MATLAB中利用测段已知点号和未知点号和测段水平距离求系数阵和协因数子

根据题意，我们可以列出以下方程组：

xj - xi = dij * cos(theta)
yj - yi = dij * sin(theta)

其中，xi、yi 为已知点的坐标，xj、yj 为未知点的坐标，dij 是已知点到未知点的距离，theta 是已知点到未知点的方位角。

将方程组转化为矩阵形式：

[A] * [X] = [L]

其中，

[A] = [ cos(theta1) -sin(theta1) 0 0 0 0 0 0 0 0 ]
[ 0 0 cos(theta2) -sin(theta2) 0 0 0 0 0 0 ]
[ 0 0 0 0 cos(theta3) -sin(theta3) 0 0 0 0 ]
[ 0 0 0 0 0 0 cos(theta4) -sin(theta4) 0 0 ]
[ 0 0 0 0 0 0 0 0 cos(theta5) -sin(theta5)]
[ sin(theta1) cos(theta1) 0 0 0 0 0 0 0 0 ]
[ 0 0 sin(theta2) cos(theta2) 0 0 0 0 0 0 ]
[ 0 0 0 0 sin(theta3) cos(theta3) 0 0 0 0 ]
[ 0 0 0 0 0 0 sin(theta4) cos(theta4) 0 0 ]
[ 0 0 0 0 0 0 0 0 sin(theta5) cos(theta5)]

[X] = [x2]
[y2]
[x3]
[y3]
[x4]
[y4]
[x5]
[y5]
[V]
[P]

[L] = [d12]
[d23]
[d34]
[d45]
[0]
[0]
[0]
[0]
[0]
[0]

其中，V 和 P 分别表示未知点的水平和垂直坐标，共 10 个未知数。

通过最小二乘法求解上述方程组，可以得到系数阵和协因数子。系数阵的逆矩阵即为未知点坐标的最小二乘解。