【正文】 sions, and needs some additional hardware with respect to the constituent algorithms. of bined adaptive filter Consider a system identification by the bination of two LMS algorithms with different steps. Here, the parameter q is μ,. ? ? ? ?10/, 21 ???? qqQ . The unknown system has four timeinvariant coefficients,and the FIR filters are with N = 4. We give the average mean square deviation (AMSD) for both individual algorithms, as well as for their bination,Fig. 1(a). Results are obtained by averaging over 100 independent runs (the Monte Carlo method), with μ = . The reference dk is corrupted by a zeromean uncorrelated Gaussian noise with 2n? = and SNR = 15 dB, and κ is . In the first 30 iterations the variance was estimated according to (7), and the CA picked the weighting coefficients calculated by the LMS with μ. As presented in Fig. 1(a), the CA first uses the LMS with μ and then, in the steady state, the LMS with μ/10. Note the region, between the 200th and 400th iteration,where the algorithm can take the LMS with either stepsize,in different realizations. Here, performance of the CA would be improved by increasing the number of parallel LMS algorithms with steps between these two also that, in steady state, the CA does not ideally pick up the LMS with smaller step. The reason is in the statistical nature of the approach. Combined adaptive filter achieves even better performance if the individual algorithms, instead of starting an iteration with the coefficient values taken from their previous iteration, take the ones chosen by the CA. Namely, if the CA chooses, in the kth iteration, the weighting coefficient vector PW ,then each individual algorithm calculates its weighting coefficients in the (k+1)th iteration according to: ? ?kkpk XeEWW ?21 ??? (9) Fig. 1. Average MSD for considered algorithms. Fig. 2. Average MSD for considered algorithms. Fig. 1(b) shows this improvement, applied on the previous example. In order to clearly pare the obtained results,for each simulation we calculated the AMSD. For the first LMS (μ) it was AMSD = , for the second LMS (μ/10) it was AMSD = , for the CA (CoLMS) it was AMSD = and for the CA with modification (9) it was AMSD = . 5. Simulation results The proposed bined adaptive filter with various types of LMSbased algorithms is implemented for stationary and nonstationary cases in a system identification of the bined filter is pared with the individual ones, that pose the particular bination. In all simulations presented here, the reference dk is corrupted by a zeromean uncorrelated Gaussian noise with ?n? and SNR = 15 dB. Results are obtained by averaging over 100 independent runs, with N = 4, as in the previous section. (a) Time varying optimal weighting vector: The proposed idea may be applied to the SA algorithms in a nonstationary case. In the simulation, the bined filter is posed out of three SA adaptive filters with different steps, . Q = {μ, μ/2, μ/8}。,GLMS: q ≡ a,SA:q ≡ 181。 本文的結(jié)構(gòu)如下 ， 作者認(rèn)為的 LMS 的算法概述 載于第 2 節(jié)， 第 3 節(jié)提出了 自適應(yīng)算法的 改進(jìn)和組合 標(biāo)準(zhǔn) ， 仿真結(jié)果在第 4 節(jié)。對于自適應(yīng)濾波器，它被賦 值， [3]： 組合 自適應(yīng)濾波器 合并后的自適應(yīng)濾波器的基本思想是在兩個或兩個以上自適應(yīng) LMS 算法并行實現(xiàn)與每個迭代之間的最佳選擇， [9]。 第 2 步 ： 估計 每個 算法 的方差 2q? 。加權(quán)系數(shù)的計算 并未使 并行算法增加計算時間，因為它是由硬件實現(xiàn)并行執(zhí)行 的 ，從而增加 了 硬件要求。比較聯(lián)合濾波器性能 ,以組成特定的組合。 CA 增加了對 N 的 補(bǔ)充和 N IF 的討論 .對于 VS LMS 算法 ，其 增加 了 ： 3N乘法， N的添加 ，以及決定至少 2N IF 。s Poly Theater. Their show, titled Ulan Muqir on the Grassland, depicted the history and development of the art troupe. Being from the region allowed me to embrace the culture of Inner Mongolia and being a member of the troupe showed me where I belonged, Nasun, the art troupe39。 但要注意的是， 突然的變化使系統(tǒng) 乘以 1 到 2021 次迭 代（圖 2（ b））。 組合 自適應(yīng)濾波器 能夠 達(dá)到更好的性能 如果該獨立算法能勝過他們以往所 采取的系數(shù)值迭代 ，即 采取由 CA 所選擇的那些 值 。 在 仿真中我們 估計 2q? [4]式 ： ? ? ? ?? ? ??? kWkWm e di an iiq? （ 7） 當(dāng) k = 1， 2， ... ， L 和 22 qZ ?? ?? 替代的方法是估計 2n? 為 （ 8） 有關(guān)表達(dá)式 2n? 和 2q? 在穩(wěn)定狀態(tài)為 LMS 算法 的 不同類型， 從 已知 文獻(xiàn)中可以看出 。 另一方面， 當(dāng) 偏置變大， 然后中央位置的不同間隔距離很大 ,而且他們不相交。它可以表示為： ? ?? ? ? ?? ?*kkkkk WWEWEWV ???? （ 2） 根據(jù)（ 2）， k V 是： （ 3） ? ?? ?kWbias i 是加權(quán)系數(shù)的偏 差 ， ??ki? 與方差 2? 是零均值的隨機(jī)變量差 ，它 取決于LMS 的算法類型，以及外部噪聲方差 2n? 。這些參數(shù)的選擇主要是基于一種算法質(zhì)量 的權(quán)衡 中所提到的適應(yīng)性能。 various parameters affecting the step for VS LMS). These parameters crucially in?uence the ?lter output during two adaptation phases:transient and steady state. Choice of these parameters is mostly based on some kind of tradeoff between the quality of algorithm performance in the mentioned adaptation phases. We propose a possible approach for the LMSbased adaptive ?lter performance improvement. Namely, we make a bination of several LMSbased FIR ?lters with different parameters, and provide the criterion for choosing the most suitable algorithm for different adaptation phases. This method may be applied to all the LMSbased algorithms, although we here consider only several of them. The paper is anized as follows. An overview of the considered LMSbased algorithms is given in Section 3 proposes the criterion for evaluation and bination of adaptive algorithms. Simulation results are presented in Section 4. 2. LMS based algorithms Let us de?ne the input signal vector Tk NkxkxkxX )]1()1()([ ???? ?and vector of weighting coef?cients as TNk kWkWkWW )]()()([ 110 ?? ?.The weighting coef?cients vector should be calculated according to: }{21 kkkk XeEWW ???? （ 1） where 181。 仿真 結(jié)果證實了提出的自適應(yīng)濾波器的優(yōu)點 。 正在研究中的 自適應(yīng)濾波問題在于 嘗試 調(diào)整權(quán)重系數(shù)，使系統(tǒng)的輸出 kTkk XWy ?跟蹤參考信號， kkTkk nXWd ?? * 中 n 是一個零均值與方差 2n? 的高斯噪聲， *kW 是最佳權(quán)向量（維納向量）。,GLMS: q ≡ a,SA:q ≡ 181。因此，檢查了一 對 新的 加權(quán) 系數(shù)，或者，如果 ??kDi 是最后一對，只選擇具有最小方差 的 算法 。 未知的系統(tǒng)有四個時間不變系數(shù)， 而且 FIR 濾波器的 N = 4。 圖 2（ a）顯示了每個算法的 AMSD 特點。s Zhangye city during their journey