www.pudn.com > adaptivefiltering.rar > qrd_rls_AR_pred.m

function [Wo, xp, gamma, e] = qrd_rls_AR_pred(Xi, Y, verbose, lambda, init, init_val)   
% function [Wo, xp, gamma, e] = qrd_rls_AR_pred(Xi, Y, verbose, lambda, init, init_val)   
% 
% qrd_rls_AR_pred.m - use the QR decomposition-based RLS algorithm 
% to predict complex-valued AR process 
% written for MATLAB 4.0 
% 
% Reference: Haykin, _Adaptive Filter Theory_, 2nd (corr.) ed., 1991 
% 
% 
% Input Parameters 
%       Xi      : matrix of training/test points - each row is 
%                 considered a datum 
%       Y       : vector of corresponding desired outputs for 
%                 predictor 
%       verbose : set to 1 for interactive processing 
%       lambda  : the initial value of the forgetting factor 
%                 init, 
%       init_val: initialization method and value 
%                 mvdr' - init_val is steering vector 
% 
% 
% Output Parameters: 
%       Wo      : row-wise matrix of Hermitian transposed weights 
%                 at each iteration 
%       xp      : row vector of predicted outputs 
%       gamma   : row vector of a priori to a posteriori conversion factors 
%       e       : row vector of a posteriori prediction errors Y - xp 
 
Nout = size(Xi, 2); 
 
% length of maximum number of timesteps that can be predicted 
N = size(Xi, 1); 
 
% order of predictor 
M = size(Xi, 2); 
 
% initialize weight matrix and associated parameters 
% for QRD RLS predictor 
W = zeros(Nout, 1); 
Wo = []; 
gamma = []; 
lambda_root = sqrt(lambda); 
Phi_root = zeros(M, M); 
p_H = zeros(1, M); 
W_H = zeros(1, M); 
z = zeros(1, M); 
 
% initialize predictor until Phi_root is full-rank ' 
for n = 1:M, 
	% compute post-array from pre-array via QRD. Note that computation 
	% of p_H, eta, and W_H are omitted in the initialization period. 
	u = Xi(n, :).'; 
	pre_array = [ [lambda_root*Phi_root u] ; [lambda_root*p_H Y(n)] ; [z 1] ]; 
	post_array = triu(qr(pre_array'))'; 
	Phi_root = post_array(1:M, 1:M); 
	gamma_root = post_array(M+2, M+1); 
	 
	% save results 
	Wo = [ Wo; W_H ]; 
	gamma = [gamma gamma_root^2 ]; 
	 
	% predict next sample and compute error 
	xp(n) = W_H * u; 
	e(n) = Y(n) - xp(n); 
	if (verbose ~= 0) 
		disp(['time step ', int2str(n), ': mag. pred. err. = ' , num2str(abs(e(n)))]); 
	end; 
 
end % for n 
 
% if initializing for MVDR adaptive beamforming, set the 
% auxiliary vector p after Phi_root is full-rank 
 
if (strcmp(init, 'mvdr')), 
   p_H = (Phi_root \ init_val)'; 
end; 
 
% run normally after initialization is complete 
for n = (M+1):N, 
 
	% compute post-array from pre-array via QRD 
	u = Xi(n, :).'; 
	pre_array = [ [lambda_root*Phi_root u] ; [lambda_root*p_H Y(n)] ; [z 1] ]; 
	post_array = triu(qr(pre_array'))'; 
	Phi_root = post_array(1:M, 1:M); 
	p_H = post_array(M+1, 1:M); 
	ganuna_root = post_array(M+2, M+1); 
	eta = post_array(M+1, M+1) / gamma_root; 
	W_H = (Phi_root' \ p_H')'; 
 
	if (strcmp(init, 'mvdr')), W_H = W_H / (p_H * p_H'); end; 
	 
	% save results 
	Wo = [Wo; W_H]; 
	gamma = [gamma gamma_root^2 ]; 
	 
	% predict next sample and compute error 
	xp(n) = W_H * u; 
	e(n) = Y(n) - xp(n); 
	if (verbose ~= 0) 
		disp(['time step ', int2str(n), ': mag. pred. err. = ', num2str(abs(e(n)))]); 
	end; 
    
end % for n