function [xtruth,z] = sect_4_2_gen_xz(Phi, H, Q, M, R, N)
%
% Generates the truth (xtruth) and measurements (z) when the 
% disturbance noise and measurement noise are cross-correlated.
%
% 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.
% 
%-----

% Generate propagation and measurement noise for k=1:N
EWN = [ Q, M; M, R ];
if( false )
  C = chol(EWN); C = C';
  U = randn( N, 2 ); U = U';
  X = C * U; % thes are drawn from the nessesary dynamic noise and measurement noise distribution... cross correlated
	     % check that the above statement is true
  EWN 
  mean( X, 2 )
  cov( X' )
else
  X = mvnrnd( [0;0], EWN, N ).';
end

wkm1 = X(1,:); % the process noise
nk = X(2,:); % the measurement noise

% Generate the *true* state history
xtruth = zeros(1,N+1);
for k=1:N
  xtruth(k+1) = Phi*xtruth(k) + wkm1(k);
end

% Generate the measurements (off of the true state):
z = H*xtruth(2:(N+1)) + nk;