# 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  
In order to acquire the terrain information of the target and solve the problem that the positioning algorithm based on the earth's ellipsoid model is too affected by the elevation, plenty of active positioning algorithms have been developed [19; 20; 21; 22; 23; 24; 25]. This type of algorithm mainly relies on ranging equipment such as laser range finder (LRF) to compute the distance between the camera and the target point, and calculates based on the positional relationship between the object images. The accuracy of the algorithm depends on the precision of the range finder. Since positioning models are built in various ways, there are some differences in the method of calculating the position of the target. In the ideal imaging process of the aerial camera, the spatial relationship among the target, the target's projection point, and the detector focal plane is illustrated in Figure 9. Since the distance between \(R\) the target and the optical system center of the camera is much greater than the focal length of camera, the distance between the target point projected position and camera coordinate system origin can be approximately recorded as the focal length \(f\)[26]. Furthermore, the position of the target in the camera coordinate system \(T_{E}^{\mathrm{S}}\) can be calculated according to Equation (16). \[Q_{1}= \begin{bmatrix}-R/f&0&0&0\\ 0&-R/f&0&0\\ 0&0&-R/f&0\\ 0&0&0&1\end{bmatrix} ,T_{E}^{\mathrm{S}}=Q_{1}T_{s} \tag{16}\]  
Therefore, the position of the target in the camera coordinate system can be directly derived by using a laser range finder, and the position information of the target in the earth coordinate system can be directly deducted only by using the coordinate transformation matrix. The above-mentioned method carries out a lot of approximation processing, which affects the positioning accuracy. [PERSON] proposed another more refined mathematical model than the LRF [22]. According to the geometric relationship of the aerial camera imaging model, the proportional relationship between the position of the target and the projection point is used for solution calculation with the distance information provided by the laser range finder as an input parameter. The imaging model of the aerial camera with area array CCDs as the detector is indicated in Figure 10. \(M_{1}\) is the object plane and \(M_{2}\) is the image plane. \(P\) is defined as the projection of the target \(A\) on the image plane. \(S\) means the camera coordinate system, and \(g\) denotes the geographic coordinate system. The distance between the camera and the target \(R\) can be gained by measuring the distance of the target through the airborne laser range finder. Under this model, the coordinates in the camera coordinate system of the  
Figure 9: Schematic of positional relationship for target and target projection point in the camera coordinate frame. target point can be described by Equation (17), and the position of the target in the earth coordinate system can also be calculated by using coordinate transformation [19; 22]. \[ \begin{cases}X_{s}=\frac{x_{w}\times R\times\cos p}{\cos\omega\times\sqrt{x_{w} \times w^{2}+y_{w}^{2}+f^{2}}}\\ Y_{s}=\frac{y_{w}\times R\cos p}{\cos\omega\times\sqrt{x_{w}^{2}+y_{w}^{2}+f^{2} }}\\ Z_{s}=\frac{R\times\cos p\times f}{\cos\omega\times\sqrt{x_{w}^{2}+y_{w}^{2}+f^{ 2}}}\end{cases}  \tag{17}\]  
The above two algorithms for positioning using a laser range finder directly calculate the position of a target in the camera coordinate system without solving the position through the collinear equation, leading to the outcome no longer being affected by the target elevation error. The improvement of precision and miniaturization of laser rangefinders make this kind of algorithm applied in engineering. This kind of algorithm also promotes research in the field of active positioning.