Mercurial > forge
changeset 1702:411fb819afef octave-forge
Implementation by Jose L. Guitierrez of AR estimation with RMLE added
author | schloegl |
---|---|
date | Wed, 08 Sep 2004 10:31:42 +0000 |
parents | 6b5dcfe6652b |
children | f09eab8bea5a |
files | extra/tsa/contents.m extra/tsa/rmle.m |
diffstat | 2 files changed, 102 insertions(+), 0 deletions(-) [+] |
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--- a/extra/tsa/contents.m Wed Sep 08 07:41:48 2004 +0000 +++ b/extra/tsa/contents.m Wed Sep 08 10:31:42 2004 +0000 @@ -35,6 +35,7 @@ % lpc (*) calculates the prediction coefficients form a given time series % invest0 (*) a prior investigation (used by invest1) % invest1 (*) investigates signal (useful for 1st evaluation of the data) +% rmle AR estimation using recursive maximum likelihood function % selmo (*) Select Order of Autoregressive model using different criteria % histo (*) histogram % hup (*) test Hurwitz polynomials
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/extra/tsa/rmle.m Wed Sep 08 10:31:42 2004 +0000 @@ -0,0 +1,101 @@ +function [a,VAR,S,a_aux,b_aux,e_aux,MLE,pos] = rmle(arg1,arg2); +% RMLE estimates AR Parameters using the Recursive Maximum Likelihood +% Estimator according to [1] +% +% Use: [a,VAR]=rmle(x,p) + % Input: + % x is a column vector of data + % p is the model order + % Output: + % a is a vector with the AR parameters of the recursive MLE + % VAR is the excitation white noise variance estimate +% +% Reference(s): +% [1] Kay S.M., Modern Spectral Analysis - Theory and Applications. +% Prentice Hall, p. 232-233, 1988. +% + +% Version 0.1 +% 16 Ago 2004 +% Copyright (c) 2004 by Jose Luis Gutierrez (jlg@gmx.at) +% Grupo GENESIS - UTN - Argentina + +% This library is free software; you can redistribute it and/or +% modify it under the terms of the GNU Library General Public +% License as published by the Free Software Foundation; either +% Version 2 of the License, or (at your option) any later version. +% +% This library 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 +% Library General Public License for more details. +% +% You should have received a copy of the GNU Library General Public +% License along with this library; if not, write to the +% Free Software Foundation, Inc., 59 Temple Place - Suite 330, +% Boston, MA 02111-1307, USA. + +x=arg1*1e-6; +p=arg2; + +N=length(x); +S=zeros(p+1,p+1); +a_aux=zeros(p+1,p);, a_aux(1,:)=1; +b_aux=ones(p+1,p); +e_aux=zeros(p,1);, p_aux=zeros(p,1); +MLE=zeros(3,1); +pos=1; + +for i=0:p + for j=0:p + for n=0:N-1-i-j + S(i+1,j+1)=S(i+1,j+1)+x(n+1+i)*x(n+1+j); + end + end +end + +e0=S(1,1); +c1=S(1,2); +d1=S(2,2); +coef3=1; +coef2=((N-2)*c1)/((N-1)*d1); +coef1=-(e0+N*d1)/((N-1)*d1); +ti=-(N*c1)/((N-1)*d1); +raices=roots([coef3 coef2 coef1 ti]); +for o=1:3 + if raices(o)>-1 & raices(o)<1 + a_aux(2,1)=raices(o); + b_aux(p+1,1)=raices(o); + end +end +e_aux(1,1)=S(1,1)+2*a_aux(2,1)*S(1,2)+(a_aux(2,1)^2)*S(2,2); +p_aux(1,1)=e_aux(1,1)/N; + +for k=2:p + Ck=S(1:k,2:k+1); + Dk=S(2:k+1,2:k+1); + ck=a_aux(1:k,k-1)'*Ck*b_aux(p+1:-1:p+2-k,k-1); + dk=b_aux(p+1:-1:p+2-k,k-1)'*Dk*b_aux(p+1:-1:p+2-k,k-1); + coef3re=1; + coef2re=((N-2*k)*ck)/((N-k)*dk); + coef1re=-(k*e_aux(k-1,1)+N*dk)/((N-k)*dk); + tire=-(N*ck)/((N-k)*dk); + raices=roots([coef3re coef2re coef1re tire]); + for o=1:3 + if raices(o,1)>-1 & raices(o,1)<1 + MLE(o,1)=((1-raices(o)^2)^(k/2))/(((e_aux(k-1)+2*ck*raices(o)+dk*(raices(o)^2))/N)^(N/2)); + end + end + [C,I]=max(MLE); + k_max=raices(I); + for i=1:k-1 + a_aux(i+1,k)=a_aux(i+1,k-1)+k_max*a_aux(k-i+1,k-1); + end + a_aux(k+1,k)=k_max; + b_aux(p+1-k:p+1,k)=a_aux(1:k+1,k); + e_aux(k,1)=e_aux(k-1,1)+2*ck*k_max+dk*k_max^2; + p_aux(k,1)=e_aux(k,1)/N; +end + +a=a_aux(:,p)'; +VAR=p_aux(p)*1e12;