function index=liu_resampling(W)

clear index;
N=length(W);
sum=0;
for(j=1:N) 
   a(j)=sqrt(W(j)); %update the weights
   sum=sum+a(j);	  %calculate sum(a_i)
end
for(j=1:N) 
   a(j)=a(j)*N/sum; %normalize the weights a_i to sum up to N
end
i=1;
for(j=1:N) %for each particle
   if(a(j)>=1) %accept the ones with bigger weights
      for(l=1:a(j)) %add (a(j) copies of the jth particle
         index(i)=j;
         i=i+1;
      end
   else
      R=rand(1,1);
      if a(j)>=R % accept the particle with probability aj
         index(i)=j;
         i=i+1;
      end
   end
end

a