Unbiased and stable leakage-based adaptive filters

Nascimento, Vítor H.; Sayed, Ali H.

doi:10.1109/78.806071

Cited by 34 publications

(31 citation statements)

References 24 publications

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“…However, the Leaky LMS does add bias to the solution and w n does not reach 0 except for the case α = 0 which is the case for LMS [22].…”

Section: The Weight Drift Problemmentioning

confidence: 99%

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The leaky least mean mixed norm algorithm

Nasar

Zerguine

2013

2013 Asilomar Conference on Signals, Systems and Computers

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“…However, the Leaky LMS does add bias to the solution and w n does not reach 0 except for the case α = 0 which is the case for LMS [22].…”

Section: The Weight Drift Problemmentioning

confidence: 99%

“…In this simulation, the parameters have been chosen to speed up the weight drift phenomenon as was done in [22]. we will be making use of the fundamental energy conservation relation for our analysis.…”

Section: Comparison Of Lmmn and Leaky Lmmn In Weight Drift Environmentmentioning

confidence: 99%

The leaky least mean mixed norm algorithm

Nasar

Zerguine

2013

2013 Asilomar Conference on Signals, Systems and Computers

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“…This may drive the LMS weight update to diverge as a result of inadequate input sequence [4]. The drifting problem has been shown in [5]- [7] in details.…”

Section: Introductionmentioning

confidence: 99%

“…The leaky least-mean-square (LLMS) algorithm is one of the improved LMS-based algorithms that use a leakage factor to control the weight update of the LMS algorithm [5], [6]. This leakage factor solves the problem of drifting in the LMS algorithm by bounding the parameter estimate.…”

Section: Introductionmentioning

confidence: 99%

A Modified Leaky-LMS Algorithm

Tajuddeen¹,

Salman²,

Abuhilal³

2014

IJCEE

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Abstract-The leaky least-mean-square (LLMS) algorithm was first proposed to mitigate the drifting problem of the leastmean-square (LMS) algorithm. Though the LLMS algorithm solves this problem, its performance is similar to that of the LMS algorithm. In this paper, we propose an improved version of the LLMS algorithm that brings better performance to the LLMS algorithm and similarly solves the problem of drifting in the LMS algorithm. This better performance is achieved at a negligible increase in the computational complexity. The performance of the proposed algorithm is compared to that of the conventional LLMS algorithm in a system identification and a noise cancellation settings in additive white and correlated, Gaussian and impulsive, noise environments. IndexTerms-Leaky least-mean-square, system identification, noise cancellation. I. INTRODUCTIONThe least-mean-square (LMS) algorithm [1] is one of the most famous adaptive filtering algorithms because of its simplicity and ease of analysis. This has made most researchers to improve the LMS algorithm and also to find solutions to some of its drawbacks. Some of these improved algorithms include: the normalized least-mean-square (NLMS) [2], variable step-size least-mean-square (VSSLMS) [3], etc. These improved algorithms generally improve the performance of the LMS algorithm in terms of convergence rate and mean-square-error (mse) value.One of the main drawbacks of the LMS algorithm is the drifting problem as analyzed in [4]. This is a situation where the LMS algorithm generates unbounded parameter estimates for a bounded input sequence. This may drive the LMS weight update to diverge as a result of inadequate input sequence [4]. The drifting problem has been shown in [5]-[7] in details.The leaky least-mean-square (LLMS) algorithm is one of the improved LMS-based algorithms that use a leakage factor to control the weight update of the LMS algorithm [5], [6]. This leakage factor solves the problem of drifting in the LMS algorithm by bounding the parameter estimate. It also improves the tracking capability of the algorithm, convergence and stability of the LMS algorithm.One of the main drawbacks of the LLMS algorithm is its low convergence rate compared to the other improved LMSbased algorithms. In this paper, we propose a new algorithm that improves the convergence rate of the LLMS algorithm. This is achieved by employing the sum of exponentials of the error as the cost function; this cost function is a generalized of the stochastic gradient algorithm as proposed by Boukis et al. [8]. A leakage factor is added to the sum of exponential cost function which makes the proposed algorithm a combination of the generalized of the mixednorm stochastic gradient algorithm with a leaky factor. This paper is organized as follows. In Section II, a review of the LLMS is introduced. In Section III, the proposed algorithm is introduced. In Section IV, experimental results are presented and discussed. Finally, the conclusions are drawn. II. LEAKY LEAST MEAN SQUARE ALGORITHMIn sy...

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“…It is worth noting that other modifications to MRAC have been presented (for example [26]). The modification presented here is similar to the gain "leakage" strategies, which have been applied to integral only adaptive gain strategies [27,28]. However, the localized stability analysis of system [25] shows theoretically why these modifications give the system improved stability and robustness.…”

Section: Introductionmentioning

confidence: 99%

Model reference adaptive control of a nonsmooth dynamical system

Neild

Wagg

et al. 2006

Nonlinear Dyn

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In this paper a modified model reference adaptive control (MRAC) technique is presented which can be used to control systems with nonsmooth characteristics. Using unmodified MRAC on (noisy) nonsmooth systems leads to destabilization of the controller. A localized analysis is presented which shows that the mechanism behind this behavior is the presence of a time invariant zero eigenvalue in the system. The modified algorithm is designed to eliminate this zero eigenvalue, making all the system eigenvalues stable.Both the modified and unmodified strategies are applied to an experimental system with a nonsmooth deadzone characteristic. As expected the unmodified algorithm cannot control the system, whereas the modified algorithm gives stable robust control, which has significantly improved performance over linear fixed gain control.

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Unbiased and stable leakage-based adaptive filters

Cited by 34 publications

References 24 publications

The leaky least mean mixed norm algorithm

The leaky least mean mixed norm algorithm

A Modified Leaky-LMS Algorithm

Model reference adaptive control of a nonsmooth dynamical system

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