# Review of Target Geo-Location Algorithms for Aerial Remote Sensing Cameras without Control Points
## 2 Bibliometric Study and Typical Aerial Camera-to-Ground Target Localization Algorithm
### Active Positioning Algorithm Based on Laser Ranging Sensor
It has certain reference significance with SLAM, 3D point clouds, and laser point clouds, and can be extended to industrial scenes such as robots and robot arms. Generally speaking, these algorithms are mostly applied to military equipment because it is usually difficult to carry laser rangefinders with sufficient accuracy in small civil UAVs. However, distance limitation restricts the LRF's further application. To be specific, the effective working distance of the LRF is in most cases limited within 20-30 km to ensure accuracy. With the development of aerial cameras for high-altitude and long-distance imaging, the positioning algorithm based on ranging equipment cannot meet the demand of target positioning with an image distance of more than 50 km. Target Location Algorithm Based on Single-Machine Two-Point Measurement or Double-Machine Intersection Measurement  
The intersection measurement algorithm is proposed to solve the issue that the single-machine and single-point measurement is greatly affected by random errors. The traditional two-point intersection positioning algorithm generally relies on the angle sensor carried by the camera to obtain the shooting angles at different times and calculates in the earth coordinate system through the equation of LOS. As shown in Figure 11, the two points A and B represent different positions of a same target shot by an airborne camera. The respective target LOS pointing vectors (\(L_{Ci}\)) can be obtained by angle information through the projection position of the target on the CCD, and its cosine of direction can be expressed in the camera coordinate system by  
Figure 10: Schematic of positional relationship for target and target projection point in the camera coordinate frame. Equation (18) [33; 34; 35; 36], where \(x\) and \(y\) are the coordinate values of target projection point on the camera coordinate system. \[L_{Ci}=\left[\frac{x^{2}}{\sqrt{x^{2}+y^{2}+f^{2}}},\frac{y^{2}}{\sqrt{x^{2}+y^{2 }+f^{2}}},\frac{f^{2}}{\sqrt{x^{2}+y^{2}+f^{2}}},1\right]^{T} \tag{18}\]  
\[L_{Ei}= \begin{pmatrix}l_{Ei}\\ m_{Ei}\\ g_{Ei}\\ 1\end{pmatrix} =C_{NED}^{ECEF}\times C_{A}^{NED}\times C_{C}^{A}\times L_{Ci} \tag{19}\]  
In addition, the actual position of aircraft or cameras in the earth coordinate system can be directly calculated by Equation (5) and the position information provided by the GPS/POS system. Combined with the direction vector in the earth coordinate system (\(L_{Ei}\)) provided by Equation (19), two target line-of-sight equations can be constructed, as shown in Equation (20) [35; 37]. \[L_{i}:\frac{x-x_{i}}{l_{Ei}}=\frac{y-y_{i}}{m_{Ei}}=\frac{z-z_{i}}{g_{Ei}}=t_{ i},i=1,2 \tag{20}\]  
LOS is rotationally invariant in space. The intersection of the two LOS equations is the position of the target in the ECEF coordinate system. Therefore, the coordinate value of the target can be calculated by the following equation. \[\left\{ \begin{array}{l}T_{E}=(x_{1}+l_{E1}t,y_{1}+m_{E1}t,z_{1}+n_{E1}t)\\ t=\frac{m_{E2}(x_{2}-x_{1})-L_{2}(y_{2}-y_{1})}{l_{E1}n_{E2}-l_{E2}m_{E1}}\\ \end{array} \right. \tag{21}\]  
The positioning algorithm of the single-machine two-point intersection can also reduce the influence of the elevation error, and it selects the angle information as parameters for calculation, which is not limited by imaging distance. However, this type of positioning algorithm can only locate the fixed target on the ground; once the target moves, the positioning accuracy will be greatly decreased. For dealing with this issue, the positioning algorithm for double-aircraft intersection measurement is established by using two aerial cameras to co-loc  
Figure 11: Two-point intersection positioning model. positions \(A\) and \(B\), which can gain all the parameters required by the intersection positioning algorithm in real-time, and then calculate the target position [37,38,41].