Principle of rear intersection method

The rear intersection method is a method to measure the position of geo-spatial targets, and its principle is based on the triangulation principle.

The process of measuring the geo-spatial target position by the back intersection method includes the following steps:

1. Take two or more photos of the target, and determine the photographic baseline of each photo and the optical center position of the camera.

2. Select at least three points with the same name in each photo (that is, landmark features that can be seen in multiple photos) and measure their pixel coordinates in different photos.

3. Calculate the ground coordinates of points with the same name by triangulation principle.

4. Determine the external orientation elements of at least two observation cameras (i.e., camera positions and shooting azimuth angles).

5. Use the relative orientation method to calculate the external orientation elements of other cameras (that is, camera position and shooting orientation).

6. Carry out the rear intersection of the ground coordinates of points with the same name to determine the position of the target on the ground.

It should be noted that the camera distortion needs to be considered in the measurement process of the back intersection method, so it is usually necessary to correct the photos before calculation.

Principle of triangulation:

Triangulation is a measurement method to calculate the angle and side length of other triangles by knowing the length of an angle and its corresponding two sides. The famous Pythagorean theorem is a special case of triangulation.

The basic principle of triangulation is to calculate the position of the target point by using the geometric relationship in the triangle.

Assuming that the position of the target point can be represented by a right triangle, the distance from the target point to two known points (i.e. two sides) can be measured first, and then the included angle (i.e. an angle) between the positions of the two known points can be measured. According to the sine theorem and cosine theorem of triangle, the position of the target point can be calculated.

Triangulation method can be used in space elevation measurement, photogrammetry, geographic information system, navigation and positioning and other fields. However, in the actual measurement, due to the existence of errors, some methods need to be adopted to improve the accuracy and reliability, such as using multiple angles and side length information in the triangle to measure, and using numerical method to process the data.