Local polynomial modeling and bandwidth selection for time-varying linear models

This paper proposes a local polynomial modeling approach and bandwidth selection algorithm for estimating time-varying linear models (TVLM). The time-varying coefficients of a TVLM are modeled locally by polynomials and estimated using least-squares estimation with a kernel having a certain bandwidth or support. Asymptotic behavior of the proposed estimator is established and it shows that there exists an optimal local bandwidth which minimizes the weighted mean squared error (MSE). A data-driven variable bandwidth selection method is also proposed to estimate this optimal bandwidth. Simulation results show that the proposed LPM method with adaptive bandwidth selection outperforms conventional TVLM identification methods in a large variety of testing conditions. ©2009 IEEE.published_or_final_versionThe 7th International Conference on Information, Communications and Signal Processing (ICICS 2009), Macau, China, 8-10 December 2009. In Proceedings of the International Conference on Information, Communications and Signal Processing, 2009, p. 1-

Local polynomial modeling and variable bandwidth selection for time-varying linear systems

This paper proposes a local polynomial modeling (LPM) approach and variable bandwidth selection (VBS) algorithm for identifying time-varying linear systems (TVLSs). The proposed method models the time-varying coefficients of a TVLS locally by polynomials, which can be estimated by least squares estimation with a kernel having a certain bandwidth. The asymptotic behavior of the proposed LPM estimator is studied, and the existence of an optimal local bandwidth which minimizes the local mean-square error is established. A new data-driven VBS algorithm is then proposed to estimate this optimal variable bandwidth adaptively and locally. An individual bandwidth is assigned for each coefficient instead of the whole coefficient vector so as to improve the accuracy in fast-varying systems encountered in fault detection and other applications. Important practical issues such as online implementation are also discussed. Simulation results show that the LPM-VBS method outperforms conventional TVLS identification methods, such as the recursive least squares algorithm and generalized random walk Kalman filter/smoother, in a wide variety of testing conditions, in particular, at moderate to high signal-to-noise ratio. Using local linearization, the LPM method is further extended to identify time-varying systems with mild nonlinearities. Simulation results show that the proposed LPM-VBS method can achieve a satisfactory performance for mildly nonlinear systems based on appropriate linearization. Finally, the proposed method is applied to a practical problem of voltage-flicker-tracking problem in power systems. The usefulness of the proposed approach is demonstrated by its improved performance over other conventional methods. © 2006 IEEE.published_or_final_versio

Harmonic analysis of power system signals using a new regularized adaptive windowed lomb periodogram

This paper proposes a new regularized adaptive windowed Lomb periodogram (RAWLP) method for time-frequency analysis of non-stationary power signals. It extends the conventional Lomb periodogram by estimating the periodogram locally using the weighted least-squares (WLS) estimator. Instead of employing one constant window in WLS, variable window bandwidth is adaptively selected by the intersection of confidence intervals (ICI) method to achieve a better tradeoff between time resolution and frequency resolution. Furthermore, regularization techniques are incorporated in the AWLP to further improve its performance by reducing the variance of the estimator. Simulation results show that the proposed RAWLP method has superior performance over windowed Lomb periodogram with one constant bandwidth for estimating the harmonic and interharmonic frequencies in power systems. © 2010 IEEE.published_or_final_versionThe 1st International Conference on Green Circuits and Systems (ICGCS 2010), Shanghai, China, 21-23 June 2010. In Proceedings of the 1st ICGCS, 2010, p. 567-57

Recursive Parametric Frequency/Spectrum Estimation for Nonstationary Signals With Impulsive Components Using Variable Forgetting Factor

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A new Kalman filter-based algorithm for adaptive coherence analysis of non-stationary multichannel time series

IEEE International Symposium on Circuits and Systems, Island of Kos, Greece, 21-24 May 2006This paper proposes a new Kalman filter-based algorithm for multichannel autoregressive (AR) spectrum estimation and adaptive coherence analysis with variable number of measurements. A stochastically perturbed k -order difference equation constraint model is used to describe the dynamics of the AR coefficients and the intersection of confidence intervals (ICI) rule is employed to determine the number of measurements adaptively to improve the timefrequency resolution of the AR spectrum and coherence function. Simulation results show that the proposed algorithm achieves a better time-frequency resolution than conventional algorithms for non-stationary signals. © 2006 IEEE.published_or_final_versio

On Kernel Selection of Multivariate Local Polynomial Modelling and its Application to Image Smoothing and Reconstruction

This paper studies the problem of adaptive kernel selection for multivariate local polynomial regression (LPR) and its application to smoothing and reconstruction of noisy images. In multivariate LPR, the multidimensional signals are modeled locally by a polynomial using least-squares (LS) criterion with a kernel controlled by a certain bandwidth matrix. Based on the traditional intersection confidence intervals (ICI) method, a new refined ICI (RICI) adaptive scale selector for symmetric kernel is developed to achieve a better bias-variance tradeoff. The method is further extended to steering kernel with local orientation to adapt better to local characteristics of multidimensional signals. The resulting multivariate LPR method called the steering-kernel-based LPR with refined ICI method (SK-LPR-RICI) is applied to the smoothing and reconstruction problems in noisy images. Simulation results show that the proposed SK-LPR-RICI method has a better PSNR and visual performance than conventional LPR-based methods in image processing. © 2010 The Author(s).published_or_final_versio

Local polynomial modeling and bandwidth selection for time-varying linear models

This paper proposes a local polynomial modeling approach and bandwidth selection algorithm for estimating time-varying linear models (TVLM). The time-varying coefficients of a TVLM are modeled locally by polynomials and estimated using least-squares estimation with a kernel having a certain bandwidth or support. Asymptotic behavior of the proposed estimator is established and it shows that there exists an optimal local bandwidth which minimizes the weighted mean squared error (MSE). A data-driven variable bandwidth selection method is also proposed to estimate this optimal bandwidth. Simulation results show that the proposed LPM method with adaptive bandwidth selection outperforms conventional TVLM identification methods in a large variety of testing conditions. ©2009 IEEE.published_or_final_versionThe 7th International Conference on Information, Communications and Signal Processing (ICICS 2009), Macau, China, 8-10 December 2009. In Proceedings of the International Conference on Information, Communications and Signal Processing, 2009, p. 1-

A new transform-domain regularized recursive least M-estimate algorithm for a robust linear estimation

This brief proposes a new transform-domain (TD) regularized M-estimation (TD-R-ME) algorithm for a robust linear estimation in an impulsive noise environment and develops an efficient QR-decomposition-based algorithm for recursive implementation. By formulating the robust regularized linear estimation in transformed regression coefficients, the proposed TD-R-ME algorithm was found to offer better estimation accuracy than direct application of regularization techniques to estimate system coefficients when they are correlated. Furthermore, a QR-based algorithm and an effective adaptive method for selecting regularization parameters are developed for recursive implementation of the TD-R-ME algorithm. Simulation results show that the proposed TD regularized QR recursive least M-estimate (TD-R-QRRLM) algorithm offers improved performance over its least squares counterpart in an impulsive noise environment. Moreover, a TD smoothly clipped absolute deviation R-QRRLM was found to give a better steady-state excess mean square error than other QRRLM-related methods when regression coefficients are correlated. © 2006 IEEE.published_or_final_versio

A recursive frequency estimator using linear prediction and a Kalman-filter-based iterative algorithm

This paper proposes a new Kalman-filter-based recursive frequency estimator for discrete-time multicomponent sinusoidal signals whose frequencies may be time-varying. The frequency estimator is based on the linear prediction approach and it employs the Kalman filter to track the linear prediction coefficients (LPCs) recursively. Frequencies of the sinusoids can then be computed using the estimated LPCs. Due to the coloredness of the linear prediction error, an iterative algorithm is employed to estimate the covariance matrix of the prediction error and the LPCs alternately in the Kalman filter in order to improve the tracking performance. Simulation results show that the proposed Kalman-filter-based iterative frequency estimator can achieve better tracking results than the conventional recursive least-squares-based estimators. © 2008 IEEE.published_or_final_versio

A new regularized transform-domain NLMS adaptive filtering algorithm

The transform domain normalized LMS (TD-NLMS)-adaptive filtering algorithm is an efficient adaptive filter with fast convergence speed and reasonably low arithmetic complexity. However, it is sensitive to the level of the excitation signal, which may vary significantly over time in speech and audio signals. This paper proposes a new regularized transform domain NLMS (R-TDNLMS) algorithm and studies its mean and mean square convergence performance. The proposed algorithm extends the conventional TDNLMS algorithm by imposing a regularization term on the coefficients to reduce the variance of the estimator. The mean and mean square convergence behaviors of the proposed algorithm are studied to characterize its convergence condition and steady-state excess mean squares error (MSE). It shows that regularization can help to reduce the MSE for coloured inputs by trading slight bias for variance. Moreover, the immunity to varying input signal level is significantly reduced. Computer simulations are conducted to examine the effectiveness of the proposed algorithm and they are in good agreement with the theoretical analysis. © 2010 IEEE.published_or_final_versionThe 2010 IEEE Asia Pacific Conference on Circuits and Systems (APCCAS 2010), Kuala Lumpur, Malaysia, 6-9 December 2010. In Proceedings of APCCAS, 2010, p. 696-69