外文資料翻譯--基于lms算法的自適應組合濾波器

1、英文原文Combined Adaptive Filter with LMS-Based AlgorithmsAbstract: A combined adaptive filter is proposed. It consists of parallel LMS-based adaptive FIR filters and an algorithm for choosing the better among them. As a cri

2、terion for comparison of the considered algorithms in the proposed filter, we take the ratio between bias and variance of the weighting coefficients. Simulations results confirm the advantages of the proposed adaptive fi

3、lter.Keywords: Adaptive filter, LMS algorithm, Combined algorithm,Bias and variance trade-off1．IntroductionAdaptive filters have been applied in signal processing and control, as well as in many practical problems, [1, 2

4、]. Performance of an adaptive filter depends mainly on the algorithm used for updating the filter weighting coefficients. The most commonly used adaptive systems are those based on the Least Mean Square (LMS) adaptive al

5、gorithm and its modifications (LMS-based algorithms).The LMS is simple for implementation and robust in a number of applications [1–3]. However, since it does not always converge in an acceptable manner, there have been

6、many attempts to improve its performance by the appropriate modifications: sign algorithm (SA) [8], geometric mean LMS (GLMS) [5], variable step-size LMS(VS LMS) [6, 7].Each of the LMS-based algorithms has at least one p

7、arameter that should be defined prior to the adaptation procedure (step for LMS and SA; step and smoothing coefficients for GLMS; various parameters affecting the step for VS LMS). These parameters crucially influence th

8、e filter output during two adaptation phases:transient and steady state. Choice of these parameters is mostly based on some kind of trade-off between the quality of algorithm performance in the mentioned adaptation phase

9、s.We propose a possible approach for the LMS-based adaptive filter performance improvement. Namely, we make a combination of several LMS-based FIR filters with different parameters, and provide the criterion for choosing

10、 the most suitable algorithm for different adaptation phases. This method may be applied to all the LMS-based algorithms, although we here consider only several of them.The paper is organized as follows. An overview of t

11、he considered LMS-based algorithms is given in Section 2.Section 3 proposes the criterion for evaluation and combination of adaptive algorithms. Simulation results are presented in Section 4.2. LMS based algorithmsbased

12、algorithm. In that sense, in the analysis that follows we will assume thatdepends only 2 ?on the algorithm type, i.e. on its parameters.An important performance measure for an adaptive filter is its mean square deviatio

13、n (MSD) of weighting coefficients. For the adaptive filters, it is given by, [3]: . ? ? kT k k V V E MSD? ? ? lim3. Combined adaptive filterThe basic idea of the combined adaptive filter lies in parallel implementation o

14、f two or more adaptive LMS-based algorithms, with the choice of the best among them in each iteration [9]. Choice of the most appropriate algorithm, in each iteration, reduces to the choice of the best value for the weig

15、hting coefficients. The best weighting coefficient is the one that is, at a given instant, the closest to the corresponding value of the Wiener vector.Let be the i ?th weighting coefficient for LMS-based algorithm with t

16、he chosen ? ? q k Wi ,parameter q at an instant k. Note that one may now treat all the algorithms in a unified way (LMS: q ≡ µ,GLMS: q ≡ a,SA:q ≡ µ). LMS-based algorithm behavior is crucially dependent on q. I

17、n each iteration there is an optimal value qopt , producing the best performance of the adaptive al-gorithm. Analyze now a combined adaptive filter, with several LMS-based algorithms of the same type, but with different

18、parameter q.The weighting coefficients are random variables distributed around the ,with ? ? k Wi*and the variance , related by [4, 9]: ? ? ? ? q k W bias i , 2 q ?, (4) ? ? ? ? ? ? ? ? q i i i q k

19、 W bias k W q k W ?? ? ? ? , , *where (4) holds with the probability P(κ), dependent on κ. For example, for κ = 2 and a Gaussian distribution,P(κ) = 0.95 (two sigma rule).Define the confidence intervals for : ? ? ] 9 ,

20、4 [ , ,q k Wi(5) ? ? ? ? ? ? ? ? q i q i i q k W k q k W k D ?? ? 2 , , 2 , ? ? ?Then, from (4) and (5) we conclude that, as long as , , ? ? ? ? q i q k W bias ?? ? , ? ? ? ? k D k W i i ? *independently on q. This mea

21、ns that, for small bias, the confidence intervals, for different of s q?the same LMS-based algorithm, of the same LMS-based algorithm, intersect. When, on the other hand, the bias becomes large, then the central positio

22、ns of the intervals for different are far s q?apart, and they do not intersect.Since we do not have apriori information about the ,we will use a specific ? ? ? ? q k W bias i ,statistical approach to get the criterion