An Affine Combination of Two LMS Adaptive Filters—Transient Mean-Square Analysis

Bershad, N.J.; Bermudez, J.C.M.; Tourneret, J.-Y.

doi:10.1109/tsp.2007.911486

Cited by 139 publications

(180 citation statements)

References 10 publications

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“…Taking advantage of such sparse prior information can improve the identifying performance. However, the proposed two combination structure filters [2] [4] do not exploit such information due to the fact that they adopted standard LMS filters. Thus, there is a great interest in exploiting the sparse structure information to improve the filtering performance in sparse systems.…”

Section: A Background and Motivationmentioning

confidence: 99%

“…This setup generalizes the combination of adaptive filter outputs, and can be used to study the properties of the optimal combination. In [4], the authors proposed the optimal affine combiner , 8…”

Section: Organizations and Notationsmentioning

confidence: 99%

“…However, it cannot be utilized in reality. Employing a stochastic gradient search method, suboptimal affine combiner [4] was proposed as follows 1 , 9 where 1 and are parameters for tracking the adaptation of and .…”

Section: Organizations and Notationsmentioning

confidence: 99%

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Two Are Better Than One: Adaptive Sparse System Identification Using Affine Combination of Two Sparse Adaptive Filters

Gui

Kumagai

Mehbodniya

et al. 2014

2014 IEEE 79th Vehicular Technology Conference (VTC Spring)

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Abstract-Sparse system identification problems often exist in many applications, such as echo interference cancellation, sparse channel estimation, and adaptive beamforming. One of popular adaptive sparse system identification (ASSI) methods is adopting only one sparse least mean square (LMS) filter. However, the adoption of only one sparse LMS filter cannot simultaneously achieve fast convergence speed and small steady-state mean state deviation (MSD). Unlike the conventional method, we propose an improved ASSI method using affine combination of two sparse LMS filters to simultaneously achieving fast convergence and low steady-state MSD. First, problem formulation and standard affine combination of LMS filters are introduced. Then an approximate optimum affine combiner is adopted for the proposed filter according to stochastic gradient search method. Later, to verify the proposed filter for ASSI, computer simulations are provided to confirm effectiveness of the proposed filter which can achieve better estimation performance than the conventional one and standard affine combination of LMS filters.

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Section: A Background and Motivationmentioning

confidence: 99%

Section: Organizations and Notationsmentioning

confidence: 99%

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Two Are Better Than One: Adaptive Sparse System Identification Using Affine Combination of Two Sparse Adaptive Filters

Gui

Kumagai

Mehbodniya

et al. 2014

2014 IEEE 79th Vehicular Technology Conference (VTC Spring)

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“…The outputs of the filters are combined through a mixing parameter λ. The performance of this scheme has been studied for some parameter update schemes Arenas-Garcia et al (2006); Bershad et al (2008); Silva et al (2010) and Candido et al (2010) present transient analysis of a slightly modified versions of this scheme. The parameter λ is in those papers found using an LMS type adaptive scheme and possibly computing the sigmoidal function of the result.…”

Section: Introductionmentioning

confidence: 99%

“…The parameter λ is in those papers found using an LMS type adaptive scheme and possibly computing the sigmoidal function of the result. The reference Bershad et al (2008) takes another approach computing the mixing parameter using an affine combination. This paper uses the ratio of time averages of the instantaneous errors of the filters.…”

Section: Introductionmentioning

confidence: 99%

Transient Analysis of a Combination of Two Adaptive Filters

Trump¹

2011

Adaptive Filtering

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A numerically stable, finite memory, fast array recursive least squares filter for broadband active noise control

Ophem

Berkhoff

2015

Adaptive Control & Signal

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For broadband active noise control applications with a rapidly changing primary path, it is desirable to find algorithms with a rapid convergence, a fast tracking performance, and a low computational cost. Recently, a promising algorithm has been presented, called the fast-array Kalman filter, which uses rotation matrices to calculate the filter parameters. However, when this algorithm is implemented, it can show unstable behavior because of finite precision error propagation. In this paper, a novel algorithm is presented, which exhibits the fast convergence and tracking properties and the linear calculation complexity of the fast-array Kalman filter but does not suffer from the mentioned numerical problems. This is accomplished by running two finite length growing memory recursive least squares filters in parallel and using a convex combination of the two filters when the control signal is calculated. A reset of the filter parameters with proper re-initialization is enforced periodically. The mixing parameters will be chosen in such a way that the total available information used for the calculation of the control signal will be approximately equal at every time instance. The performance of the filter is shown in numerical simulations and real-time lab experiments. The numerical experiments show that the algorithm performs better numerically than the fast-array sliding window recursive least squares filter, while achieving a comparable convergence rate and tracking performance. The real-time lab experiments confirm the behavior shown in the simulations. 32S. VAN OPHEM AND A. P. BERKHOFF fxLMS [2], fast affine projections, and preconditioned LMS [1]. Another way to improve the rate of convergence can be obtained by reformulating the ANC problem as a state estimation problem, as proposed by Sayyarrodsari et al. [3].The assumption of the linear time-invariant adaptive filter and secondary path also potentially influences the tracking performance of primary path changes. These changes will occur when the primary noise source is moving relative to the ANC system or the reference microphone is moving. Some examples of moving noise sources are airplanes and cars. With such noise sources, the primary path can change rapidly, violating the assumption of a system with slowly variating dynamics. Some examples of ANC with moving noise sources are given by Omoto and Fujiwara [4], Berkhoff [5], and Van Ophem and Berkhoff [6].The availability of affordable, high-performance digital signal processors makes it possible to implement more advanced signal processing algorithms with a potentially better performance than the fxLMS algorithms. Therefore, recent research has been focused on alternatives, such as the modified filtered-reference Recursive Least Squares (RLS) algorithm. This algorithm has a high rate of convergence, but is computationally demanding. It was shown by Fraanje et al.[7] that the modified filtered-RLS algorithm is a special case of a Kalman filter, which allows an efficient implementation in the form of a fast...

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An Affine Combination of Two LMS Adaptive Filters—Transient Mean-Square Analysis

Cited by 139 publications

References 10 publications

Two Are Better Than One: Adaptive Sparse System Identification Using Affine Combination of Two Sparse Adaptive Filters

Two Are Better Than One: Adaptive Sparse System Identification Using Affine Combination of Two Sparse Adaptive Filters

Transient Analysis of a Combination of Two Adaptive Filters

A numerically stable, finite memory, fast array recursive least squares filter for broadband active noise control

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