间接平差程序matlab

在 Matlab 中进行间接平差的程序如下：

1. 定义输入数据

% 观测数据：观测值、方差、观测边
L = [3.456, 0.01, 1, 2, 3; 
     5.678, 0.04, 2, 3, 4; 
     4.321, 0.09, 3, 4, 1];
 
% 初始值：未知量的个数、未知量初始值、观测边的个数、观测边的初始值
N = 4;
X = [0; 0; 0; 0];
B = 3;
P = [1 2 1; 2 3 1; 3 1 1];
A = [1 0 -1 0; 0 1 0 -1; -1 0 1 0; 0 -1 0 1];

2. 进行最小二乘解

% 代数式中的系数矩阵
N = size(A, 2);
M = size(P, 1);
A_ = zeros(2*M, N);
for i = 1:M
    a = P(i, 1);
    b = P(i, 2);
    c = P(i, 3);
    A_(2*i-1, a) = 1;
    A_(2*i-1, b) = -1;
    A_(2*i, b) = 1;
    A_(2*i, c) = -1;
end

% 代数式中的常数矩阵
L_ = zeros(2*M, 1);
for i = 1:M
    l = L(i, 1);
    s = L(i, 2);
    L_(2*i-1, 1) = l + s/2;
    L_(2*i, 1) = l - s/2;
end

% 最小二乘解
X_ = inv(A_'*A_)*A_'*L_;

3. 进行观测值平差

% 残差
v = A*X_ - L_(:, 1);

% 方差-协方差矩阵
N_ = zeros(M, M);
for i = 1:M
    s = L(i, 2);
    N_(i, i) = s;
end

% 权矩阵
Q_ = inv(N_);

% 单位权方差
sigma_0 = v'*Q_*v/(M-N);

% 单位权方差矩阵
Q = sigma_0*Q_;

% 观测值平差
L_ = L_ - A_*X_ + ones(2*M, 1)*sigma_0;

4. 进行未知量平差

% 未知量平差
N_ = zeros(N, N);
b_ = zeros(N, 1);
for i = 1:M
    a = P(i, 1);
    b = P(i, 2);
    c = P(i, 3);
    s = L_(2*i-1, 1) - L_(2*i, 1);
    N_(a, a) = N_(a, a) + 1/sigma_0;
    N_(a, b) = N_(a, b) - 1/sigma_0;
    N_(b, b) = N_(b, b) + 1/sigma_0;
    N_(b, c) = N_(b, c) - 1/sigma_0;
    N_(c, c) = N_(c, c) + 1/sigma_0;
    N_(c, a) = N_(c, a) - 1/sigma_0;
    b_(a, 1) = b_(a, 1) + L_(2*i-1, 1)/sigma_0;
    b_(b, 1) = b_(b, 1) - L_(2*i-1, 1)/sigma_0 + L_(2*i, 1)/sigma_0;
    b_(c, 1) = b_(c, 1) - L_(2*i, 1)/sigma_0;
end
X = inv(N_)*b_;

5. 输出结果

% 输出最终结果
disp('未知量平差结果：');
disp(X);

% 输出单位权方差
disp('单位权方差：');
disp(sigma_0);

以上就是进行间接平差的 Matlab 程序。需要注意的是，这只是一个简单的程序，实际应用中可能需要更多的处理和优化。