%
% Written by:
% -- 
% John L. Weatherwax                2005-08-14
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clear; close all; clc; 
clear functions; 

Htilde = [ 0, 1; 3, 4 ];

Z1 = [ 0, 1, 7, 8, 5, 7, 9, 10, 6, 4 ]; Z1 = Z1(:); 
Z2 = [ 10, 7, 4, 5, 5, 3, 0, 2, 2, 4 ]; Z2 = Z2(:); 
Z = [ Z1, Z2 ]; 
% All two by one measurement vectors stacked on top of each other: 
T = Z'; Zstacked = T(:);

nMeasurements = length(Z1);

% Stack many copies of Htilde on top of each other
H = [];
for ii=1:nMeasurements, 
  H = [ H; Htilde ];
end

% If the true x is given then the pure measurements for all is then given by
% H x and we want to pick x such that H x is a close to Zstacked as possible 
% in  a least squares sense
%
xhat = ( H' * H ) \ ( H' * Zstacked );

figure; plot( Zstacked, 'bo' ); hold on;
plot( H * xhat, 'xr' );