# 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
### Filter Positioning Algorithm Based on Single-Machine Multiple Measurements  
With the development of high-altitude oblique imaging aerial cameras, the camera can not only image the target, but track the target and continuously acquire target images through multiple shoots. During the tracking process, a large amount of data can be obtained, so the algorithm tracks and positions the motion target by using filter algorithms, which tend to be proposed and applied in corresponding engineering projects [42, 43, 44, 45, 46, 47, 48, 49, 50]. In addition to the typical filter positioning algorithms like Kalman Filter (KF) and extended Kalman filter (EKF), a filter localization algorithm for stationary targets will be presented in this section. In the process of multiple measurements of the target by the aerial camera, the state quantity of the system is regarded as the geographical position of the target, then the state equation and measurement equation of the system can be expressed as Equation (22) [46,47],  
\[ \begin{cases}X_{k+1}=\phi_{k+1,k}X_{k}+W_{k}\\ Z_{k}=h(X_{k})+V_{k}\end{cases}  \tag{22}\]  
where \(X_{k}\) is the initial position information of the target, which can be obtained by the positioning algorithm based on the earth ellipsoid model. \(W_{k}\) and \(V_{k}\) are zero-mean white Gaussian noise, which are uncorrelated and represent systematic and random noise, respectively. Since the target is fixed, the state transition matrix \(\phi_{k+1,k}\) and the covariance matrix \(Q_{k}\) of the systematic error can be expressed as Equation (23). \[\phi_{k+1,k}= \begin{bmatrix}1&0&0\\ 0&1&0\\ 0&0&1\end{bmatrix} ,Q_{k}= \begin{bmatrix}0&0&0\\ 0&0&0\\ 0&0&0\end{bmatrix}  \tag{23}\]  
The positioning algorithm for calculating and finding the target location can be transformed into an algorithm for calculating the optimal estimation multiple times according to the state equation and measurement equation of the system. The Kalman filter is generally divided into two steps. The first is the prediction of state and mean square error, as shown in Equation (24), where \(X\) is the system state and \(P\) is the mean square error. \[X_{k+1|k}=\phi_{k+1,k}X_{k},P_{k+1|k}=\phi_{k+1,k}P_{k}+Q_{k} \tag{24}\]The second step of the filtering algorithm is to update the system state, as shown in Equation (26), where \(K\) is the filtering gain and \(I\) is the identity matrix. \[\left\{ \begin{aligned} & K_{k}=P_{k+1|k}H_{k+1}^{T}[H_{k+1}P_{k+1|k}H_{k+1 }^{T}+R_{k+1}]^{-1}\\ & X_{k+1}=X_{k+1|k}+K_{k+1}[Z_{k+1}-h(X_{k+1|k})]\\ & P_{k+1}=[I-K_{k+1}H_{k+1}]P_{k+1|k}\end{aligned} \right. \tag{25}\]  
Therefore, the state estimator \(X_{k}\) at time \(k\) can be derived by recursive calculation through the initial state estimator \(X_{0}\) and its covariance matrix \(P_{0}\) and the observation \(Z_{k}\) at time \(k\), where \(X_{k}\) means the position of the target [48]. As mentioned above, the Kalman filter algorithm can be used for the high-precision positioning of stationary targets. However, considering that most of the error sources are random errors, the system state should be nonlinear. Meanwhile, the Kalman filter is a linear filtering algorithm, so position accuracy cannot be guaranteed. In order to solve this issue, scholars have explored many target localization algorithms based on nonlinear filters, such as Extended Kalman Filter (EKF), unscented Kalman Filter (UKF), and Particle Filter (PF), to improve the stability of the filter positioning algorithm. Target tracking is one of the important requirements in the remote sensing field. A target location algorithm based on filtering is one of the most efficient and reliable options. The research of related algorithms has also expanded from static targets to mobile targets and multi-target monitoring. In addition to the initial application to Earth observation, similar algorithms have also been applied to space exploration fields such as space-based target tracking and debris monitoring.