sensors Article Geometric Self-Calibration of YaoGan-13 Images Using Multiple Overlapping Images Guo Zhang 1 , Mingjun Deng 1,2,*, Chenglin Cai 2 and Ruishan Zhao 3 1 State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China; [email protected] 2 School of Information Engineering, Xiangtan University, Xiangtan 411000, China; [email protected] 3 School of Geomatics, Liaoning Technical University, Fuxin 123000, China; [email protected] * Correspondence: [email protected]; Tel.: +86-027-68778266 Received: 4 April 2019; Accepted: 17 May 2019; Published: 23 May 2019 Abstract: Geometric calibration is an important means of improving the absolute positioning accuracy of space-borne synthetic aperture radar imagery. The conventional calibration method is based on a calibration field, which is simple and convenient, but requires a great deal of manpower and material resources to obtain ground control points. Although newer cross-calibration methods do not require ground control points, calibration accuracy still depends on a periodically updated reference image. Accordingly, this study proposes a geometric self-calibration method based on the positioning consistency constraint of conjugate image points to provide rapid and accurate calibration of the YaoGan-13 satellite. The proposed method can accurately calibrate geometric parameters without requiring ground control points or high-precision reference images. To verify the absolute positioning accuracy obtained using the proposed self-calibration method, YaoGan-13 Stripmap images of multiple regions were collected and evaluated. The results indicate that high-accuracy absolute positioning can be achieved with a plane accuracy of 3.83 m or better for Stripmap data, without regarding elevation error. Compared to the conventional calibration method using high-accuracy control data, the difference between the two methods is only about 2.53 m, less than the 3-m resolution of the image, verifying the effectiveness of the proposed self-calibration method. Keywords: YaoGan-13; geometric accuracy; self-calibration 1. Introduction The Chinese YaoGan-13 (YG-13) satellite mission, launched in November 2015, is equipped with a high-resolution synthetic aperture radar (SAR) X-band sensor. Synthetic aperture radar image products can be acquired using ScanSAR, Stripmap, and Sliding-spot modes, with the last of these providing SAR images at a very high resolution of about 0.5 m. The launch of YG-13 provided China with the ability to acquire high-resolution SAR images globally [1,2]. However, despite the strong capability of YG-13 in acquiring high-resolution SAR images, most of the images obtained by the satellite have exhibited poor absolute positioning accuracy, due to systematic timing offsets in the SAR system, including the time shift between the radar time and Global Positioning System (GPS) time (i.e., azimuth or along-track), and the internal electronic delay of the SAR instrument itself (i.e., the range delay time) [3]. As a result, the application of YG-13 images in activities such as resource monitoring has been significantly restricted. Using high-accuracy control data, a conventional geometric calibration method can eliminate systematic errors, such as those experienced by YG-13 (including the internal electronic delay of the instrument and systematic azimuth shifts), improving the geometric positioning accuracy of the images. The conventional geometric calibration method has been thoroughly studied by many researchers Sensors 2019, 19, 2367; doi:10.3390/s19102367 www.mdpi.com/journal/sensors Sensors 2019, 19, 2367 2 of 11 and fully validated using the ERS-1/2, ENVISAT-ASAR, ALOS-PALSAR, TerraSAR-X/TanDEM-X, Sensors 2019, 19, x FOR PEER REVIEW 2 of 12 Sentinel-1A/1B, YaoGan-13, GaoFen-3, and other high-resolution satellites [4–14]. However, the conventionalX/TanDEM-X, calibration Sentinel-1A/1B, method YaoGan-13, requires satellites GaoFen-3 to, and acquire otherimages high-resolution of calibration satellites fields [4–14]. prior to conductingHowever, geometric the conventional calibration, calibration reducing method its timeliness requires satellites in practical to acquire applications. images of Additionally, calibration the conventionalfields prior calibration to conducting method geometric typically calibration, uses a high-precisionreducing its timeliness corner in reflector practical to applications. generate control data,Additionally, which can bethe expensive. conventional calibration method typically uses a high-precision corner reflector to generateIn the opticalcontrol data, remote which sensing can be field,expensive. many scholars have researched methods for geometric self-calibrationIn the optical that doremote not sensing rely on field, control many data, schola achievingrs have researched notable successmethods [for15, 16geometric]. In the self- field of calibration that do not rely on control data, achieving notable success [15,16]. In the field of SAR SAR geometric calibration, researchers have also begun to study geometric calibration without field geometric calibration, researchers have also begun to study geometric calibration without field calibration control data. Deng et al. performed cross calibration without using corner reflectors or calibration control data. Deng et al. performed cross calibration without using corner reflectors or high-precisionhigh-precision digital digital elevation elevation models models to improve to improv thee absolutethe absolute positioning positioning accuracy accuracy of images of images collected by thecollected GaoFen-3 by the (GF-3) GaoFen-3 satellite (GF-3) [2]. satellite However, [2]. thisHowever, method this does method not completelydoes not completely eliminate eliminate dependence on controldependence data, on as control it still requiresdata, as it high-precision still requires high-precision reference images. reference To theimages. authors’ To the knowledge, authors’ no studiesknowledge, of completely no studies independent of completely SAR independent geometric SA self-calibrationR geometric self-calibrati have beenon reportedhave been to reported date. toIn date. this paper, a novel self-calibration method is proposed to determine the systematic timing offsets inIn the this SAR paper, system, a novel independent self-calibration of ground method control is proposed points to (GCPs). determineThis the method systematic uses attiming least three imagesoffsets containing in the SAR overlapping system, independent areas and of takes ground advantage control points of the (GCPs). spatial intersectionThis method residualuses at least between three images containing overlapping areas and takes advantage of the spatial intersection residual conjugate points in these images to detect the timing offsets. The proposed method is free from the between conjugate points in these images to detect the timing offsets. The proposed method is free constraintfrom the of fieldconstraint control of datafield presentcontrol data in traditional present in calibration traditional methods.calibration To methods. demonstrate To demonstrate the accuracy of the proposedthe accuracy method, of the aproposed series of method, experiments a series using of experiments Stripmap imagesusing Stripm collectedap images by YG-13 collected is presented. by The resultsYG-13 is show presented. that the The proposed results show method that is the able prop to effectivelyosed method eliminate is able theto effectively systematic eliminate errors, due the to the internalsystematic electronic errors, delay due of to the the instrument internal electronic and the delay systematic of the instrument azimuth shifts. and the After systematic calibration, azimuth the plane absoluteshifts. positioning After calibration, accuracy the ofplane the YaoGan-13absolute posi Stripmaptioning accuracy image wasof the better YaoGan-13 than 3.83 Stripmap m, just image larger than the 3-mwas resolutionbetter than of3.83 the m, images, just larger verifying than the the 3-m effectiveness resolution of of the the images, proposed verifying method. the effectiveness of the proposed method. 2. Methodology 2. Methodology 2.1. Fundamental Theory of the Proposed Method 2.1. Fundamental Theory of the Proposed Method Figure1 illustrates the proposed method of SAR image geometric self-calibration. In Figure1a, Figure 1 illustrates the proposed method of SAR image geometric self-calibration. In Figure 1a, S1 and S2 correspond to the two SAR antenna phase centers when the ground surface at Point A is S1 and S2 correspond to the two SAR antenna phase centers when the ground surface at Point A is photographedphotographed twice. twice.The The slant slant range range between between S1S1 and A is is R1 R1 and and the the slant slant range range between between S2 and S2 and A A is R2, andis R2, so and the so intersection the intersection point point between between R1 R1 and and R2 R2 is is Point Point A. A. If If aa slantslant range measurement measurement error error DR exists△ dueR exists to thedue geolocationto the geolocat parameterion parameter error, error, the the slant slant range range R1 R1 becomes becomes R1R1 + △DR,R, the the slant slant range range R2 becomesR2 becomes R2 + D R2R, and+ △R, the and new the spatialnew spatial intersection intersection is at is Point at Point B. B. In In this this way, way, the the spatial spatial intersectionintersection point is affectedpoint is by affected the error by ofthe