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

function [Wo, xp, alpha, e] = rls_AR_pred(Xi, Y, verbose, lambda, delta) 
% function [Wo, xp, alpha, e] = rls_AR_pred(Xi, Y, verbose, lambda, delta) 
% 
% rls_AR_pred.m - use basic RLS algorithm to predict real-valued AR process 
% written for MATLAB 4.0 
% 
% Reference: Haykin, _Adaptive Filter Theory_, 2nd (corr.) ed., 1991 
% 
% Note that we use the algorithm in Table 13.2, i.e., 
% we do not exploit the Hermitian property of P(n), to 
% minimize the possibility of numerical instability. 
% 
% 
% 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 
%       delta  : the initial value for the diagonal P matrix 
% 
% Output parameters: 
%       Wo     : column-wise matrix of weights at each iteration 
%       xp     : row vector of predicted outputs 
%       alpha  : row vector of a priori prediction errors 
%       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 
d = size(Xi, 2); 
 
% initialize weight matrix and associated parameters for RLS predictor 
W  = zeros(Nout, 1); 
Wo = [];  
P  = eye(d) / delta; 
 
for n = 1:N, 
   % save weights 
	Wo = [Wo W]; 
 
	% adapt weight matrix 
	u = Xi(n, :)'; 
	p = u' * P; 
	kappa = lambda + p * u; 
	k = P * u / kappa; 
	alpha(n) = Y(n) - W' * u; 
	W  = W + k * alpha(n); 
	Pp = k * p; 
	P  = (P - Pp) / lambda; 
 
	% predict next sample and compute error 
	xp(n) = W' * 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