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本帖最后由 破晓 于 2015-8-20 14:46 编辑
LMS 算法:
LMS算法的更新迭代公式是:w(n+1) = w(n) + 2ηe * (n) x(n), 算法每次迭代计算仅需要 M + 1 次惩罚和M次加法计算
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- %LMS自适应滤波器性能分析
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- clear
- clc
- close all
- %%%%%%%%%%%%%%参数设置%%%%%%%%%%%%%%%%%%%%%%%
- w=3;
- % step_len=0.075;%步长
- step_len=0.05;%步长
-
- variance_v=0.01;%方差
- repeat_times=20;%重复次数
- iteration_times=500;%迭代次数
- filt_len=2;%滤波器长度
- delay=fix(filt_len/2)-1;
- delay1=1;
-
-
-
- %%%%%%%%%%%%%%%%%%%%变量及数组初始化%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- Chan_factor=(1+cos(2*pi*([1:1:3]-2)/w))/2
- Square_err=zeros(repeat_times,iteration_times);
- % Chan_factor1=[-0.195 0.95]
- Chan_factor1=[-0.195 0.95]
- X=zeros(filt_len,1);
- W1=[];
- W2=[];
- Wm1=[repeat_times,iteration_times];
- Wm2=[repeat_times,iteration_times];
-
-
- %%%%%%%%%%%%%外循环,重复做repeat_timws次实验,平均值%%%%%%%%%%%%%%%%
-
- for loop1=1:repeat_times%循环次数
-
- %%%%%%%%%%%%%%内循环变量及数组初始化%%%%%%%%%%%%%%%%%%%%%%%%
- Source=zeros(iteration_times,1);
- W=zeros(filt_len,1);
-
- %%%%%%%%%%%%%内循环,做iteration_times次迭代%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- for i=1:iteration_times
- %%%%%%%%%%%%%%信源,产生等概率分布的正负1%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- if rand<0.5
- Source(i)=-1;
- else
- Source(i)=1;
- end
- end
- %%%%%%%%%%%%%%信道,滤波和加噪声%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- Revdata=filter(Chan_factor1,1,Source)+randn(iteration_times,1)*sqrt(variance_v);
- % Revdata=filter(Chan_factor,1,Source)+randn(iteration_times,1)*sqrt(variance_v);
- % Revdata=filter(Chan_factor1,1,Source);
-
- % RT=filter(Chan_factor1,1,Source);
- %%%%%%%%%%%%%%均衡器,基于LMS算法%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- for loop2=1:iteration_times-filt_len+1
-
- % U=Revdata(loop2:loop2+filt_len-1);
- % y(n)=W'*U=W'*x(n),U=x(n)=输入
- % d为输出
- U=Source(loop2:loop2+filt_len-1);
- d=Revdata(loop2+1);
- % d=Source(loop2+delay);
- % X= x(3)=v(3)-a1*x(2)-a2*x(1);
-
- % d=RT(loop2+delay1);
- % Y(loop2)=W'*U;
- e=d-W'*U;
- % e=d-W'*U;
- W=W+step_len*U*e;
-
- Wm1(loop2,loop1)=W(1);
- Wm2(loop2,loop1)=W(2);
- % W1(loop2)=W(1);
- % W2(loop2)=W(2);
- Square_err(loop1,loop2)=e.^2;
- end
-
-
- end
-
-
-
- %%%%%%%%%%%%%%作图,显示结果%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- Square_err_mean=sum(Square_err(:,:))/repeat_times;
- % Wm2
- W1=Wm1(:,repeat_times);
- W2=Wm2(:,repeat_times);
- meanW1=mean(Wm1');
- meanW2=mean(Wm2');
- Square_err;
- %semilogy(Square_err_mean);
- figure(1);
- plot(Square_err_mean);
- hold on;
- plot(Square_err(1,:),'r');
- legend('20次重复试验平均误差','单次误差');
- xlabel('迭代次数');
- ylabel('均方误差');
- title('步长为0.075,500次迭代均方误差变化曲线');
- grid on;
- hold on;
-
- figure(2);
- plot(W1);
- hold on;
- plot(W2,'r');
- hold on;
- plot(meanW1,'k');
- hold on;
- plot(meanW2,'--k');
- legend('W1','W2','20次重复试验W1','20次重复试验W2');
- xlabel('迭代次数');
- ylabel('抽头权值');
- title('步长为0.075,500次迭代权值学习曲线');
- grid on;
复制代码
RLS 算法
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- %RLS自适应滤波器性能分析
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- clear all
- %clc
- %close all
- %%%%%%%%%%%%%%参数设置%%%%%%%%%%%%%%%%%%%%%%%
- w=2.9;
- % forget_factor=0.995;
- forget_factor=0.5;
- variance_v=0.001;
- repeat_times=20;
- iteration_times=500;
- filt_len=2;
- delay=fix(filt_len/2)-1;
- %%%%%%%%%%%%%%%%%%%%变量及数组初始化%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- Chan_factor=(1+cos(2*pi*([1:1:3]-2)/w))/2;
- Chan_factor1=[-0.195,0.95]
- Square_err=zeros(repeat_times,iteration_times);
- W1=[];
- W2=[];
- Wm1=[repeat_times,iteration_times];
- Wm2=[repeat_times,iteration_times];
-
-
- %%%%%%%%%%%%%外循环,重复做repeat_times次实验,平均值%%%%%%%%%%%%%%%%
- for loop1=1:repeat_times
-
-
- %%%%%%%%%%%%%%内循环变量及数组初始化%%%%%%%%%%%%%%%%%%%%%%%%
- Source=zeros(iteration_times,1);
- W=zeros(filt_len,1);
- P=eye(filt_len);
- Pi=zeros(filt_len,1);
- K=zeros(filt_len,1);
-
-
-
- %%%%%%%%%%%%%内循环,做iteration_times次迭代%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- for i=1:iteration_times
- %%%%%%%%%%%%%%信源,产生等概率分布的正负1%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- if rand<0.5
- Source(i)=-1;
- else
- Source(i)=1;
- end
- end
- %%%%%%%%%%%%%%信道,滤波和加噪声%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- Revdata=filter(Chan_factor1,1,Source)+randn(iteration_times,1)*sqrt(variance_v);
- %%%%%%%%%%%%%%均衡器,基于RLS算法%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- for loop2=1:iteration_times-filt_len+1
-
- % U=Revdata(loop2:loop2+filt_len-1);
- % d=Source(loop2+delay);
- U=Source(loop2:loop2+filt_len-1);
- d=Revdata(loop2+1);
- Pi=P*U;
- K=Pi/(forget_factor+U'*Pi);
- e=d-W'*U;
- W=W+K*e;
- P=P/forget_factor-K*U'*P/forget_factor;
-
- Wm1(loop2,loop1)=W(1);
- Wm2(loop2,loop1)=W(2);
-
- Square_err(loop1,loop2)=e.^2;
- end
- end
- %%%%%%%%%%%%%%作图,显示结果%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- Square_err_mean=sum(Square_err(:,:))/repeat_times;
-
-
- W1=Wm1(:,repeat_times)
- W2=Wm2(:,repeat_times)
- meanW1=mean(Wm1');
- meanW2=mean(Wm2');
- %semilogy(Square_err_mean);
- figure(1);
- plot(Square_err_mean);
- hold on;
- plot(Square_err(1,:),'r');
- legend('20次重复试验平均误差','单次误差');
- xlabel('迭代次数');
- ylabel('均方误差');
- title('遗忘因子为0.8,500次迭代均方误差变化曲线');
- grid on;
- hold on;
-
- plot(Square_err_mean);
- hold off;
-
- figure(2);
-
- plot(W1);
- hold on;
- plot(W2,'r');
- hold on;
- plot(meanW1,'k');
- hold on;
- plot(meanW2,'--k');
- legend('W1','W2','20次重复试验W1','20次重复试验W2');
- xlabel('迭代次数');
- ylabel('抽头权值');
- title('遗忘因子为0.8,500次迭代权值学习曲线');
- grid on;
复制代码
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