/usr/share/octave/packages/3.2/tsa-4.1.0/amarma.m is in octave-tsa 4.1.0+svn20110501-1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 | function [z,e,REV,ESU,V,Z,SPUR] = amarma(y, Mode, MOP, UC, z0, Z0, V0, W);
% Adaptive Mean-AutoRegressive-Moving-Average model estimation
% [z,E,ESU,REV,V,Z,SPUR] = amarma(y, mode, MOP, UC, z0, Z0, V0, W);
% Estimates AAR parameters with Kalman filter algorithm
% y(t) = sum_i(a(i,t)*y(t-i)) + mu(t) + E(t)
%
% State space model:
% z(t)=G*z(t-1) + w(t) w(t)=N(0,W)
% y(t)=H*z(t) + v(t) v(t)=N(0,V)
%
% G = I,
% z = [µ(t)/(1-sum_i(a(i,t))),a_1(t-1),..,a_p(t-p),b_1(t-1),...,b_q(t-q)];
% H = [1,y(t-1),..,y(t-p),e(t-1),...,e(t-q)];
% W = E{(z(t)-G*z(t-1))*(z(t)-G*z(t-1))'}
% V = E{(y(t)-H*z(t-1))*(y(t)-H*z(t-1))'}
%
% Input:
% y Signal (AR-Process)
% Mode
% [0,0] uses V0 and W
%
% MOP Model order [m,p,q], default [0,10,0]
% m=1 includes the mean term, m=0 does not.
% p and q must be positive integers
% it is recommended to set q=0.
% UC Update Coefficient, default 0
% z0 Initial state vector
% Z0 Initial Covariance matrix
%
% Output:
% z AR-Parameter
% E error process (Adaptively filtered process)
% REV relative error variance MSE/MSY
%
%
% see also: AAR
%
% 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.
% [2] Schlögl A, Lee FY, Bischof H, Pfurtscheller G
% Characterization of Four-Class Motor Imagery EEG Data for the BCI-Competition 2005.
% Journal of neural engineering 2 (2005) 4, S. L14-L22
%
% More references can be found at
% http://www.dpmi.tu-graz.ac.at/~schloegl/publications/
% $Id: amarma.m 5376 2008-10-13 15:53:47Z schloegl $
% Copyright (C) 1998-2002,2005,2006,2007,2008 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 nargin<2 Mode=0;
elseif isnan(Mode) return; end;
if nargin<3, MOP=[0,10,0]; end;
if nargin<8, W = nan ; end;
if length(MOP)==0, m=0;p=10; q=0; MOP=p;
elseif length(MOP)==1, m=0;p=MOP(1); q=0; MOP=p;
elseif length(MOP)==2, fprintf(1,'Error AMARMA: MOP is ambiguos\n');
elseif length(MOP)>2, m=MOP(1); p=MOP(2); q=MOP(3);MOP=m+p+q;
end;
if prod(size(Mode))>1
aMode=Mode(1);
eMode=Mode(2);
end;
%fprintf(1,['a' int2str(aMode) 'e' int2str(eMode) ' ']);
e = zeros(nc,1);
V = zeros(nc,1);V(1)=V0;
T = zeros(nc,1);
ESU = zeros(nc,1)+nan;
SPUR = zeros(nc,1)+nan;
z = z0(ones(nc,1),:);
dW = UC/MOP*eye(MOP); % Schloegl
%------------------------------------------------
% First Iteration
%------------------------------------------------
H = zeros(MOP,1);
if m,
%M0 = z0(1)/(1-sum(z0(2:p+1))); %transformierter Mittelwert
H(1) = 1;%M0;
%z0(1)= 1;
end;
Z = Z0;
zt= z0;
A1 = zeros(MOP); A2 = A1;
%------------------------------------------------
% Update Equations
%------------------------------------------------
for t=1:nc,
%H=[y(t-1); H(1:p-1); E ; H(p+1:MOP-1)]
if t<=p, H(m+(1:t-1)) = y(t-1:-1:1); %H(p)=mu0; % Autoregressive
else H(m+(1:p)) = y(t-1:-1:t-p); %mu0];
end;
if t<=q, H(m+p+(1:t-1)) = e(t-1:-1:1); % Moving Average
else H(m+p+(1:q)) = e(t-1:-1:t-q);
end;
% Prediction Error
E = y(t) - zt*H;
e(t) = E;
if ~isnan(E),
E2 = E*E;
AY = Z*H;
% [zt, t, y(t), E,ESU(t),V(t),H,Z],pause,
ESU(t) = H'*AY;
if eMode==0
V(t) = V0;
elseif eMode==1
V0 = V(t-1);
V(t) = V0*(1-UC)+UC*E2;
elseif eMode==2
V0 = 1;
V(t) = V0; %V(t-1)*(1-UC)+UC*E2;
elseif eMode==3
V0 = 1-UC;
V(t) = V0; %(t-1)*(1-UC)+UC*E2;
elseif eMode==4
V0 = V0*(1-UC)+UC*E2;
V(t) = V0;
elseif eMode==5
V(t)=V0;
%V0 = V0;
elseif eMode==6
if E2>ESU(t)
V0=(1-UC)*V0+UC*(E2-ESU(t));
end;
V(t)=V0;
elseif eMode==7
V0=V(t);
if E2>ESU(t)
V(t) = (1-UC)*V0+UC*(E2-ESU(t));
else
V(t) = V0;
end;
elseif eMode==8
V0=0;
V(t) = V0; % (t-1)*(1-UC)+UC*E2;
end;
%[t,size(H),size(Z)]
k = AY / (ESU(t) + V0); % Kalman Gain
zt = zt + k'*E;
%z(t,:) = zt;
if aMode==0
%W = W; %nop % Schloegl et al. 2003
elseif aMode==2
T(t)=(1-UC)*T(t-1)+UC*(E2-Q(t))/(H'*H); % Roberts I 1998
Z=Z*V(t-1)/Q(t);
if T(t)>0 W=T(t)*eye(MOP); else W=zeros(MOP);end;
elseif aMode==5
Q_wo = (H'*C*H + V(t-1)); % Roberts II 1998
T(t)=(1-UC)*T(t-1)+UC*(E2-Q_wo)/(H'*H);
if T(t)>0 W=T(t)*eye(MOP); else W=zeros(MOP); end;
elseif aMode==6
T(t)=(1-UC)*T(t-1)+UC*(E2-Q(t))/(H'*H);
Z=Z*V(t)/Q(t);
if T(t)>0 W=T(t)*eye(MOP); else W=zeros(MOP); end;
elseif aMode==11
%Z = Z - k*AY';
W = sum(diag(Z))*dW;
elseif aMode==12
W = UC*UC*eye(MOP);
elseif aMode==13
W = UC*diag(diag(Z));
elseif aMode==14
W = (UC*UC)*diag(diag(Z));
elseif aMode==15
W = sum(diag(Z))*dW;
elseif aMode==16
W = UC*eye(MOP); % Schloegl 1998
elseif aMode==17
Z = 0.5*(Z+Z');
W = UC*Z;
elseif aMode==18
W = 0.5*UC*(Z+Z');
%W=W;
end;
Z = Z - k*AY'; % Schloegl 1998
else
V(t) = V0;
end;
if any(any(isnan(W))), W=UC*Z; end;
z(t,:) = zt;
Z = Z + W; % Schloegl 1998
SPUR(t)=trace(Z);
end;
if 0,m,
z(:,1)=M0*z(:,1)./(1-sum(z(:,2:p),2));
end;
REV = mean(e.*e)/mean(y.*y);
if any(~isfinite(Z(:))), REV=inf; end;
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