An in-depth discussion on the technical principles of absolute positioning accuracy evaluation indicators

To explore the technical principles of absolute positioning accuracy evaluation indicators, specific code examples are required

Abstract:
Absolute positioning is a very important part of modern navigation systems. In order to evaluate the accuracy of absolute positioning, some evaluation indicators need to be used. This article will introduce some commonly used absolute positioning accuracy evaluation indicators and explain their technical principles in detail. At the same time, some specific code examples will also be given to help readers better understand these evaluation indicators and how to implement them.

1. Introduction
   1.1 Background
   In modern navigation systems, absolute positioning is the basis for achieving precise positioning. Whether it is GPS, Beidou or GLONASS, absolute positioning is required to determine the user's accurate location. However, due to various reasons such as signal propagation, there are often certain errors in actual positioning results. In order to evaluate the accuracy of these positioning results, some evaluation metrics need to be used.

1.2 Purpose of this article
The purpose of this article is to introduce some commonly used absolute positioning accuracy evaluation indicators and explain their technical principles in detail. At the same time, in order to help readers better understand these indicators, we will also give some specific code examples. By reading this article, readers can have a deeper understanding of the accuracy evaluation process of absolute positioning.

2. Commonly used absolute positioning accuracy evaluation index
   2.1 RMSE (root mean square error)
   RMSE is a commonly used absolute positioning accuracy evaluation index. It measures the gap between actual positioning results and the true location. The calculation formula of RMSE is as follows:

import numpy as np

def rmse(estimated, true):
    error = estimated - true
    sqr_error = np.square(error)
    mean_error = np.mean(sqr_error)
    return np.sqrt(mean_error)

2.2 MAE (Mean Absolute Error)
MAE is also a commonly used absolute positioning accuracy evaluation index. It is similar to RMSE, except that it uses the absolute value of the error. The calculation formula of MAE is as follows:

import numpy as np

def mae(estimated, true):
    error = estimated - true
    abs_error = np.abs(error)
    mean_error = np.mean(abs_error)
    return mean_error

3. Technical Principle
   3.1 RMSD (Root Mean Square Distance)
   RMSD is a commonly used distance measurement index between cubes. It can measure the distance between the estimated value and the true value of the target position in three-dimensional space. The calculation formula of RMSD is as follows:

import numpy as np

def rmsd(estimated, true):
    diff = estimated - true
    sqr_diff = np.square(diff)
    mean_diff = np.mean(sqr_diff)
    return np.sqrt(mean_diff)

3.2 RPE (Relative Pose Error)
RPE is also a commonly used distance measurement index between cubes. It can measure the target position error in the estimation of relative attitude. The calculation formula of RPE is as follows:

import numpy as np

def rpe(estimated, true):
    abs_diff = np.abs(estimated - true)
    abs_diff_norm = np.linalg.norm(abs_diff, axis=1)
    mean_error = np.mean(abs_diff_norm)
    return mean_error

4. Conclusion
   This article introduces some commonly used absolute positioning accuracy evaluation indicators and explains their technical principles in detail. At the same time, some specific code examples are also given to help readers better understand these indicators. By using these indicators together, we can more accurately evaluate the accuracy of absolute positioning, thereby improving the performance of the navigation system.

References:
[1] Zhang, H., Pillai, S. U., & Nebot, E. M. (2020). Performance Evaluation Metrics for Mobile Robot Localization. arXiv preprint arXiv:2005.02011.

The above is the detailed content of An in-depth discussion on the technical principles of absolute positioning accuracy evaluation indicators. For more information, please follow other related articles on the PHP Chinese website!