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

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Prabhath Manuranga 2024-2-21

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https://ww2.mathworks.cn/matlabcentral/answers/2084723-i-need-some-help-to-solve-non-linear-equation-with-three-unknowns-and-three-knowns-with-having-170-d

评论： Walter Roberson 2024-3-12

采纳的回答： Torsten

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.

采纳的回答

Torsten 2024-2-21

编辑：Torsten 2024-2-21

在 MATLAB Online 中打开

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)

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Torsten 2024-2-23

在 MATLAB Online 中打开

:-)

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 2024-2-28

Thanks Mr. Torsten

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Prabhath Manuranga 2024-2-28

编辑：Prabhath Manuranga 2024-2-28

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?

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Torsten 2024-2-28

在 MATLAB Online 中打开

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

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Prabhath Manuranga 2024-3-12

编辑：Walter Roberson 2024-3-12

在 MATLAB Online 中打开

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

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Walter Roberson 2024-3-12

在 MATLAB Online 中打开

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