# Geometric Processing and Accuracy Verification of Zhuhai-1 Hyperspectral Satellites
## 2 Methods
### Production  
Orbita has considered both the amount of image data and the practical application requirements. The basic products released to the outside world are the 32-band registration image products of the single CMOS, and the regional mosaic image is used as a value-added product. Therefore, although the single imaging width of the hyperspectral satellite can reach 150 km, the width of the basic product released by the company is 50 km. OHS basic product processing is mainly performed for 32-band registration and Rational Function Coefficients (RPC) generation.  
The essence of spectral registration is to determine the correspondence of homonymous points between different spectral segments. Figure 3 shows a schematic of a synonymous point with four spectral segments as examples. As shown, any imaging point on B1 can be used to determine the location of homonymous image points on B2, B3, and B4 based on the principle that homonymous points should be located at the same position on the ground (positioning consistency constraint). The accuracy of the corresponding relationship is mainly limited by the accuracy of the geometric positioning parameters, including the accuracy of the attitude and orbit used in positioning, the accuracy of orientation elements in the camera, and the accuracy of the elevation data.  
Geometric calibration accurately restored the camera's interior orientation elements and determined the exact position relationship of the 32 spectral segments on the focal plane. Therefore, the influence of the interior orientation element error on the determination of homonymous points can be ignored. For elevation fluctuation caused by stereoscopic parallax, the maximum difference in the view angle between the OHS spectrum (band 1 and band 32) is less than 3\({}^{\circ}\), considering geometric positioning in the global 90 m grid SRTM as elevation data, an elevation accuracy of 16 m, and the effect of stereoscopic parallax for identical point determination being less than 0.1 pixels, which can be neglected. For attitude and orbit measurement errors, the imaging time interval between adjacent spectral segments for identical objects is less than 0.1 s, while the attitude and orbit measurement errors over a short period are mainly systematic errors, which do not affect the accuracy of the identical point relationship determination. Therefore, the registration of OHS spectral segments can be realized based on the consistency constraint of homonymous point location. The algorithm is as follows:  
1. Using the geometric calibration results, establish a geometric positioning model for each spectral segment of the OHS according to Equation (4);  
Figure 3: Schematic of correspondence between homonymous points in different spectral segments.  
* Select the intermediate spectral segment as the reference spectral segment (such as the 15 th spectral segment), which has an image size of \(w_{r}\times h_{r}\). Based on the spectral segment geometric positioning model established in (1), the terrain-independent method is used to generate the RPC parameters of the spectral segment;
* For any of the spectral segments N (N\(\
eq\)15), generate a new image of size \(w_{r}\times h_{r}\) as follows:
* For any image point \((x,y)\) on the image, calculate the ground coordinate \((X,Y,Z)\) corresponding to \((x,y)\) using the geometric positioning model of the reference spectral segment;
* Calculate \((X,Y,Z)\) corresponding to the image point coordinate \((x,y)\) in spectral segment N by using the positioning model of N;
* Calculate the gray value at \((x,y)\) using the linear interpolation method and assign \((x,y)\) to the new image;
* Repeat steps (a)-(c) until all pixels of the new image have been calculated.
* Repeat step (3) until all segments have been resampled.