NaN Error Help?

Hello,

I am trying to run a simple program that iterates an equation to calculate system error. However, I keep getting errors due to certain parts returning NaN. I've tried to simplify my program to prevent this, but have had no luck. Any tips are appreciated. Thanks!

c = 3*10^8;

%define user coordinates
xu = 100;
yu = 883;
zu = 134;

%define arbitrary starting location
xn = 1;
yn = 1;
zn = 1;
tn = 1;

%define satellite offset
offset = 534;

%define coordinates of satellite
x1 = 11000*1852;
y1 = 0;
z1 = 0;
x2 = 0;
y2 = 11000*1852;
z2 = 0;
x3 = 0;
y3 = 0;
z3 = 11000*1852;
x4 = 11000*1852;
y4 = 0;
z4 = 0;

%calculate output location matrix
m= ones(4,4);
i = 1;
count = 0;

while i > 0

      %calculate pseudorange measured by user to satellite 1

      R1 = sqrt((xu-x1)^2 + (yu-y1)^2 + (zu-z1)^2 + offset);

      %calculate nominal pseudorange to satellite

      Rn1 = sqrt((xn-x1)^2 + (yn-y1)^2 + (zn-z1)^2 + c*tn);
      deltaR1 = R1 - Rn1;

      alphaX1 = (xn-x1)/(Rn1 - c*tn);
      alphaY1 = (yn-y1)/(Rn1 - c*tn);
      alphaZ1 = (zn-z1)/(Rn1 - c*tn);

      new_row1 = [alphaX1, alphaY1, alphaZ1, c];

      m(1,:) = new_row1;

      %calculate pseudorange measured by user to satellite 2

      R2 = sqrt((xu-x2)^2 + (yu-y2)^2 + (zu-z2)^2 + offset);

      %calculate nominal pseudorange to satellite

      Rn2 = sqrt((xn-x2)^2 + (yn-y2)^2 + (zn-z2)^2 + c*tn);
      deltaR2 = R2 - Rn2;

      alphaX2 = (xn-x2)/(Rn2 - c*tn);
      alphaY2 = (yn-y2)/(Rn2 - c*tn);
      alphaZ2 = (zn-z2)/(Rn2 - c*tn);

      new_row2 = [alphaX2, alphaY2, alphaZ2, c];

      m(2,:) = new_row2;

      %calculate pseudorange measured by user to satellite 3

      R3 = sqrt((xu-x3)^2 + (yu-y3)^2 + (zu-z3)^2 + offset);

      %calculate nominal pseudorange to satellite

      Rn3 = sqrt((xn-x3)^2 + (yn-y3)^2 + (zn-z3)^2 + c*tn);
      deltaR3 = R3 - Rn3;

      alphaX3 = (xn-x3)/(Rn3 - c*tn);
      alphaY3 = (yn-y3)/(Rn3 - c*tn);
      alphaZ3 = (zn-z3)/(Rn3 - c*tn);

      new_row3 = [alphaX3, alphaY3, alphaZ3, c];

      m(3,:) = new_row3;

      %calculate pseudorange measured by user to satellite 4

      R4 = sqrt((xu-x4)^2 + (yu-y4)^2 + (zu-z4)^2 + offset);

      %calculate nominal pseudorange to satellite

      Rn4 = sqrt((xn-x4)^2 + (yn-y4)^2 + (zn-z4)^2 + c*tn);
      deltaR4 = R4 - Rn4;

      alphaX4 = (xn-x4)/(Rn4 - c*tn);
      alphaY4 = (yn-y4)/(Rn4 - c*tn);
      alphaZ4 = (zn-z4)/(Rn4 - c*tn);

      new_row4 = [alphaX4, alphaY4, alphaZ4, c];

      m(4,:) = new_row4;

      %calculate result

      A = inv(m);
      final = A*[deltaR1; deltaR2; deltaR3; deltaR4];

      deltaX = final(1,1);
      deltaY = final(2,1);
      deltaZ = final(3,1);
      deltaT = final(4,1);

      xn = xn + deltaX;
      yn = yn + deltaY;
      zn = zn + deltaZ;
      tn = tn + deltaT;

      erms = sqrt((1/3)*((xn-xu)^2 + (yn-yu)^2 + (zn-zu)^2));

      count = count + 1;

      if erms < 1e-6
          i = -1;  
      end

end

disp(count)
disp(tn)

[David Goodmanson]

Hi bau, Since satellite positions 1 and 4 are identical, that means rows 1 and 4 of matrix m are identical, so m has no inverse. Even if that were not the case, row 4 of m consists of four elements of size 3e8, while the other entries of m are all less than 1e-1. The matrix is badly scaled and there may be problems with the inverse even if all four rows were different.

Answer 1

[Jan]

The problem is a warning, not an error:

 Warning: Matrix is singular, close to singular or badly scaled.
 Results may be inaccurate. RCOND = NaN. 
 > A = inv(m);

This means, that the created matrix m is singular and the inversion fails. A simplification of the code will not help, because it is a mathematical problem. The comments in the code are not clear enough to understand, what you want to calculate, so based on the failing code only I cannot guess, if there is a bug in the implementation or in the algorithm.