function [xls_new, Pinvsr_new ] = bqr_rls( Pinvsr, xls, a, y )
% function [xls_new, Pinvsr_new ] = bqr_rls( Pinvsr, xls, a, y )
%
% Block QR version of recursive least-squares estimator for solving y=Px.
% 'a' are new rows of matrix P, and 'y' are the associated target values.
%
% 'Pinvsr' is the square root of Pinv=(P'*P)^-1,
%    and should be LOWER triangular (Pinvsr*Pinvsr'=Pinv).
% 'a' should be specified as a column vector.
% 'y' may be a row vector, in which case 'xls' will be a matrix.
%
% This version does not include a forgetting factor.
%
% D. Wingate 5/12/2006 
%

  err = y - a'*xls;
  n = size(Pinvsr,1);
  nrows = size( a, 2 );

  M = [ eye(nrows), a'*Pinvsr ; zeros( n, nrows ), Pinvsr ];

%  [Q,R] = qr( M );
  R = triu( qr( M' ) );

  Pinvsr_new = R( 1+nrows:nrows+n, 1+nrows:nrows+n )';

  Kt = R(1:nrows, 1+nrows:nrows+n )' * inv( R(1:nrows,1:nrows)' );

  xls_new = xls + Kt * err;

return;