lms.m

matlab算法集 matlab算法集

function [theta,x,e] = lms (u,y,x,theta,mu,m)
%-----------------------------------------------------------------------
% Usage:       [theta,x,e] = lms (u,y,x,theta,mu,m)
%
% Description: Use the current input samples u and output sample y to
%              update the (m+1) by 1 parameter vector theta of a MA
%              model using the least-mean square (LMS) method.  The
%              MA model has the following transfer function.
%
%              Y(z)/U(z) = theta(1) + theta(2)*z^(-1) +...+ theta(m+1)*z^(-m)
%
% Inputs:      u     = current value of system input
%              y     = current value of system output
%              x     = (m+1) by 1 vector containing current state of
%                      MA model: [u(k),u(k-1),...,u(k-m)]'.
%              theta = (m+1) by 1 vector containing estimated values
%                      of MA model parameters.
%              mu    = step size used for stepest descent search (mu > 0)
%              m     = order of MA model (m >= 0)
%
% Outputs:     theta = (m+1) by 1 vector containing updated estimate of
%                       of MA model parameters.
%              x     = (m+1) by 1 vector containing updated state of
%                        MA model with x(1) = 0.
%              e     = error between actual output y and output predicted
%                      by MA moded, e = x'*theta - y 
% 
% Notes:       For the LMS method to converge, the step size mu must not
%              be too large.  If P(u) denotes the average power of the
%              input signal u(k), then the step size should be in the
%              range:
%
%                   0 < mu < 1/[(m+1)*P(u)] 
%-----------------------------------------------------------------------
   
% Initialize

   chkvec (x,3,'lms');
   chkvec (theta,4,'lms');
   mu = args (mu,eps,mu,5,'lms');
   m = args (m,0,m,6,'lms');
   x1 = zeros (m+1,1);

% Update theta 

   x1 = x;                                % save original x
   x1(1) = u;				  % update first element 
   [x,y1] = arma (u,theta,x,0,m);
   e = y - y1;
   for i = 1 : m+1
      theta(i) = theta(i) + 2*mu*e*x1(i);
   end   
%-----------------------------------------------------------------------