--- /dev/null
+function [a,e,REV,TOC,CPUTIME,ESU] = aar(y, Mode, arg3, arg4, arg5, arg6, arg7, arg8, arg9);
+% Calculates adaptive autoregressive (AAR) and adaptive autoregressive moving average estimates (AARMA)
+% of real-valued data series using Kalman filter algorithm.
+% [a,e,REV] = aar(y, mode, MOP, UC, a0, A, W, V);
+%
+% The AAR process is described as following
+% y(k) - a(k,1)*y(t-1) -...- a(k,p)*y(t-p) = e(k);
+% The AARMA process is described as following
+% y(k) - a(k,1)*y(t-1) -...- a(k,p)*y(t-p) = e(k) + b(k,1)*e(t-1) + ... + b(k,q)*e(t-q);
+%
+% Input:
+% y Signal (AR-Process)
+% Mode is a two-element vector [aMode, vMode],
+% aMode determines 1 (out of 12) methods for updating the co-variance matrix (see also [1])
+% vMode determines 1 (out of 7) methods for estimating the innovation variance (see also [1])
+% aMode=1, vmode=2 is the RLS algorithm as used in [2]
+% aMode=-1, LMS algorithm (signal normalized)
+% aMode=-2, LMS algorithm with adaptive normalization
+%
+% MOP model order, default [10,0]
+% MOP=[p] AAR(p) model. p AR parameters
+% MOP=[p,q] AARMA(p,q) model, p AR parameters and q MA coefficients
+% UC Update Coefficient, default 0
+% a0 Initial AAR parameters [a(0,1), a(0,2), ..., a(0,p),b(0,1),b(0,2), ..., b(0,q)]
+% (row vector with p+q elements, default zeros(1,p) )
+% A Initial Covariance matrix (positive definite pxp-matrix, default eye(p))
+% W system noise (required for aMode==0)
+% V observation noise (required for vMode==0)
+%
+% Output:
+% a AAR(MA) estimates [a(k,1), a(k,2), ..., a(k,p),b(k,1),b(k,2), ..., b(k,q]
+% e error process (Adaptively filtered process)
+% REV relative error variance MSE/MSY
+%
+%
+% Hint:
+% The mean square (prediction) error of different variants is useful for determining the free parameters (Mode, MOP, UC)
+%
+% REFERENCE(S):
+% [1] A. Schloegl (2000), The electroencephalogram and the adaptive autoregressive model: theory and applications.
+% ISBN 3-8265-7640-3 Shaker Verlag, Aachen, Germany.
+%
+% More references can be found at
+% http://www.dpmi.tu-graz.ac.at/~schloegl/publications/
+
+%
+% $Id: aar.m 8383 2011-07-16 20:06:59Z schloegl $
+% Copyright (C) 1998-2003 by Alois Schloegl <a.schloegl@ieee.org>
+%
+% This program is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+%
+% This program is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this program. If not, see <http://www.gnu.org/licenses/>.
+
+
+[nc,nr]=size(y);
+%if nc<nr y=y'; end; tmp=nr;nc=nr; nr=tmp;end;
+
+if nargin<2 Mode=0; end;
+% check Mode (argument2)
+if prod(size(Mode))==2
+ aMode=Mode(1);
+ vMode=Mode(2);
+end;
+if any(aMode==(0:14)) && any(vMode==(0:7)),
+ fprintf(1,['a' int2str(aMode) 'e' int2str(vMode) ' ']);
+else
+ fprintf(2,'Error AAR.M: invalid Mode argument\n');
+ return;
+end;
+
+% check model order (argument3)
+if nargin<3 MOP=[10,0]; else MOP= arg3; end;
+if length(MOP)==0 p=10; q=0; MOP=p;
+elseif length(MOP)==1 p=MOP(1); q=0; MOP=p;
+elseif length(MOP)>=2 p=MOP(1); q=MOP(2); MOP=p+q;
+end;
+
+if nargin<4 UC=0; else UC= arg4; end;
+
+a0=zeros(1,MOP);
+A0=eye(MOP);
+if nargin>4,
+ if all(size(arg5)==([1,1]*(MOP+1))); % extended covariance matrix of AAR parameters
+ a0 = arg5(1,2:size(arg5,2));
+ A0 = arg5(2:size(arg5,1),2:size(arg5,2)) - a0'*a0;
+ else
+ a0 = arg5;
+ if nargin>5
+ A0 = arg6;
+ end;
+ end;
+end;
+
+if nargin<7, W = []; else W = arg7; end;
+
+if all(size(W)==MOP),
+ if aMode ~= 0,
+ fprintf(1,'aMode should be 0, because W is given.\n');
+ end;
+elseif isempty(W),
+ if aMode == 0,
+ fprintf(1,'aMode must be non-zero, because W is not given.\n');
+ end;
+elseif any(size(W)~=MOP),
+ fprintf(1,'size of W does not fit. It must be %i x %i.\n',MOP,MOP);
+ return;
+end;
+
+if nargin<8, V0 = []; else V0 = arg8; end;
+if all(size(V0)==nr),
+ if vMode ~= 0,
+ fprintf(1,'vMode should be 0, because V is given.\n');
+ end;
+elseif isempty(V0),
+ if aMode == 0,
+ fprintf(1,'vMode must be non-zero, because V is not given.\n');
+ end;
+else
+ fprintf(1,'size of V does not fit. It must be 1x1.\n');
+ return;
+end;
+
+% if nargin<7 TH=3; else TH = arg7; end;
+% TH=TH*var(y);
+% TH=TH*mean(detrend(y,0).^2);
+MSY=mean(detrend(y,0).^2);
+
+e=zeros(nc,1);
+Q=zeros(nc,1);
+V=zeros(nc,1);
+T=zeros(nc,1);
+%DET=zeros(nc,1);
+SPUR=zeros(nc,1);
+ESU=zeros(nc,1);
+a=a0(ones(nc,1),:);
+%a=zeros(nc,MOP);
+%b=zeros(nc,q);
+
+mu=1-UC; % Patomaeki 1995
+lambda=(1-UC); % Schloegl 1996
+arc=poly((1-UC*2)*[1;1]);b0=sum(arc); % Whale forgettting factor for Mode=258,(Bianci et al. 1997)
+
+dW=UC/MOP*eye(MOP); % Schloegl
+
+
+%------------------------------------------------
+% First Iteration
+%------------------------------------------------
+Y=zeros(MOP,1);
+C=zeros(MOP);
+%X=zeros(q,1);
+at=a0;
+A=A0;
+E=y(1);
+e(1)=E;
+if ~isempty(V0)
+ V(1) = V0;
+else
+ V(1) = (1-UC) + UC*E*E;
+end;
+ESU(1) = 1; %Y'*A*Y;
+
+A1=zeros(MOP);A2=A1;
+tic;CPUTIME=cputime;
+%------------------------------------------------
+% Update Equations
+%------------------------------------------------
+T0=2;
+
+for t=T0:nc,
+
+ %Y=[y(t-1); Y(1:p-1); E ; Y(p+1:MOP-1)]
+
+ if t<=p Y(1:t-1)=y(t-1:-1:1); % Autoregressive
+ else Y(1:p)=y(t-1:-1:t-p);
+ end;
+
+ if t<=q Y(p+(1:t-1))=e(t-1:-1:1); % Moving Average
+ else Y(p+1:MOP)=e(t-1:-1:t-q);
+ end;
+
+ % Prediction Error
+ E = y(t) - a(t-1,:)*Y;
+ e(t) = E;
+ E2=E*E;
+
+ AY=A*Y;
+ esu=Y'*AY;
+ ESU(t)=esu;
+
+ if isnan(E),
+ a(t,:)=a(t-1,:);
+ else
+ V(t) = V(t-1)*(1-UC)+UC*E2;
+ if aMode == -1, % LMS
+ % V(t) = V(t-1)*(1-UC)+UC*E2;
+ a(t,:)=a(t-1,:) + (UC/MSY)*E*Y';
+ elseif aMode == -2, % LMS with adaptive estimation of the variance
+ a(t,:)=a(t-1,:) + UC/V(t)*E*Y';
+
+ else % Kalman filtering (including RLS)
+ if vMode==0, %eMode==4
+ Q(t) = (esu + V0);
+ elseif vMode==1, %eMode==4
+ Q(t) = (esu + V(t));
+ elseif vMode==2, %eMode==2
+ Q(t) = (esu + 1);
+ elseif vMode==3, %eMode==3
+ Q(t) = (esu + lambda);
+ elseif vMode==4, %eMode==1
+ Q(t) = (esu + V(t-1));
+ elseif vMode==5, %eMode==6
+ if E2>esu
+ V(t)=(1-UC)*V(t-1)+UC*(E2-esu);
+ else
+ V(t)=V(t-1);
+ end;
+ Q(t) = (esu + V(t));
+ elseif vMode==6, %eMode==7
+ if E2>esu
+ V(t)=(1-UC)*V(t-1)+UC*(E2-esu);
+ else
+ V(t)=V(t-1);
+ end;
+ Q(t) = (esu + V(t-1));
+ elseif vMode==7, %eMode==8
+ Q(t) = esu;
+ end;
+
+ k = AY / Q(t); % Kalman Gain
+ a(t,:) = a(t-1,:) + k'*E;
+
+ if aMode==0, %AMode=0
+ A = A - k*AY' + W; % Schloegl et al. 2003
+ elseif aMode==1, %AMode=1
+ A = (1+UC)*(A - k*AY'); % Schloegl et al. 1997
+ elseif aMode==2, %AMode=11
+ A = A - k*AY';
+ A = A + sum(diag(A))*dW;
+ elseif aMode==3, %AMode=5
+ A = A - k*AY' + sum(diag(A))*dW;
+ elseif aMode==4, %AMode=6
+ A = A - k*AY' + UC*eye(MOP); % Schloegl 1998
+ elseif aMode==5, %AMode=2
+ A = A - k*AY' + UC*UC*eye(MOP);
+ elseif aMode==6, %AMode=2
+ T(t)=(1-UC)*T(t-1)+UC*(E2-Q(t))/(Y'*Y);
+ A=A*V(t-1)/Q(t);
+ if T(t)>0 A=A+T(t)*eye(MOP); end;
+ elseif aMode==7, %AMode=6
+ T(t)=(1-UC)*T(t-1)+UC*(E2-Q(t))/(Y'*Y);
+ A=A*V(t)/Q(t);
+ if T(t)>0 A=A+T(t)*eye(MOP); end;
+ elseif aMode==8, %AMode=5
+ Q_wo = (Y'*C*Y + V(t-1));
+ C=A-k*AY';
+ T(t)=(1-UC)*T(t-1)+UC*(E2-Q_wo)/(Y'*Y);
+ if T(t)>0 A=C+T(t)*eye(MOP); else A=C; end;
+ elseif aMode==9, %AMode=3
+ A = A - (1+UC)*k*AY';
+ A = A + sum(diag(A))*dW;
+ elseif aMode==10, %AMode=7
+ A = A - (1+UC)*k*AY' + sum(diag(A))*dW;
+ elseif aMode==11, %AMode=8
+
+ A = A - (1+UC)*k*AY' + UC*eye(MOP); % Schloegl 1998
+ elseif aMode==12, %AMode=4
+ A = A - (1+UC)*k*AY' + UC*UC*eye(MOP);
+ elseif aMode==13
+ A = A - k*AY' + UC*diag(diag(A));
+ elseif aMode==14
+ A = A - k*AY' + (UC*UC)*diag(diag(A));
+ end;
+ end;
+ end;
+end;
+
+%a=a(end,:);
+TOC = toc;
+CPUTIME = cputime - CPUTIME;
+%REV = (e'*e)/(y'*y);
+
+REV = mean(e.*e)./mean(y.*y);
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff