What are the basic principles and concepts of static positioning measurement?

What are the basic concepts and principles of static positioning measurement principles?

With the rapid development of modern technology, positioning technology plays an important role in various fields. Static positioning is one of the commonly used positioning methods, and its basic concepts and principles are crucial to achieving accurate positioning.

Static positioning is to obtain the three-dimensional coordinates of the target point by collecting control points with known positions in the environment and visible satellite signals received by the receiver, and using the differential model to perform calculations. The basic principle is to use the arrival time difference of satellite signals to calculate the distance difference between the receiver and the control point, thereby obtaining the position of the target point.

The core of static positioning is the differential model, which is based on the following two assumptions:

1. The clock bias of the receiver is unknown, but the arrival time of the satellite signal is measurable.
2. The speed of satellite signals is constant during transmission.

Based on the above assumptions, static positioning can be performed through the following steps:

1. Collect the coordinates of the control point and the satellite signal data received by the receiver.
2. To process satellite signal data, you must first find satellites that are visible in both the receiver and the control point.
3. For each visible satellite, calculate the pseudorange observation between the receiver and the satellite, which is the difference between the time the signal was received and the time the signal was emitted multiplied by the speed of light.
4. According to the coordinates of the control point and receiver and the pseudorange observation values, use the difference model to calculate and solve the position of the receiver.

The following uses Python code examples to illustrate the implementation process of static positioning.

import numpy as np

# 定义控制点的坐标
X = np.array([[1, 2, 3],
              [4, 5, 6],
              [7, 8, 9]])

# 定义接收器的观测值
P = np.array([10, 11, 12])

# 定义接收器与控制点的距离差
dP = np.array([-1, 2, 3])

# 定义观测值与距离差的关系矩阵
A = np.array([[-1, 0, 0],
              [0, 2, 0],
              [0, 0, 3]])

# 求解接收器的坐标
X_ = X - np.linalg.inv(A.T @ A) @ A.T @ dP

print("接收器的坐标为：", X_)

In the above code example, we first define the coordinate matrix X of the control point and the observation value matrix P of the receiver. Then, through the relationship matrix A between the observation value and the distance difference, the least squares method is used to solve the coordinates X_ of the receiver.

This is just a simple example of static positioning. In practical applications, many factors need to be considered, such as satellite system errors, atmospheric delays, etc. However, based on the above principles and steps, static positioning can achieve accurate measurement and positioning of target points.

To summarize, the basic concept of the static positioning measurement principle is to calculate the position of the target point through the coordinates of the control point and the satellite signal received by the receiver. The core principle is to use the arrival time difference of satellite signals to calculate the distance difference, and then use the difference model to calculate and solve for the position of the receiver. I hope the above introduction can be helpful to the concept and implementation principles of static positioning.

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