function data = full_calibration_data(noise_mult)
% Synthetic data to use with full\_calibration.m

% pose of the laser
data.true_laser = [0.2; 0.02; deg2rad(5)];
data.true_laser = [0; 0; -deg2rad(0.5)];
% radius  
data.true_r_l = 0.02;     
data.true_r_r = 0.0205;    
% distance between wheels
data.true_d = 0.09; 

% noise: scan matching error
data.true_std_laser =  noise_mult *   diag([0.01 0.01 deg2rad(1)]);
% noise: axis measurement error
data.true_std_phi =    noise_mult * 0.01;
% noise: unmodeled slip
data.true_std_unmodeled =   noise_mult * diag([0.002 0.002 deg2rad(0.2)]);

% generate measurements
data.n = 700;
data.true_phi_r =0.3*( 1 + rand(1, data.n));
data.true_phi_l =0.3*( -1 + rand(1, data.n));

for i=1:data.n
	if i < data.n * 0.5
		data.true_phi_r(i) = - data.true_phi_r(i);
		data.true_phi_l(i) = - data.true_phi_l(i);
	else
	
	end
end

data.phi_r = data.true_phi_r + data.true_std_phi * randn(1, data.n);
data.phi_l = data.true_phi_l + data.true_std_phi * randn(1, data.n);
data.T = repmat(1,1,data.n)  +  0.1 * randn(1, data.n);

data.true_v0  = (0.5*data.true_r_l) * data.true_phi_l + ...
                (0.5*data.true_r_r) * data.true_phi_r;
data.true_w0  = (data.true_r_l/data.true_d)   * data.true_phi_l + ...
                (-data.true_r_r/data.true_d)  * data.true_phi_r;

for k=1:data.n
	v0 = data.true_v0(k);
	w0 = data.true_w0(k);
	T = data.T(k);
	if abs(w0 * T) > 1e-7
		o(1,1) = (v0 * T) * ( sin(w0*T) / (w0*T)  );
		o(2,1) = (v0 * T) * (1-cos(w0*T))/ (w0*T);
	else
		o(1,1) = (v0 * T);
		o(2,1) = 0;
	end
	o(3,1) = w0 * T;
	
	% the true displacement takes into account an unmodeled slip
	data.true_spost(:,k) = o;
	data.true_od(:,k) = o + data.true_std_unmodeled * randn(3,1);
	data.true_sm(:,k) = oplus( ...
		oplus( ...
			ominus( data.true_laser), ...
			data.true_od(:,k) ...
		), ...
		data.true_laser);
	data.sm(:,k) = data.true_sm(:,k) + data.true_std_laser * randn(3,1);
end

data.true_params = [data.true_d;data.true_r_l;data.true_r_r;data.true_laser];