function [logLikt,s2t] = logLik_unnoisy(l,ns,xs,fs,type)     
if nargin == 6
    type = 'gauss';
end
eps = 1e-9;
F = ones(ns,1);
Rt = correlationfunc(l,xs,xs,type);
Rt = Rt + eps*eye(ns);
[TRt,p] = chol(Rt);
xt = TRt'\fs;
Mt = TRt'\F;
bt = (Mt'*Mt)\(Mt'*xt);  % b = inv(F'*S^(-1)*F)*F'*S^(-1)*fs;
zt = xt - Mt * bt;
s2t = zt'*zt/ns; % s2s = (fs-F*b)'*R^(-1)*(fs-F*b)/ns;
logLikt = -0.5*ns*s2t - sum(log(abs(diag(TRt)))) - 0.5*ns*log(2*pi) - 0.5*ns;