已知15幅影像的内外方位元素,341个地面点,每个点至少6幅影像上的像点坐标。根据摄站中心、地面点及对应像点间的共线方程式,采用间接平差方法编程求解这些地面点的物方坐标,要求使用Python。
时间: 2024-02-20 17:59:44 浏览: 117
已知内方位元素和四个控制点的地面坐标及相应像点坐标求外方位元素
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以下是一个Python实现的参考代码,采用最小二乘法进行间接平差计算:
```python
import numpy as np
# 影像数
n = 15
# 地面点数
m = 341
# 初始化矩阵
A = np.zeros((m * 2, n + 3))
L = np.zeros((m * 2, 1))
# 像点坐标数据,每行6个像点坐标
X = np.array([
[x1, y1, x2, y2, x3, y3, x4, y4, x5, y5, x6, y6, x7, y7],
[x1, y1, x2, y2, x3, y3, x4, y4, x5, y5, x6, y6, x7, y7],
...
[x1, y1, x2, y2, x3, y3, x4, y4, x5, y5, x6, y6, x7, y7]
])
# 内外方位元素数据,每行13个元素
P = np.array([
[w1, k1, f1, x01, y01, z01, om1, phi1, kap1, x1, y1, z1, s1, t1],
[w2, k2, f2, x02, y02, z02, om2, phi2, kap2, x2, y2, z2, s2, t2],
...
[w15, k15, f15, x015, y015, z015, om15, phi15, kap15, x15, y15, z15, s15, t15]
])
# 地面点坐标数据,每行3个坐标
G = np.array([
[X1, Y1, Z1],
[X2, Y2, Z2],
...
[X341, Y341, Z341]
])
# 首先计算出每个像点的像空间坐标
for i in range(m):
for j in range(n):
w, k, f, x0, y0, z0, om, phi, kap, x, y, z, s, t = P[j]
Xw = np.array([[x], [y], [z]])
R = np.array([
[-np.sin(phi) * np.sin(kap) * np.sin(om) + np.cos(phi) * np.cos(om), -np.sin(phi) * np.sin(kap) * np.cos(om) - np.cos(phi) * np.sin(om), -np.sin(phi) * np.cos(kap)],
[np.cos(phi) * np.sin(kap) * np.sin(om) + np.sin(phi) * np.cos(om), np.cos(phi) * np.sin(kap) * np.cos(om) - np.sin(phi) * np.sin(om), np.cos(phi) * np.cos(kap)],
[np.cos(kap) * np.sin(om), -np.cos(kap) * np.cos(om), np.sin(kap)]
])
Xc = R.dot(Xw - np.array([[x0], [y0], [z0]]))
fX = f * Xc[0, 0] / Xc[2, 0] + s
fY = f * Xc[1, 0] / Xc[2, 0] + t
A[i * 2, j] = f / Xc[2, 0]
A[i * 2, n] = -fX / Xc[2, 0]
A[i * 2, n + 1] = -fY / Xc[2, 0]
A[i * 2, n + 2] = fX * Xc[1, 0] / Xc[2, 0] - fY * Xc[0, 0] / Xc[2, 0]
A[i * 2 + 1, j] = 0
A[i * 2 + 1, n] = f / Xc[2, 0]
A[i * 2 + 1, n + 1] = -fY / Xc[2, 0]
A[i * 2 + 1, n + 2] = fY * Xc[1, 0] / Xc[2, 0]
# 计算L矩阵
for i in range(m):
L[i * 2, 0] = X[i, 0]
L[i * 2 + 1, 0] = X[i, 1]
# 进行最小二乘计算
AT = np.transpose(A)
ATA = AT.dot(A)
ATL = AT.dot(L)
N = np.linalg.inv(ATA)
X = N.dot(ATL)
# 输出结果
print(X)
```
其中,X矩阵即为求解出的地面点的物方坐标。注意,代码中的变量名和数据格式需要根据实际情况进行修改。
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