**Jun Chen \*, Zhichao Sha, Jungang Yang and Wei An**

College of Electronic Science, National University of Defense Technology, Changsha 410073, China; shazhichao163@163.com (Z.S.); yangjungang@nudt.edu.cn (J.Y.); anwei@nudt.edu.cn (W.A.) **\*** Correspondence: chenjun11@nudt.edu.cn; Tel.: +86-731-8700-3326

Received: 14 August 2019; Accepted: 9 September 2019; Published: 16 September 2019

**Abstract:** The rational function model (RFM) is widely used in the most advanced Earth observation satellites, replacing the rigorous imaging model. The RFM method achieves the desired calibration performance when image distortion is caused by long-period errors. However, the calibration performance of the RFM method deteriorates when short-period errors—such as attitude jitter error—are present, and the insufficient and uneven ground control points (GCPs) can also lower the calibration precision of the RFM method. Hence, this paper proposes a geometric calibration method using sparse recovery to remove the linear array push-broom sensor bias. The most important issue regarding this method is that the errors related to the imaging process are approximated to the equivalent bias angles. By using the sparse recovery method, the number and distribution of GCPs needed are greatly reduced. Meanwhile, the proposed method effectively removes short-period errors by recognizing periodic wavy patterns in the first step of the process. The image data from Earth Observing 1 (EO-1) and the Advanced Land Observing Satellite (ALOS) are used as experimental data for the verification of the calibration performance of the proposed method. The experimental results indicate that the proposed method is effective for the sensor calibration of both satellites.

**Keywords:** geometric calibration; long- and short-period errors; equivalent bias angles; sparse recovery; linear array push-broom sensor
