function [xtruth,z_k] = sect_6_2_gen_xz(x_0, Phi, Gamma, u_k, Q, ref_pt_1, ref_pt_2, R, N)
%
% Generates the truth (xtruth) and measurements (z) for the specified nonlinear model.
%
% Inputs: 
%     N = the number of measurements to process (xtruth has then one more sample corresponding to \hat{x](0))
%         between the times t_0 and t_final.
%
% Checked: 2011-07-17 (error found in need to generate *non* linear measurements)
% 
% 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.
% 
%-----

n = length(x_0);

% Generate the *true* state history
xtruth      = zeros(n,N+1);
xtruth(:,1) = x_0(:); % the initial condtion on the state
for km1 = 1:N
  w = mvnrnd( zeros(1,n), Q );
  xtruth(:,km1+1) = Phi * xtruth(:,km1) + Gamma * u_k + w(:);
end

% Generate the *nonlinear* measurements (off of the true state x(t)):
z_k = zeros(n,N);
for km1 = 1:N,
  [h,H] = sect_6_2_h_fn(xtruth(:,km1+1), ref_pt_1, ref_pt_2);
  z_k(:,km1) = h + mvnrnd( zeros(n,1), R, 1 ).';
end