.1007/s11265-009-0405-9

Cited by 39 publications

(39 citation statements)

References 41 publications

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“…We can see that the computation of robust SPE and robust T 2 score in (31) and (32) only requires the eigenvectors and eigenvalues of the tracked subspace, which is in contrast to their conventional counterparts in (8) and (10), respectively. Motivated by [32] and [38], the following robust recursive location and variance estimates for the robust SPE and robust T 2 score are proposed:…”

Section: Robust Recursive Detection Criteriamentioning

confidence: 99%

“…Here, Δ SPE (t) and Δ T 2 (t) are instantaneous deviations of the SP E(t) and T 2 (t) scores from their robust estimates defined in (37) and (38). Γ SPE and Γ T 2 are the threshold parameters chosen to control the degree of suppression of the faulty samples.…”

Section: E Robust Subspace Trackingmentioning

confidence: 99%

“…Motivated by [22], [32], and [38], we further propose to update the thresholds Γ SPE and Γ T 2 using the adaptive threshold …”

Section: E Robust Subspace Trackingmentioning

confidence: 99%

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Robust Recursive Eigendecomposition and Subspace-Based Algorithms With Application to Fault Detection in Wireless Sensor Networks

Chan

Tsui

2012

IEEE Trans. Instrum. Meas.

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Abstract-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.Index Terms-Fault detection, orthonormal projection approximation subspace tracking (PAST) (OPAST), outlier detection, PAST algorithm with deflation (PASTd), recursive principal component analysis (R-PCA), robust statistics, subspace eigendecomposition (ED), wireless sensor networks (WSNs).

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Section: Robust Recursive Detection Criteriamentioning

confidence: 99%

Section: E Robust Subspace Trackingmentioning

confidence: 99%

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Robust Recursive Eigendecomposition and Subspace-Based Algorithms With Application to Fault Detection in Wireless Sensor Networks

Chan

Tsui

2012

IEEE Trans. Instrum. Meas.

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“…[3][4][5][6][7][8] However, the performances of these filters are limited due to nonstationary nature of the PQ events and also the steady state error behavior during estimation. Stochastic gradient-based filtering algorithms like LMS and normalized LMS 3,4 have simpler structures, but the estimation accuracies are poor due to gradient noise amplification in case of time-varying and nonstationary disturbances. Though RLS has faster convergence, the estimation performance is limited due to an increase in computational complexity through calculation of matrix inversion lemma and a proper choice of forgetting factor.…”

Section: Introductionmentioning

confidence: 99%

Tracking of power quality disturbances using sparse model–based extended Kalman filters

Sahoo

Subudhi

Mishra

2018

Adaptive Control & Signal

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Accurate estimation and tracking of power quality (PQ) disturbances requires efficient adaptive model-based techniques, which should have elegant structures to be applicable in practical systems. Though extended Kalman filter (EKF) has been used as a popular estimator to track the time-varying PQ events, the performance is limited due to higher-order nonlinearity exists in system dynamics.Moreover, the computational complexity and sensitivity to the measurement noise affect the estimation accuracy and error convergence properties. If the underlying sparse behavior of adaptive filters can be exploited through norm penalty, then significant improvement can be achieved in terms of convergence speed, stability, and steady state excess mean square error performance. In this paper, a modification to EKF is proposed by using sparse model to estimate PQ disturbances with better estimation accuracy and faster convergence speed.A thorough comparison is presented in terms of simulation results by using a family of existing algorithms like least mean square, recursive least square, and EKF. Adaptive estimation model incorporates real and complex state space representations to represent discrete time PQ disturbances. The convergence of the proposed sparse model-based filter is also mathematically proved considering the mean square error performance.

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“…Then, a modified Huber function is incorporated into the conventional LPCR to remove samples that are detected as mislabeled observations using the logistic error. Though the concept of robust M-estimation based on automatic threshold selection (ATS) and the modified Huber function has been reported in [6] for robust estimation in linear systems, the incorporation of 2 T score, squared prediction error (SPE) and logistic error, and its application to non-linear LR is to our best knowledge new. Experimental results show that the proposed robust LPCR offers much better classification accuracy than the conventional LPCR in the presence of outliers, while the performance is also highly comparable under normal situation.…”

Section: Introductionmentioning

confidence: 99%

Robust Logistic Principal Component Regression for classification of data in presence of outliers

Chan

Tsui

2012

2012 IEEE International Symposium on Circuits and Systems

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The Logistic Principal Component Regression (LPCR) has found many applications in classification of highdimensional data, such as tumor classification using microarray data. However, when the measurements are contaminated and/or the observations are mislabeled, the performance of the LPCR will be significantly degraded. In this paper, we propose a new robust LPCR based on M-estimation, which constitutes a versatile framework to reduce the sensitivity of the estimators to outliers. In particular, robust detection rules are used to first remove the contaminated measurements and then a modified Huber function is used to further remove the contributions of the mislabeled observations. Experimental results show that the proposed method generally outperforms the conventional LPCR under the presence of outliers, while maintaining a performance comparable to that obtained under normal condition.

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On the Performance Analysis of the Least Mean M-Estimate and Normalized Least Mean M-Estimate Algorithms with Gaussian Inputs and Additive Gaussian and Contaminated Gaussian Noises

Cited by 39 publications

References 41 publications

Robust Recursive Eigendecomposition and Subspace-Based Algorithms With Application to Fault Detection in Wireless Sensor Networks

Robust Recursive Eigendecomposition and Subspace-Based Algorithms With Application to Fault Detection in Wireless Sensor Networks

Tracking of power quality disturbances using sparse model–based extended Kalman filters

Robust Logistic Principal Component Regression for classification of data in presence of outliers

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