function [xtruth,z] = sect_4_4_gen_xz(Phi, H, Q, Psi, Q_nu, N)
%
% Generates the truth (xtruth) and measurements (z) when the 
% measurement noise is time-correlated.
%
% Inputs: 
%     N = the number of measurements to process (xtruth has then one more sample corresponding to \hat{x](0))
%
% 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.
% 
%-----

wkm1 = mvnrnd( [0;0], Q, N ).'; % the process noise of size [N,2] 

nk = zeros([2,N]); % storage for the measurement noise
for k=1:(N-1)
  nk(:,k+1) = Psi * nk(:,k) + mvnrnd( [0;0], Q_nu ).';
end

% Generate the *true* state history
xtruth = zeros(2,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;