I need some help to solve non-linear equation with three unknowns and three knowns with having 170 different values for one known.

Xw, Yw, Zw (170 * 1 matrices) are known with 170 different values.

Xe, Ye, Ze are the unknowns.

Tx, Ty, Tz, Rx, Ry, Rz, and neta are some of other knowns.

I want to find the values for Xe, Ye, and Ze.

Answer 1

[Torsten]

M = [eta+1,Rz,-Ry;-Rz,eta+1,Rx;Ry,-Rx,eta+1];
M = repmat(M,170,1);
b = [];
for i = 1:170
  b = [b;Xw(i)-Tx;Yw(i)-Ty;Zw(i)-Tz];
end
sol = M\b;
Xe = sol(1)
Ye = sol(2)
Ze = sol(3)

[Prabhath Manuranga]

Thanks Mr. Torsten.

This give only one value for each Xe, Ye, and Ze. But i need to get all values that comes for each Xe, Ye, and Ze value. if Xw, Yw and Zw is having 170 values for each, when solving the equations for each Xw, Yw and Zw should gives its respective Xe, Ye and Ze value (170 different values for each). How to get that?

[Torsten]

You wrote you want to determine three unknowns for all your 170 data points, i.e. a solution for Xe, Ye and Ze that solves the system optimal for all data points in some kind of average sense.

If you want to have three solutions for each of the 170 data points, just use

M = [eta+1,Rz,-Ry;-Rz,eta+1,Rx;Ry,-Rx,eta+1];
Minv = inv(M);
Xe = zeros(170,1);
Ye = zeros(170,1);
Ze = zeros(170,1);
for i = 1:170
    b = [Xw(i)-Tx;Yw(i)-Ty;Zw(i)-Tz];
    sol = Minv*b;
    Xe(i) = sol(1);
    Ye(i) = sol(2);
    Ze(i) = sol(3);
end

[Prabhath Manuranga]

Thanks Mr. Torsten.

[Walter Roberson]

M = [eta+1,Rz,-Ry;-Rz,eta+1,Rx;Ry,-Rx,eta+1];
Xe = zeros(170,1);
Ye = zeros(170,1);
Ze = zeros(170,1);
for i = 1:170
    b = [Xw(i)-Tx;Yw(i)-Ty;Zw(i)-Tz];
    sol = M\b;
    Xe(i) = sol(1);
    Ye(i) = sol(2);
    Ze(i) = sol(3);
end

[Torsten]

:-)

M = [eta+1,Rz,-Ry;-Rz,eta+1,Rx;Ry,-Rx,eta+1];
dM = decomposition(M);
Xe = zeros(170,1);
Ye = zeros(170,1);
Ze = zeros(170,1);
for i = 1:170
    b = [Xw(i)-Tx;Yw(i)-Ty;Zw(i)-Tz];
    sol = dM\b;
    Xe(i) = sol(1);
    Ye(i) = sol(2);
    Ze(i) = sol(3);
end

[Prabhath Manuranga]

Thanks Mr. Torsten

Answer 2

[Prabhath Manuranga]

g_mean = g_i + 0.0424*H_i % Equation 01

H_i = (W_lvd - W_i)/g_mean % Equation 02

Here g_i, H_i, and W_i is known.

W_lvd is unkonwn.

There are 172 row values per g_i and H_i (170 by 1 matrix).

How to solve this?

[Torsten]

W_lvd = H_i.*(g_i+0.0424*H_i)+W_i

if you want W_lvd as a 170x1 matrix

W_lvd = 1/170*sum(H_i.*(g_i+0.0424*H_i)+W_i)

if you want W_lvd as the best approximate value for the vector values H_i.*(g_i+0.0424*H_i)+W_i

Answer 3

[Prabhath Manuranga]

X_ISMD = 995152.969208341;
Y_ISMD = 996113.117131325; 

for i = 1:length(data1)
    D1(i) = sqrt((X_ISMD - X_WGS84(i)).^2 + (Y_ISMD - Y_WGS84(i)).^2); 
end
D1

length(data1) is 172. X_WGS84(i) and Y_WGS84(i) are 172 by 1 matrix. according to the above matlab code i ma getting following output (1 by 172 matrix). but i want to have 172 by 1 matrix. could you please suggest where should i change in my code? Thanks.

D1 =

Column 1

140911.995295475

Column 2

123232.133401588

Column 3

115208.35805542

Column 4

93127.1628328772

[Walter Roberson]

X_ISMD = 995152.969208341;
Y_ISMD = 996113.117131325; 

D1 = zeros(length(data1),1);

for i = 1:length(data1)
    D1(i) = sqrt((X_ISMD - X_WGS84(i)).^2 + (Y_ISMD - Y_WGS84(i)).^2); 
end
D1