--- /dev/null
+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.
+%
+
+% $Id: rmle.m 9609 2012-02-10 10:18:00Z schloegl $
+% Copyright (C) 2004 by Jose Luis Gutierrez <jlg@gmx.at>
+% Grupo GENESIS - UTN - Argentina
+%
+% 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/>.
+
+
+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;