Stochastic analysis of the least mean fourth algorithm for non-stationary white Gaussian inputs

Eweda, Eweda; Bershad, N.J.; Bermudez, J.C.M.

doi:10.1007/s11760-013-0519-1

Cited by 31 publications

(6 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, the stability of NLMF3 depends on the weight vector initialization and the noise variance [16], [17]. The fourth NLMF algorithm, NLMF4, is proposed in [18] and it is given by (11) The idea of this algorithm is a combination of the ideas of NLMF2 (9) and NLMF3 (10). The normalizing term in (11) is a fourth order polynomial in .…”

Section: Problem Formulationmentioning

confidence: 99%

“…This property stabilizes the algorithm against the increase of the input variance, since is a fourth order polynomial in . The normalizing term in (11) also includes . This property stabilizes the algorithm against the increase of the noise variance and against the increase of the squared weight deviation, since .…”

Section: Problem Formulationmentioning

confidence: 99%

“…Assumptions A1-A5 are frequently used in the adaptive filtering literature to enable mathematical tractability of the analysis, e.g., [7]- [11]. Assumption A2 implies that the adaptive filter input is white.…”

Section: A Assumptionsmentioning

confidence: 99%

“…Equations (1)-(4) and (11) imply that (14) (15) Due to (14) and (15), is a function of . Hence, Assumptions A1, A3-A5 imply that (16) Premultiplying (14) by and taking the expectation, (15) and (16) imply that (17) Rewrite (17) …”

Section: A Bounding Recurrence Of the Msdmentioning

confidence: 99%

“…I N a recent paper [1], a new stability problem of the least mean fourth (LMF) algorithm [1]- [11] is detected. It concerns the case when the algorithm is used for tracking a Markov plant.…”

Section: Introductionmentioning

confidence: 99%

See 4 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