function Result = GPS(Guess)
% Givens
p = 26570;

c = 299792.458;

%x = 0;
%y = 0;
%z = 6370;
%d = 0.0001;

%Creates A_i, B_i, C_i, t_i
for i=0:3
    m = (pi/2)*(1/3)*i;
    n = (2*pi)*(1/3)*i;
    
    A(i+1) = p*cos(m)*cos(n); 
    B(i+1) = p*cos(m)*sin(n); 
    C(i+1) = p*sin(m);
    
    R = sqrt((A(i+1)-Guess(1))^2+(B(i+1)-Guess(2))^2+(C(i+1)-Guess(3))^2);
    t(i+1) = Guess(4) + R/c;
    
    % Maximum position error: -1, -1, -1, 1
end


max = 0;
dt = t;
maxOne = t;
maxf = 0;
for k = 1:500 
    one = 10^-8 * randi([-1,1],1,4);
    dt = t + one;
    % Multi-variable Newton's Method
    F=@(IN) [(IN(1)-A(1))^2+(IN(2)-B(1))^2+(IN(3)-C(1))^2-(c*(dt(1)-IN(4)))^2 ;...
    (IN(1)-A(2))^2+(IN(2)-B(2))^2+(IN(3)-C(2))^2-(c*(dt(2)-IN(4)))^2 ;...
    (IN(1)-A(3))^2+(IN(2)-B(3))^2+(IN(3)-C(3))^2-(c*(dt(3)-IN(4)))^2 ;...
    (IN(1)-A(4))^2+(IN(2)-B(4))^2+(IN(3)-C(4))^2-(c*(dt(4)-IN(4)))^2 ];

    D=@(IN) [2*(IN(1)-A(1)) 2*(IN(2)-B(1)) 2*(IN(3)-C(1)) 2*(c^2*(dt(1)-IN(4)));...
    2*(IN(1)-A(2)) 2*(IN(2)-B(2)) 2*(IN(3)-C(2)) 2*(c^2*(dt(2)-IN(4)));...
    2*(IN(1)-A(3)) 2*(IN(2)-B(3)) 2*(IN(3)-C(3)) 2*(c^2*(dt(3)-IN(4)));...
    2*(IN(1)-A(4)) 2*(IN(2)-B(4)) 2*(IN(3)-C(4)) 2*(c^2*(dt(4)-IN(4)))];

    x0 = Guess;
    for i = 1:10
        v = D(x0)\(-F(x0));
        x1 = x0' + v;
        x0 = x1';
    end

    % Error Magnification Factor
    foward(1) = x0(1)-Guess(1); 
    foward(2) = x0(2)-Guess(2);
    foward(3) = x0(3)-Guess(3);

    f_error = norm(foward, inf);
    b_error = c * 10^-8;
    emf = f_error/b_error;
    
    if(emf > max)
        maxf = f_error; 
        max = emf;
        maxOne = one;
    end
end

x0'
maxOne'
maxf
Result = max;