A normalized least mean fourth algorithm with improved stability

Eweda, Eweda; Zerguine, Azzedine

doi:10.1109/acssc.2010.5757551

Cited by 22 publications

(16 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To deal with this problem, we also proposed a normalized version of SSLMF which is designed using the concept of a recently introduced normalized LMF [36] variant that is proven to be stable under any circumstances. Consequently, by employing the concept of [36], it can be shown that the stable normalized version of the proposed SSLMF algorithm is given by following recursion…”

Section: Derivation Of Proposed Sslmfmentioning

confidence: 99%

State Space Least Mean Fourth Algorithm for Dynamic State Estimation in Power Systems

Ahmed¹,

Moinuddin²,

Al‐Saggaf³

2015

Arab J Sci Eng

View full text Add to dashboard Cite

Power system dynamic state estimation (DSE) has always been a critical problem in studying power systems. One of the essential parts of power systems are synchronous machines. In this work, we dealt with the problem of DSE of a synchronous machine by introducing a novel state space-based least mean fourth (SSLMF) algorithm. The rationale behind the proposed algorithm is the fact that a power system may encounter non-Gaussian disturbances/state errors and the least mean fourth algorithm is proven to be better in such environments. Moreover, we have also introduced a normalized version of the proposed algorithm, namely state space normalized least mean fourth (SSNLMF) algorithm to deal with the stability issue under Gaussian disturbances. Another motivation for developing the SSLMF algorithm is its simplicity as compared to other model-based nonlinear filtering algorithms such as Kalman filter, extended Kalman filter (EKF). Moreover, we also investigate the performance of the recently introduced state space least mean square (SSLMS). Performance of the SSLMF and the SSLMS is compared with existing EKF in both Gaussian and non-Gaussian noise environments. Extensive simulation results are presented which show superiority B Muhammad Moinuddin of the proposed algorithms, and hence, it verifies our rationale behind the work.

show abstract

Section: Derivation Of Proposed Sslmfmentioning

confidence: 99%

State Space Least Mean Fourth Algorithm for Dynamic State Estimation in Power Systems

Ahmed¹,

Moinuddin²,

Al‐Saggaf³

2015

Arab J Sci Eng

View full text Add to dashboard Cite

show abstract

“…In [15]- [17], it is shown that the stability of the algorithms (8) and (9) depends on the mean square input of the adaptive filter. This is due to the fact that (2) implies that in both (8) and (9), the numerator of the weight vector update term is fourth order in , while the denominator is second order in .…”

Section: Problem Formulationmentioning

confidence: 99%

“…Due to (25), (28) and (29), has an upper bound that depends on the noise only through its variance . Due to (37) and (15), the highest power of under the expectation sign in the upper bound of is 2. Consequently, conditions on noise moments with order higher than 2 are not needed for the boundedness of the MSD of NLMF4.…”

Section: A Bounding Recurrence Of the Msdmentioning

confidence: 99%

“…This algorithm will be called NLMF2. While NLMF1 and NLMF2 improve the stability of the LMF algorithm, it has been found that they diverge when the input variance exceeds a threshold value that depends on the algorithm step-size [15]- [17]. This is due to the fact that in both algorithms, the numerator of the weight vector update term is fourth order in the regressor, while the denominator is second order in the regressor.…”

Section: Introductionmentioning

confidence: 99%

“…This is due to the fact that in both algorithms, the numerator of the weight vector update term is fourth order in the regressor, while the denominator is second order in the regressor. In an attempt to overcome this problem, [15] has proposed NLMF3 in which the weight vector update term is normalized by the fourth power of the norm of the regressor. This NLMF algorithm remains stable as the input variance increases.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Mean-Square Stability Analysis of a Normalized Least Mean Fourth Algorithm for a Markov Plant

Eweda¹

2014

IEEE Trans. Signal Process.

Self Cite

View full text Add to dashboard Cite

Recently, it has been shown that the stability of the least mean fourth (LMF) algorithm depends on the nonstationarity of the plant. The present paper investigates the possibility of overcoming this problem by normalization of the weight vector update term. A rigorous mean-square stability analysis is provided for a recent normalized LMF algorithm, which is normalized by a term that is second order in the estimation error and fourth order in the regressor. The analysis is done for a Markov plant with a stationary white input with even probability density function and a stationary zero-mean white noise. It is proved that the mean-square deviation (MSD) of the algorithm is bounded for all finite values of the input variance, noise variance, initial MSD, and mean-square plant parameter increment. Analytical results are supported by simulations.Index Terms-Adaptive filters, least mean fourth algorithm, mean square stability, tracking. 1053-587X

show abstract

New insights into the normalization of the least mean fourth algorithm

Eweda

Zerguine

2011

SIViP

View full text Add to dashboard Cite

A normalized least mean fourth algorithm with improved stability

Cited by 22 publications

References 4 publications

State Space Least Mean Fourth Algorithm for Dynamic State Estimation in Power Systems

State Space Least Mean Fourth Algorithm for Dynamic State Estimation in Power Systems

Mean-Square Stability Analysis of a Normalized Least Mean Fourth Algorithm for a Markov Plant

New insights into the normalization of the least mean fourth algorithm

Contact Info

Product

Resources

About