# Review of Target Geo-Location Algorithms for Aerial Remote Sensing Cameras without Control Points
## 3 Error Analysis Model and Influencing Factors of Positioning Algorithm
### Influencing Factors of Positioning Algorithm Accuracy  
The error factors affecting the positioning algorithm are mainly divided into systematic error and random error. Systematic errors can be compensated by camera calibration in the laboratory. Therefore, the random error caused by the measurement of various sensors is the main factor. Scholars have conducted extensive research on the error sources of the positioning algorithm. Table 2 briefly introduces some common error terms and their distribution [91; 92; 93; 94; 95]. Different positioning models are corresponding to various error terms, which affect the accuracy of the positioning algorithm. Therefore, adding error terms based on the actual algorithm situation to error models is important, which is \begin{table}
\begin{tabular}{c c} \hline \hline
**Error Classification** & **Error Distribution Form** \\ \hline Camera Latitude & normal distribution \\ Camera Longitude & normal distribution \\ Camera elevation & normal distribution \\ Aerial carrier pitch angle & normal distribution \\ Aerial carrier roll angle & normal distribution \\ Aircraft yaw angle & normal distribution \\ Three-axis vibration error of shock absorber & uniform distribution \\ Image point position measurement error & normal distribution \\ Laser ranging error & normal distribution \\ Frame angle measurement error & normal distribution \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Major Error Terms and Their Distribution. simulation analysis. If the camera does not carry a laser rangefinder, then there is no laser ranging error; some aerial cameras carry a POS system that is rigidly connected to itself, so there is no vibration error from shock absorbers. Meanwhile, the same error source has different weights for different positioning models. For positioning algorithms based on the earth ellipsoid model, the error of sight pointing and target elevation are the primary error sources. For the laser range finder position algorithm, the accuracy of the LRF has a greater impact than other error sources. Taking the earth's ellipsoid model positioning algorithm as an example, Figure 12 illustrates the relationship between positioning error and imaging angle error when the airborne camera position is (35\({}^{\circ}\) N, 110\({}^{\circ}\) E, 7000 m). It is obvious that positioning error shows a positive correlation with measurement error, and positioning accuracy is significantly influenced by the measurement accuracy of angle. The algorithm, positioning a target by imaging angle alone, is incapable to deal with the impact of the target's elevation error, which means it is highly affected by topographic relief, as shown in Figure 13. Consequently, giving a predicted value of the target's height to this algorithm before calculating is crucial. In addition to the main error items shown in Table 2, many small error sources are ignored in the traditional positioning algorithm analysis. For example, the LOS error generated by the fast reflector in the optical system has not been considered. Moreover, the  
Figure 12: Positioning errors caused by imaging angle error. Figure 13: Positioning errors caused by target elevation error. influence of the atmospheric environment on the positioning results is usually overlooked. The complex imaging environment will lead to image distortion, which usually brings neglected localization error in positioning algorithms. Figure 14 is a schematic diagram of the positioning error caused by image distortion. It can be concluded that the positioning error increases steadily along with the growth of distortion rate. When the image edge distortion rate reaches 0.06, the positioning error will be as high as 70 m. Correspondingly, the error caused by the synthesis of traditional error terms is about 75 m [96]. Most of the existing algorithms or theories are aimed at the height error caused by topographic relief, and do not take the height of target itself into consideration.