tfar_est_mlu2.m

用于模拟时变非平稳的ARMA过程

function [A, B, exitflag, output]= tfar_est_mlu2(Ayy, Aml0, B0l0, re_im, opts)
% function [A, B, exitflag, output]= tfar_est_mlu2(Ayy, Aml0, B0l0, re_im, opts)
%   This file is part of the TFPM toolbox v1.0 (c)
%   [e-mail] and underlies the GPL.
% 
% Asymptotic ML estimator for TFAR(M, L; N; 1/2) models. The switch
% re_im decides how the parameters are optimized! Crucial? 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if(0)% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear;tfpm;
N    =  64;
MAR  =   2;
LAR  =   2;
MMA  =   0;
LMA  = LAR;
re_im= 'i';
mo_no= 'n';
tfpm_file_gen;
%-------------
beta = 1/2;
B0l= Bml;

y= tfarma_gen(randn(N, 1), Aml, Bml, beta);
qyy= corr_est(y, y, -1, 1/2);
ayy= fft(qyy);
ayy= [ayy(N/2+1:N, :); ayy(1:N/2, :)];
Psi= tf_multiwin(N, MAR, LAR, 5, 3, 1);
Ayy= ayy.*conj(Psi);

ayy= ayy(N/2+1-3*LAR:N/2+1+3*LAR, N/2+1-MAR:N/2+1+MAR);
[AA, BB]= tfar_est_tfywu(ayy, N);
Aml0= AA(:, :, end);
B0l0= BB(:, :, end);
opts= optimset('MaxIter', 300, 'MaxFunEvals', 10000);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
end;% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Dimensions:
[MAR, LAR]= param_dim(Aml0);

% Check for re_im:
if(re_im=='r')
   Aml0= param_hermite(Aml0);
   Aml0= [real(Aml0(1:LAR+1, 2:end)); imag(Aml0(LAR+2:end, 2:end))];
else
   Aml0= [real(Aml0(:, 2:end)) imag(Aml0(:, 2:end))];
end;
B0l0= param_hermite(B0l0);
B0l0= [real(B0l0(1:LAR+1, :)); imag(B0l0(LAR+2:end, :))];

% Combine the parameters:
AB= [Aml0 B0l0];

Pyy= real(nm_to_nk(ml_to_nm(Ayy)));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if(0)% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Call fminunc:
[X, lX, exitflag, output]= fminunc('tfar_llfu2', AB, opts, Pyy, re_im);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
end;% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Call fmincon:
[X, lX, exitflag, output]= fmincon('tfar_llfu2', AB, [], [], [], [], -3*ones(size(AB)), 3*ones(size(AB)), [], opts, Pyy, re_im);

% Check for re_im:
if(re_im=='r')
   A= [[zeros(LAR, 1); 1; zeros(LAR, 1)] X(:, 1:end-1)];
   A= [A(1:LAR+1, :); flipud(A(1:LAR, :))] + j*[flipud(-A(LAR+2:end, :)); zeros(1, MAR+1); A(LAR+2:end, :)];
else
   A= [[zeros(LAR, 1); 1; zeros(LAR, 1)] X(:, 1:MAR)] + j*[zeros(2*LAR+1, 1) X(:, MAR+1:2*MAR)];
end
B= X(:, end);
B= [B(1:LAR+1); flipud(B(1:LAR))] + j*[flipud(-B(LAR+2:end)); 0; B(LAR+2:end)];

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if(0)% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
param_norm([AA(:, :, end) BB(:, :, end)], [Aml B0l], 1)
param_norm([A             B            ], [Aml B0l], 1)
AA(:, :, end)-A
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
end;% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if(0)% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear;tfpm;
N    =  32;
MAR  =   2;
LAR  =   2;
MMA  =   0;
LMA  = LAR;
re_im= 'r';
mo_no= 'm';
tfpm_file_gen;
%-------------
beta = 1/2;
B0l= Bml;
MM= 20;
opts= optimset('MaxIter', 300, 'MaxFunEvals', 10000, 'Diagnostics', 'off', 'Display', 'off');

AMLyw= zeros(2*LAR+1, MAR+2, MM);
AMLml= zeros(2*LAR+1, MAR+2, MM);

Iter= [];
NFun= [];
EFLG= [];
Psi= tf_multiwin(N, MAR, LAR, 5, 3, 1);
for mm= 1:MM
   mm
   y= real(tfarma_gen(randn(N, 1), Aml, B0l, beta));
   Qyy= corr_est(y, y, -1, 1/2);
   Ayy= fft(Qyy);
   Ayy= [Ayy(N/2+1:N, :); Ayy(1:N/2, :)].*conj(Psi);
   ayy= Ayy(N/2+1-3*LAR:N/2+1+3*LAR, N/2+1-MAR:N/2+1+MAR);
   [AA, BB]= tfar_est_tfywu(ayy, N);
   Aml0= AA(:, :, end);
   B0l0= BB(:, :, end);
   [A, B, exitflag, output]= tfar_est_mlu2(Ayy, Aml0, B0l0, re_im, opts);
   Iter= [Iter; output.iterations];
   NFun= [NFun; output.funcCount];
   EFLG= [EFLG; exitflag];
   figure(1);clf;plot(Iter);drawnow
   figure(2);clf;plot(NFun);drawnow
   AMLyw(:, :, mm)= [Aml0 B0l0];
   AMLml(:, :, mm)= [A B];
end;
[mean(Iter) mean(NFun)]
[Myw, Vyw, Byw]= param_mse(AMLyw, [Aml B0l])
[Mml, Vml, Bml]= param_mse(AMLml, [Aml B0l])
[norm(Myw) norm(Mml)]
mean(AMLyw, 3)
mean(AMLml, 3)
sum(EFLG)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
end;% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%