qrrls2.m

《自适应滤波算法与实现》（第二版）源码

%QRRLS2 Problem 1.1.1.2.8
%
%   'ifile.mat' - input file containing:
%      I - members of ensemble
%      K - iterations
%      a1 - coefficient of input AR process
%      sigmax - standard deviation of input
%      Wo - coefficient vector of plant
%      sigman - standard deviation of measurement noise
%      lambda - forgetting factor
% 
%   'ofile.mat' - output file containing:
%      ind - sample indexes 
%      M - misadjustment 

clear all	% clear memory
load ifile;	% read input variables
sigmav=sigmax*sqrt(1-a1^2);	
		% standard deviation of input to AR process
L=length(Wo);		% plant and filter length
L1=L+1;			% auxiliary constant
N=L-1;			% plant and filter order
MSE=zeros(K,1);		% prepare to accumulate MSE*I
MSEmin=zeros(K,1);	% prepare to accumulate MSEmin*I

for i=1:I,		% ensemble
  X=zeros(L,1);		% initial memory
  W=zeros(L,1);		% initial coefficient vector
  v=randn(K,1)*sigmav;		% input to AR process
  x=filter([1,0],[1,a1],v);	% input 
  n=randn(K,1)*sigman;		% measurement noise 
  dq2p=zeros(L,1);
  Up=zeros(L,L);
  for k=1:L,		% initialization iterations
    X=[x(k)	
       X(1:N)];		% new input vector
    Up=lambda^(1/2)*[X'
                     Up((1:N),:)];
    d(k)=Wo'*X+n(k);	% noisy desired signal sample
    dq2p=lambda^(1/2)*[d(k) 
                       dq2p(1:N)];
    ep=d(k)-W'*X;	% a priori error sample
    MSE(k)=MSE(k)+ep^2;	% accumulate MSE*I
    MSEmin(k)=MSEmin(k)+(n(k))^2;% accumulate MSEmin*I
    W(1)=d(1)/x(1);
    if k>1,
      for l=2:k,
        aux=0;
        for ll=2:l,
	  aux=aux+x(ll)*W(l-ll+1);
        end
        W(l)=(-aux+d(l))/x(1);
      end
    end		% new coefficient vector
  end
  for k=L1:K,		% iterations
    gammap=1;
    X=[x(k)
       X(1:N)];		% new input vector
    xp=X';
    d(k)=Wo'*X+n(k);	% noisy desired signal sample
    dp=d(k);
    for l=1:L,
      c=sqrt((Up(l,L1-l))^2+(xp(L1-l))^2);
      costheta=Up(l,L1-l)/c;
      gammap=gammap*costheta;
      sintheta=xp(L1-l)/c;
      Qthetap=sparse([1 1:(l+1) (l+1):(N+2)]',...
              [1 l+1 2:l 1 (l+1):(N+2)]',...
              [costheta -sintheta ones(1,l-1) sintheta costheta ones(1,N-(l-1))]',...
              N+2,N+2);
      AUX=Qthetap*[xp
                   Up];
      xp=AUX(1,:);
      Up=AUX(2:L1,:);
      AUX=Qthetap*[dp
                   dq2p];
      dp=AUX(1);
      dq2p=AUX(2:L1); 
    end
    ep=dp/gammap;	% a priori error sample
    MSE(k)=MSE(k)+ep^2;		% accumulate MSE*I
    MSEmin(k)=MSEmin(k)+(n(k))^2;	% accumulate MSEmin*I
    Up=lambda^(1/2)*Up;
    dq2p=lambda^(1/2)*dq2p;   
  end
end

ind=0:(K-1);		% sample indexes
M=MSE./MSEmin-1;	% calculate misadjustment
save ofile ind M;	% write output variables