function [ newmean, newcov ] = ukf_prediction( mean, cov, u, R, motion)
%UKF_PREDICTION Computes the UKF prediction step

% YOUR CODE STARTS HERE:
[S w]=ukf_sigma_points(mean,cov,1/3);
n=size(w,1);
Snew=zeros(size(S));

for i=1:n
    [Snew(:,i), G]=motion(S(:,i),u);
end

[newmean, newcov]=ukf_estimate_normal(Snew,w);
newcov=newcov+R;


% YOUR CODE ENDS HERE:

end