# 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
### Basic Coordinate Transformation of Target Positioning Algorithm  
The geo-location information of the target includes latitude (\(\varphi\)), longitude (\(\lambda\)), and altitude (\(h\)). The positioning algorithm needs to establish corresponding coordinate systems based on numerous parameters transferred from the aircraft and the camera, and unify the target, projection point, camera, aircraft, and other related elements in the same coordinate system via the coordinate transformation matrix. According to the information provided by the global positioning system (GPS) or the positioning and attitude system (POS) carried by aircraft and the camera, the actual position of the target is calculated through the positional relationship between the referred elements. The target positioning algorithm without control points generally requires four basic coordinate systems, which are the earth coordinate system, the geographic coordinate system, the aircraft coordinate system, and the camera coordinate system. The position of a space point in different coordinate systems can be calculated by the transformation matrix \(C_{A}^{B}\). Equation (1) represents the transformation matrix of a point whose coordinate value is \((X_{A},Y_{A},Z_{A})\) from the A coordinate system to the B coordinate system [14]. \[ \begin{bmatrix}X_{B}\\ Y_{B}\\ Z_{B}\end{bmatrix} = \begin{bmatrix}X_{A}\\ Y_{A}\\ Z_{A}\end{bmatrix} \times C_{A}^{B},\ C_{B}^{A}=\left(C_{A}^{B}\right)^{-1} \tag{1}\]  
The earth coordinate system is also known as the earth-centered and earth-fixed system (ECEF). Since the earth's shape is an irregular sphere, an approximate mathematical model needs to be built to describe it. The positioning algorithm mainly uses the ellipsoid model exploited in the WGS-84 coordinate system (World Geodetic System-1984) as the earth model, which is declared by the 17 th Congress of the Union of Geodesy and Geophysics. It proposed a series of parameters defined as follows [17; 19]. Earth ellipsoid model:  
\[\frac{x^{2}}{R_{e}^{2}}+\frac{y^{2}}{R_{e}^{2}}+\frac{z^{2}}{R_{p}^{2}}=1 \tag{2}\]  
The first eccentricity of the earth ellipsoid (\(e\)):  
\[e=\frac{\sqrt{{R_{e}}^{2}-{R_{p}}^{2}}}{R_{e}} \tag{3}\]  
When the latitude is \(\varphi\), the radius of curvature of the unitary circle is as follows:  
\[R_{n}=\frac{R_{e}}{\sqrt{1-e^{2}\sin^{2}\varphi}} \tag{4}\]  
where \(R_{e}\) is the semi-major axis, \(R_{e}=6,378,137\) m, \(R_{p}\) is the semi-minor axis, \(R_{p}=6,356,752\) m.  
The origin of the ECEF coordinate system is at the earth's center of mass, the \(X\)-axis points to the intersection of the equator and the prime meridian, the \(Z\)-axis points to the geographic North Pole, and the \(Y\)-axis and the other two axes form a right-handed coordinate system [12; 63; 64]. The GPS/POS carried by aircraft or camera can upload its attitude and position information (\(\lambda\), \(\varphi\), \(h\)). According to Equation (5) [17], the position of the camera in the earth coordinate system \((X_{E},Y_{E},Z_{E})\) can be presented as  
\[ \begin{bmatrix}X_{E}\\ Y_{E}\\ Z_{E}\end{bmatrix} = \begin{bmatrix}(R_{n}+h)\cos\varphi\cos\lambda\\ (R_{n}+h)\cos\varphi\sin\lambda\\ (R_{n}(1-e^{2})+h)\sin\varphi\end{bmatrix}  \tag{5}\]  
Using Equation (5) to solve the longitude and latitude through the earth coordinates will involve the solution of transcendental equations, so the accurate analytical solution cannot be directly obtained, and the solution process is also complicated. On the other hand, the commonly used methods for calculating geographic location information mainly include the direct method, iterative method, and quartic equation method. Among them, the iterative method is relatively simple to calculate and has high accuracy. The iterative algorithm described by Equations (6) and (7) can ensure that the latitude error is less than 0.0001 and the height accuracy reaches 0.001 m when the number of iterations is more than four times [63]. \[\left\{