- refactored

2022-06-30 13:32:40 +02:00
parent 77cd5261b1
commit 776932e5d1
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+% RLS-Algorithmus
+% ---------------
+% function [dd,e,wf,fpo] = rls(x,d,N,mu,rho,wi)
+%
+% Parameter:
+% x    : Eingangssignal
+% d    : erwünschtes Signal (Referenzsignal)
+% N    : Filterordnung
+% mu   : konstante Schrittweite
+% rho  : Vergessensfaktor 
+% wi   : Startwerte der Filterkoeffizienten im Zeitbereich
+%
+% Rückgabewerte:
+% dd   : Schätzung d' des Referenzsignals d aus x
+% e    : Fehler d - d'
+% wf   : Filterkoeffizienten am Ende der Adaption im Zeitbereich
+% fpo  : Anzahl der benötigten Floating-Point Operationen
+
+% -------------------------------------------------------------------------
+% Datum : 27.3.2002
+% Autor : Jens Ahrensfeld
+% Thema : Diplomarbeit
+% Datei : rls.m
+%
+% -------------------------------------------------------------------------
+function [dd,e,wf,fpo] = rls(x,d,N,mu,rho,wi)
+
+% -------------------------------------------------------------------------
+% Initialisierung RLS
+% -------------------------------------------------------------------------
+wf  = wi;
+dd  = zeros(length(x),1);
+e   = zeros(length(x),1);
+eta = 1000000;               
+R_  = eta * eye(N);          % inverse Autokorrelationsmatrix R
+flops(0);
+
+% -------------------------------------------------------------------------
+% RLS Adaptation
+% -------------------------------------------------------------------------
+for n = N : length(x)
+	xs    = x(n:-1:n-N+1);                  % Eingangsvektor
+	dd(n) = xs' * wf;                       % Filterung 
+	e(n)  = d(n) - dd(n);                   % a priori-Fehler
+    z     = R_ * xs;                        % gefilterter Datenvektor z
+    vn    = 1/(rho + xs'*z);           		% Normierungskonstante
+    zn    = vn*z;                      		% Normierung
+    wf    = wf + mu*e(n)*zn;           		% Aktualisierung der Filterkoeffizienten
+    R_    = 1/rho * (R_ - zn*xs'*R_);  		% Aktualisierung der inversen 
+                                            % Autokorrelationsmatrix R
+end ;
+fpo = flops;
+
+% -------------------------------------------------------------------------
+% Ende rls.m
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+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%                                                    %
+%                 RLS Algorithm                      %
+%                                                    %
+% Written By: Sundar Sankaran and A. A. (Louis) Beex %
+%             DSP Research Laboratory                %
+%             Dept. of Electrical and Comp. Engg     %
+%             Virginia Tech                          %
+%             Blacksburg VA 24061-0111               %
+%                                                    %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+randn('seed', 0) ;
+rand('seed', 0) ;
+
+NoOfData = 8000 ;	% Set no of data points used for training
+Order = 32 ;		% Set the adaptive filter order
+
+Lambda = 0.98 ;		% Set the forgetting factor
+Delta = 0.001 ;		% R initialized to Delta*I
+
+x = randn(NoOfData, 1) ;% Input assumed to be white
+h = rand(Order, 1) ;	% System picked randomly
+d = filter(h, 1, x) ;	% Generate output (desired signal)
+
+% Initialize RLS
+
+P = Delta * eye ( Order, Order ) ;
+w = zeros ( Order, 1 ) ;
+
+% RLS Adaptation
+
+for n = Order : NoOfData ;
+		
+	u = x(n:-1:n-Order+1) ;
+	pi_ = u' * P ;
+	k = Lambda + pi_ * u ;
+	K = pi_'/k;
+	e(n) = d(n) - w' * u ;
+	w = w + K * e(n) ;
+	PPrime = K * pi_ ;
+	P = ( P - PPrime ) / Lambda ;
+	w_err(n) = norm(h - w) ;
+
+end ;
+
+
+% Plot results
+
+figure ;
+plot(20*log10(abs(e))) ;
+title('Learning Curve') ;
+xlabel('Iteration Number') ;
+ylabel('Output Estimation Error in dB') ;
+
+figure ;
+semilogy(w_err) ;
+title('Weight Estimation Error') ;
+xlabel('Iteration Number') ;
+ylabel('Weight Error in dB') ;
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+%===================================================================
+%-------------------------------------------------------------------
+%
+%         Adaptive Filter 
+%
+%         Simulationen  
+%         
+%         [E,W,w,inv_R]=rls(N,X,D,w_start,rho)
+%
+%         RLS-Algorithmus
+%
+%         E       = Fehlersignal E[.]
+%         W       = Filterkoeffizienten im zeitlichen Verlauf
+%         w       = Filterkoeffizienten am Ende der Adaption
+%         inv_R   = Inverse deterministische Korrelationsmatrix
+%		    nach Adaptionsende
+%         N       = Anz. Filterkoeffizienten = Filterordnung+1
+%         X       = Filtereingang X[.]
+%         D       = erwuenschtes Signal D[.]
+%         w_start = Startwerte Filterkoeffizienten 
+%         rho     = Vergessensfaktor
+%
+%-------------------------------------------------------------------
+
+%
+%	  author:  Markus Hofbauer
+%                  ISI, ETH Zuerich (Switzerland)
+%
+%         created: 7/2000  
+%         
+%
+%-------------------------------------------------------------------
+%
+% File     :  rls.m
+%
+% Startfile:  simX.m
+%
+%-------------------------------------------------------------------
+%===================================================================
+
+function [E,W,w,inv_R]=rls(N,X,D,w_start,rho)
+
+p0=1000000;            % Initialisierung von
+inv_R=p0*eye(N);       % inv_R 
+
+adaptlen=length(X);
+w= w_start;          
+W=zeros(N,adaptlen);
+E=zeros(adaptlen,1); 
+
+%-------------------------------------------------------------------
+% RLS Update Loop
+%-------------------------------------------------------------------
+
+for i=N:adaptlen
+
+   W(:,i)=w;
+ 
+   x      = X(i:-1:i-N+1); % Eingangsvektor (x[k],x[k-1],..,x[k-N+1])
+   y=x'*w;                 % Filterausgang
+   e=D(i)-y;               % Fehler
+  
+   c=1/(rho+x'*inv_R*x);                
+   inv_R=1/rho*(inv_R-c*inv_R*x*x'*inv_R);  % Aufdatierung von inv_R 
+   w=w+inv_R*e*x;                           % Aufdatierung von w 
+
+   E(i)=e;
+end;
+
+
+