function g = gpsNewtons4(x0,y0,z0,d0)

format long;

% (x-A1)^2 +(y-B1)^2 +(z-C1)^2 =[c(t1-d)]^2
% (x-A2)^2 +(y-B2)^2 +(z-C2)^2 =[c(t2-d)]^2
% (x-A3)^2 +(y-B3)^2 +(z-C3)^2 =[c(t3-d)]^2
% (x-A4)^2 +(y-B4)^2 +(z-C4)^2 =[c(t4-d)]^2
% vector = x={1;2;3;4} = verticle vector

iv = [x0;y0;z0;d0];

%Assigning input variables
x=x0;
y=y0;
z=z0;
d=d0;

%Speed of light in km/s
c=299792.458;

%Error of ti
dti=10^(-8);

%Pick-your-own satellite positions
%Constants
rho=26570;
%d=.0001; given from input

%Satellite 1
phi1=0;
theta1=0;
A1=rho*cos(phi1)*cos(theta1);
B1=rho*cos(phi1)*sin(theta1);
C1=rho*sin(phi1);
R1=sqrt(A1^2+B1^2+(C1-6370)^2);
t1=d+(R1/c); %Not
t1_e=d+dti+(R1/c); %Added error

%Satellite 2
phi2=pi/3;
theta2=pi/3;
A2=rho*cos(phi2)*cos(theta2);
B2=rho*cos(phi2)*sin(theta2);
C2=rho*sin(phi2);
R2=sqrt(A2^2+B2^2+(C2-6370)^2);
t2=d+(R2/c); %Not
t2_e=d+dti+(R2/c); %Added error

%Satellite 3
phi3=pi/4;
theta3=pi;
A3=rho*cos(phi3)*cos(theta3);
B3=rho*cos(phi3)*sin(theta3);
C3=rho*sin(phi3);
R3=sqrt(A3^2+B3^2+(C3-6370)^2);
t3=d+(R3/c); %Not
t3_e=d-dti+(R3/c); %Added error

%Satellite 4
phi4=1;
theta4=3*pi/2;
A4=rho*cos(phi4)*cos(theta4);
B4=rho*cos(phi4)*sin(theta4);
C4=rho*sin(phi4);
R4=sqrt(A4^2+B4^2+(C4-6370)^2);
t4=d+(R4/c); %No added error
t4_e=d+dti+(R4/c); %Added error

%no added error
f1=(x-A1)^2+(y-B1)^2+(z-C1)^2-(c*(t1-d))^2;
f2=(x-A2)^2+(y-B2)^2+(z-C2)^2-(c*(t2-d))^2;
f3=(x-A3)^2+(y-B3)^2+(z-C3)^2-(c*(t3-d))^2;
f4=(x-A4)^2+(y-B4)^2+(z-C4)^2-(c*(t4-d))^2;

F=[f1;f2;f3;f4];

J=[(2*x-2*A1) (2*y-2*B1) (2*z-2*C1) (-2*c^2*d+2*c^2*t1);
   (2*x-2*A2) (2*y-2*B2) (2*z-2*C2) (-2*c^2*d+2*c^2*t2);
   (2*x-2*A3) (2*y-2*B3) (2*z-2*C3) (-2*c^2*d+2*c^2*t3);
   (2*x-2*A4) (2*y-2*B4) (2*z-2*C4) (-2*c^2*d+2*c^2*t4)];
v = -J\F;
xv = v+iv;

steps=10;
for i=1:steps
    x=xv(1);
    y=xv(2);
    z=xv(3);
    d=xv(4);

    f1=(x-A1)^2+(y-B1)^2+(z-C1)^2-(c*(t1-d))^2;
    f2=(x-A2)^2+(y-B2)^2+(z-C2)^2-(c*(t2-d))^2;
    f3=(x-A3)^2+(y-B3)^2+(z-C3)^2-(c*(t3-d))^2;
    f4=(x-A4)^2+(y-B4)^2+(z-C4)^2-(c*(t4-d))^2;

    F=[f1;f2;f3;f4];

    J=[(2*x-2*A1) (2*y-2*B1) (2*z-2*C1) (-2*c^2*d+2*c^2*t1);
   (2*x-2*A2) (2*y-2*B2) (2*z-2*C2) (-2*c^2*d+2*c^2*t2);
   (2*x-2*A3) (2*y-2*B3) (2*z-2*C3) (-2*c^2*d+2*c^2*t3);
   (2*x-2*A4) (2*y-2*B4) (2*z-2*C4) (-2*c^2*d+2*c^2*t4)];

    v = -J\F;
    xv = v+xv;
end
xv;
x=xv(1);
y=xv(2);
z=xv(3);
d=xv(4);

%using added error
f1=(x-A1)^2+(y-B1)^2+(z-C1)^2-(c*(t1_e-d))^2;
f2=(x-A2)^2+(y-B2)^2+(z-C2)^2-(c*(t2_e-d))^2;
f3=(x-A3)^2+(y-B3)^2+(z-C3)^2-(c*(t3_e-d))^2;
f4=(x-A4)^2+(y-B4)^2+(z-C4)^2-(c*(t4_e-d))^2;

F=[f1;f2;f3;f4];

J=[(2*x-2*A1) (2*y-2*B1) (2*z-2*C1) (-2*c^2*d+2*c^2*t1_e);
   (2*x-2*A2) (2*y-2*B2) (2*z-2*C2) (-2*c^2*d+2*c^2*t2_e);
   (2*x-2*A3) (2*y-2*B3) (2*z-2*C3) (-2*c^2*d+2*c^2*t3_e);
   (2*x-2*A4) (2*y-2*B4) (2*z-2*C4) (-2*c^2*d+2*c^2*t4_e)];
v = -J\F;
xv_e = v+iv;

steps=10;
for i=1:steps
    x=xv_e(1);
    y=xv_e(2);
    z=xv_e(3);
    d=xv_e(4);

    f1=(x-A1)^2+(y-B1)^2+(z-C1)^2-(c*(t1_e-d))^2;
    f2=(x-A2)^2+(y-B2)^2+(z-C2)^2-(c*(t2_e-d))^2;
    f3=(x-A3)^2+(y-B3)^2+(z-C3)^2-(c*(t3_e-d))^2;
    f4=(x-A4)^2+(y-B4)^2+(z-C4)^2-(c*(t4_e-d))^2;

    F=[f1;f2;f3;f4];

    J=[(2*x-2*A1) (2*y-2*B1) (2*z-2*C1) (-2*c^2*d+2*c^2*t1_e);
       (2*x-2*A2) (2*y-2*B2) (2*z-2*C2) (-2*c^2*d+2*c^2*t2_e);
       (2*x-2*A3) (2*y-2*B3) (2*z-2*C3) (-2*c^2*d+2*c^2*t3_e);
       (2*x-2*A4) (2*y-2*B4) (2*z-2*C4) (-2*c^2*d+2*c^2*t4_e)];

    v = -J\F;
    xv_e = v+xv_e;
end
xv_e;
x_e=xv_e(1);
y_e=xv_e(2);
z_e=xv_e(3);
d_e=xv_e(4);


%forward error = change in position ||delta x, delta y, delta z||
dX = x_e - 0;
dY = y_e - 0;
dZ = z_e - 6370;

deltaXYZ = [dX; dY; dZ]
fe = norm(deltaXYZ, inf)
emf = fe/0.003

end

Not enough input arguments.
Error in gpsNewtons4 (line 11)
iv = [x0;y0;z0;d0];

Published with MATLAB® R2017a