function

clean
format long
p1=[5888;-26724;14286];
p2=[3247;-13836;17160];
p3=[25080;-31875;-28819];
p4=[11423;-07998;13800];
p5=[16312;14238;25805];


dt1=1.02898228351555640070e-01;
dt2=1.30818116448839866228e-01;
dt3=1.65848424841278901942e-01;
dt4=6.53938229847097624026e-02;
dt5=1.12282606865692038967e-01;

c=3*10^5;

F= @(x) [((1/c)*(norm(x-p1))^2)-c*(dt1^2);
         ((1/c)*(norm(x-p2))^2)-c*(dt2^2);
         ((1/c)*(norm(x-p3))^2)-c*(dt3^2);
         ((1/c)*(norm(x-p4))^2)-c*(dt4^2);
         ((1/c)*(norm(x-p5))^2)-c*(dt5^2)];

dF= @(x) [(1/c)*2*(x(1)-p1(1)),(1/c)*2*(x(2)-p1(2)),(1/c)*2*(x(3)-p1(3));
          (1/c)*2*(x(1)-p2(1)),(1/c)*2*(x(2)-p2(2)),(1/c)*2*(x(3)-p2(3));
          (1/c)*2*(x(1)-p3(1)),(1/c)*2*(x(2)-p3(2)),(1/c)*2*(x(3)-p3(3));
          (1/c)*2*(x(1)-p4(1)),(1/c)*2*(x(2)-p4(2)),(1/c)*2*(x(3)-p4(3));
          (1/c)*2*(x(1)-p5(1)),(1/c)*2*(x(2)-p5(2)),(1/c)*2*(x(3)-p5(3))];

x0=[10;10;10];
tol=10^-6;
itmax=100;

[x,it]=gaussnewton(F,dF,x0,itmax,tol)

clear p*
clear d*