Gaofen4 (GF4) is China's first high-resolution geostationary optical satellite equipped with planar array, which is employed for remote sensing monitoring of China and its surrounding areas. The panchromatic planar array sensor on this satellite collects images with a complementary metal oxide semiconductor (CMOS) of 10240×10240 detectors. It can perform time-sharing imaging on five spectral bands through rotating filters and simultaneously obtain panchromatic and multi-spectral images with a spatial resolution of 50 m. Essential in data processing of GF4, on-orbit geometric calibration should be performed to correct the systematic geometric errors in its imaging models and ensure the geometric quality of its images. At present, on-orbit geometric calibration is also usually performed based on such an imaging model to fit the rigorous geometric imaging model adopted in the processing system of remote sensing satellites. However, although the on-orbit geometric calibration is only a simple resection in photogrammetry, the satellite is a complex imaging and measuring system integrating attitude, orbit, and time observations. The building of its rigorous imaging model involves complex processing for auxiliary data such as attitude, orbit and time and ephemeris data, as well as transformations among multiple coordinate systems. Additionally, each calibration task requires separate production of these auxiliary data in the daily operational data processing system. Therefore, the geometric calibration based on the rigorous imaging model is not only complicated in modeling but also time-consuming and laborious. Thus, this paper proposes an on-orbit geometric calibration based on the unified rational polynomial coefficient (RPC) model for the panchromatic planar array sensor on the GF4 satellite.

This paper proposes a simple on-orbit geometric calibration method based on a priori RPC model, in which the calibration is performed on the current calibration parameters and the RPC generates based on these calibration parameters. The essence is to employ the geo-positioning residual determined by the current RPC to correct the current calibration parameters. Firstly, it is still necessary to match a certain number of evenly distributed ground control points (GCPs) from the high-precision digital ortho map (DOM) and digital surface model (DSM) in the image coverage area. Secondly, the virtual image points corresponding to the GCPs are obtained by back projection of the RPC. Thirdly, based on the current calibration parameters, the on-orbit geometric calibration model is built with the virtual and real image points of GCPs. Finally, the adjustment model of the calibration parameters is built, and the least square optimization is adopted to solve the calibration parameters together to compensate for the systematic geometric errors in the planar array sensor. The sensor calibration accuracy is verified based on correcting low order errors. This method only utilizes L1B image data with an RPC instead of needing attitude, orbit, and time auxiliary data and building a complex rigorous imaging model. It has the advantages of simple and convenient processing and can obtain almost the same accuracy as traditional calibration methods.

The viewing angle of the detectors determined by this method is almost the same as that from the calibration based on the rigorous imaging model, and the maximum difference between them is only 0.01 pixels (Table 2). For the calibration image, the initial imaging model of the image has a large geo-positioning error before calibration, and there is an obvious radioactive geometric error gradually increasing from the image center to the edge. The mean square errors of comprehensive geometric residuals in the row and column directions are 1.54 and 1.85 (Table 3), but up to 3-4 pixels at the image edge (Fig. 5), which seriously affects the performance in subsequent image registration and fusion. After the proposed calibration, the absolute geo-positioning accuracy and internal geometric accuracy of the image have been significantly improved. The absolute and relative residuals of the checkpoints tend to be the same, and the direction has good randomness (Fig. 5). For the verification image, the proposed calibration has improved the internal geometric accuracy of the single image from about 1.5 pixels to about 0.8 pixels in both directions. The calibration accuracy of this method is consistent with that of calibration based on the rigorous imaging model (Table 4), which directly shows that the proposed calibration method is effective and reasonable.

This paper proposes a simple and practical on-orbit geometric calibration method for the panchromatic planar array sensor on the GF4 satellite. Different from traditional methods, this method does not need to build a complex rigorous imaging model based on multiple auxiliary data. The current calibration parameters and the corresponding generated RPC are enough to estimate the accurate calibration parameters, and such parameters can be directly adopted in the ground processing system. Compared with traditional methods, this method does not need complex auxiliary data processing and transformations among various coordinate systems, and its approach and modeling are both simple. Therefore, it is extremely suitable for satellites such as GF4 that need high-frequency on-orbit calibration. The effectiveness of this method is verified through a group of experiments and compared with traditional methods based on a rigorous imaging model. Experimental results show that this method can obtain calibration results that are almost consistent with traditional methods, and can effectively compensate the systematic geometric errors in the imaging model of a planar array satellite sensor.