# A Method of Aerial Multi-Modal Image Registration
## 2 Real Scene Acquisition and Generation of Virtual Scene Simulation
### Virtual Scene Simulation Based on OSG Imaging  
OSG (Open Scene Graph) is a cross-platform open-source scene graphics programming interface (API), which plays an important role in 3D applications. The visual simulation based on OSG can change the digital information in the simulation process into an intuitive, graphical and image representation, and present the simulation process changing with time and space to the observer. Based on the static data and real-time flight parameter data including airport database and terrain database, this paper generates a virtual scene, shown in Figure 2.  
In this paper, the flight parameters are obtained by the attitude and azimuth integrated navigation system. The traditional inertial navigation system has the advantages of being independent of external information, good concealment, strong anti-interference and all-weather operation. It is a completely autonomous navigation system that can provide multiple navigation parameters. However, its accuracy varies with time, and large errors will be accumulated during long-time operation, which makes the inertial navigation system unsuitable for long-time navigation. GPS has high navigation accuracy, but due to the mobile change of the moving carrier, it is often difficult for the receiver to capture and track the satellite carrier signal, or even lose the lock on the tracked signal. In order to give full play to the advantages of the two technologies, improve the product performance more effectively and comprehensively, and enhance the reliability, availability and dynamics of the system, this project adopts an attitude and azimuth integrated navigation system that combines satellite positioning and inertial measurement.  
Because the low refresh rate of flight parameter data cannot match the frame rate of visual stimulation, sometimes there is an error or jitter. Through experiments, it is found that, especially when the aircraft turns, roll, pitch and other parameters will produce some jitter errors. Therefore, the flight parameter data should be smoothed and interpolated. Assuming that the flight path falls on a smooth surface of degree p in a short time, and let the surface equation be  
\[z=\sum_{i=0}^{p}\sum_{j=0}^{i}c_{i,j}x^{j}y^{i-j} \tag{6}\]  
where \(c_{i,j}(i=0,\ 1,\ \ldots,\ p,\ j=0,\ 1,\ \ldots,\ i)\) is an undetermined coefficient, with \(n=\frac{(p+1)(p+2)}{2}\) items in total. Select \(m(>=n)\) observation data \((x_{k},\ y_{k},\ z_{k}),k=1,2,\ldots,m\), sort the subscripts \((i,j)\) of the coefficients to be determined according to the dictionary, the coefficient to be determined is changed to \(c_{i}(i=1,\ 2,\ \ldots,\ n)\) (in order to prevent the introduction of too many subscripts, it is still represented by subscript \(i\)), and the linear equations are obtained:  
\[\mathbf{AC}=\mathbf{Z} \tag{7}\]  
where  
\[A=\left[\begin{array}{cccccc}1&y_{1}&x_{1}&\ldots&x_{1}^{p-1}y_{1}&x_{1}^{ p}\\ 1&y_{2}&x_{2}&\ldots&x_{2}^{p-1}y_{2}&x_{2}^{p}\\ \vdots&\vdots&\vdots&\vdots&\vdots&\vdots\\ 1&y_{m}&x_{m}&\ldots&x_{m}^{p-1}y_{m}&x_{m}^{p}\end{array}\right],\mathbf{C}=[ c_{1},c_{2},\ldots,c_{n}]^{T},\mathbf{Z}=[z_{1},z_{2},\ldots,z_{n}]^{T}.\]  
According to the definition of the generalized inverse matrix, it is the least square solution of equation group \(\mathbf{AC}=\mathbf{Z}\). For missing or abnormal flight data \((x,y)\) such as altitude, it can be fitted according to the following formula:  
\[\mathbf{a}=\left[1,y,x,\ldots,x^{p-1}y,x^{p}\right],z^{*}=\mathbf{aC} \tag{8}\]  
Figure 2: Workflow of virtual scene generation simulation platform.  
The visual analysis of two takeoff and landing aircraft attitude data after preprocessing is shown in Figure 3, in which longitude, latitude and height data are smooth.