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Multimode Hybrid Geometric Calibration of Spaceborne SAR Considering Atmospheric Propagation Delay Ruishan Zhao 1,2 , Guo Zhang 2, *, Mingjun Deng 3 , Fan Yang 1 , Zhenwei Chen 4 and Yuzhi Zheng 2 1 2 3 4

*

School of Geomatics, Liaoning Technical University, Fuxin 123000, China; [email protected] (R.Z.); [email protected] (F.Y.) State Key Laboratory of Information Engineering in Surveying Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China; [email protected] School of Remote Sensing and Information Engineering, Wuhan University, Wuhan 430079, China; [email protected] School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China; [email protected] Correspondence: [email protected]; Tel.: +86-139-0718-2592

Academic Editors: Richard Müller and Prasad Thenkabail Received: 10 February 2017; Accepted: 7 May 2017; Published: 10 May 2017

Abstract: The atmospheric propagation delay of radar signals is a systematic error that occurs in the atmospheric environment, and is a key issue in the high-precision geometric calibration of spaceborne SAR. A multimode hybrid geometric calibration method for spaceborne SAR that considers the atmospheric propagation delay is proposed in this paper. Error sources that affect the accuracy of the geometric calibration were systematically analyzed. Based on correction of the atmospheric propagation delay, a geometric calibration model for spaceborne SAR was established. The high precision geometric calibration scheme for spaceborne SAR was explored by considering the pulse-width and bandwidth of the signal. A series of experiments were carried out based on high-resolution Yaogan 13 (YG-13) SAR satellite data and ground control data. The experimental results demonstrated that the proposed method is effective. The plane positioning accuracy of YG-13 in stripmap mode without control points is better than 3 m, and the accuracy of the sliding spotlight mode is better than 1.5 m. Keywords: spaceborne SAR; geometric calibration; atmospheric propagation delay; tropospheric delay; ionospheric delay

1. Introduction Geometric calibration is a crucial component of satellite in-orbit tests of synthetic aperture radar (SAR) systems. It allows the geometric accuracy of a spaceborne SAR system to reach the theoretical limit, and is also the key factor affecting the subsequent application of SAR image data. The purpose of geometric calibration of spaceborne SAR is to improve the geometric accuracy of spaceborne SAR images without control points by calibrating the systematic error, and compensating for it using a triangle reflector on the ground. The geometric calibration of spaceborne SAR is mainly based on the calibration of two parameters: the initial start time in the azimuth direction and the initial slant range in the range direction [1]. The geometric accuracy of international advanced SAR satellites such as TerraSAR-X, ERS, ALOS-PALSAR, Sentinel-1A, and RADARSAT-2 is better than 10 m without control points after compensating for the two calibration parameters mentioned above [2–10]. The geometric accuracy of ENVISAT-ASAR is better than 0.6 pixels in range, and better than 8 pixels in azimuth after Remote Sens. 2017, 9, 464; doi:10.3390/rs9050464

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Remote Sens. 2017, 9, 464

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calibration [11]. Although the positioning accuracy of these SAR satellites can reach the ideal level after classical geometric calibration, there are still some residual errors in the range direction with changes in incident angle and imaging mode. For many of the current spaceborne SAR systems, there are a many beam positions and imaging modes, and it would take too much effort to calibrate for each beam position and each imaging mode in order to achieve better positioning accuracy. Therefore, a new calibration strategy is needed. In addition, radar signals have different delays as they cross the atmosphere in different environmental conditions. Most geometric calibration methods for current SAR satellites do not consider the influence of atmospheric propagation delay. To some extent, this affects the accuracy of the geometric calibration. Although the geometric calibration of TerraSAR-X and Sentinel-1A takes into account the influence of atmospheric propagation delay on range measurement, the delay correction value of each control point used for geometric calibration is only replaced by the delay correction value at the center of the SAR image [2–5,9]. When the imaging area is a rough mountainous area, this approach of simple substitution affects the accuracy of the geometric calibration. With the launch of high-resolution SAR satellites with multiple imaging modes by different countries, the cycle and cost of the geometric calibration tasks are becoming even more demanding, and there is a great focus on normalization and high-accuracy geometric calibration methods for spaceborne SAR. Therefore, in this paper, we propose a multimode hybrid geometric calibration method for spaceborne SAR that considers the atmospheric propagation delay. The error sources that affect the accuracy of geometric calibration are systematically analyzed. Based on correction of the atmospheric propagation delay, the geometric calibration model for spaceborne SAR is established. A high-precision geometric calibration scheme for spaceborne SAR is studied by considering the pulse-width and bandwidth (which is the range bandwidth) of the signal. Yaogan-13 (YG-13) is an X-band high-resolution SAR satellite launched by China that circles the Earth in a sun-synchronous orbit at 632 km altitude. Its incident angle range is between 20◦ and 55◦ , and it acquires radar data in three main imaging modes: StripMap, SpotLight, and ScanSAR. YG-13 is mainly used for scientific experiments, land resource surveys, crop yield estimation and disaster prevention and mitigation. A series of experiments was carried out based on the high-resolution YG-13 SAR satellite data, with automatic corner reflector equipment installed at Songshan Remote Sensing Calibration Field in Henan Province, China, as ground control data. This paper describes the multimode hybrid geometric calibration method of spaceborne SAR considering atmospheric propagation delay. Section 2 describes the atmospheric propagation delay of radar signal, including the neutral atmospheric propagation delay and the ionospheric delay. Section 3 describes the theoretical approach of the geometric calibration proposed in this paper. Some results of the atmospheric propagation delay analysis, geometric calibration accuracy analysis and accuracy verification are given in Section 4. Finally, Section 5 presents the conclusions. 2. Atmospheric Propagation Delay The radar signal is transmitted from the SAR system to the receiver, and the delay influence is affected by the atmospheric propagation, which changes with the atmospheric environment. In general, the atmospheric propagation delay correction model is [12]: ∆L =

1 cos(η )

Z ∞ z

(n(z) − 1)dz

(1)

where n(z) is the atmospheric refraction rate for the zenith direction, and η is the incident angle. Calculation of the atmospheric zenith delay depends on a precise atmosphere model, in order to obtain the atmospheric refractive index distribution model. The influence of the atmospheric propagation delay on radar signals is divided into two main parts: the neutral atmosphere and the ionosphere. The neutral atmosphere is usually divided into two parts: dry and wet [13]. According to


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the division of atmospheric composition, Puyssegur integrated the influence of the amount of clouds and free electrons, and gave the calculation model for the atmospheric refractive index [14] as:   (n − 1) = 10−6 N    P e TEC e N = k1 d + k2 + k3 2 + k4 Wcloud + k5 2 f  | {zT} | T {z T } | {z }  | {z }  liquid water  dry air

wet air

(2)

ionosphere

where Pd is the dry atmospheric pressure, e is the wet atmospheric pressure, T is the surface temperature (K), Wcloud is the water vapor content (kg/m3 ), TEC is the ionospheric electron density, f is the frequency of the electromagnetic wave signal, k1 = 77.6 K/mbar, k2 = −6.0 K/mbar, k3 = 3.75 × 105 K2 /mbar, k4 = 1.45 m3 /g, and k5 = −4.03 × 107 m3 /s2 . In Equation (2), the first term is the atmospheric delay caused by the hydrostatic effect (air pressure), the second term is the atmospheric delay caused by humidity (water vapor), the third term is the atmospheric delay caused by liquid (water droplets), and the fourth term is the ionospheric delay. 2.1. Neutral Atmospheric Propagation Delay Combined with the hydrostatic equation and the non-ideal gas formula, the range correction model for dry and wet components in the neutral atmosphere was derived by James C. Owens [15] as (

−1 · P The dry atmosphere delay : ∆L D = 10−6 k1 MR gm Sur f d The wet atmosphere delay : ∆LW = 10−6 k2 MR · PW

(3)

W

where the surface pressure Psurf = Pd + e, PW is precipitable water vapor, Md and MW are, respectively, dry and wet atmospheric molecular weights, Md = 28.9644 kg/kmoL, MW = 18.0152 kg/kmoL, and R is the molar gas constant, R = 8.31451 J/(moL·K). The k1 and k2 values are correlated with the frequency of the electromagnetic wave emitted by the satellite, and the solution formula is  −2 −2   k = 0.237134 + 68.39397 (130 + λ ) + 0.45473 (38.9 + λ ) 1 (4) (130 − λ−2 )2 (38.9 − λ−2 )2   k = 0.648731 + 0.0174174λ−2 + 3.55750 × 10−4 λ−4 + 6.1957 × 10−5 λ−6 2 According to Equation (3), it is necessary to obtain the atmospheric surface pressure and atmospheric precipitable water to solve for the dry and wet atmospheric delays. Global Atmospheric Models (GAM) can provide meteorological data recorded by satellite and meteorological base stations, including temperature, pressure, water vapor content, and wind speed. In this study, the atmospheric analysis model of the American National Center for Environmental Prediction (NCEP) was used as the external data [16]. Isobaric data stored in grid point format were provided in the model every six hours. 2.2. Ionospheric Delay The ionosphere is the part of the atmosphere that is about 60–1000 km from the ground, and the free electron density in the ionosphere is at a maximum at about 400 km. Usually, a single-layer ionosphere model, which is an ideal model, is used to replace the whole ionosphere. According to the idealized model, the free electrons in the ionosphere can be compressed in a vertical direction to a single spherical surface with a certain height as a layer over the atmosphere. Figure 1 is a schematic diagram of a single-layer ionosphere model. It can be seen that all electrons in the nadir P in the vertical direction are compressed to a point P0 , and the ionospheric delay is related to the TEC content of the compression point P0 and the angle between the line of sight and the normal direction of the


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ionosphere. As a result, the ionospheric delay of the radar signal along the propagation path can be

ionosphere. As a result, the ionospheric delay of the radar signal along the propagation path can be obtained as [17–19] obtained as [17–19] TEC TEC 11 ∆LΔI L=I =K K · ⋅ 2 2· ⋅ (5) (5) 0 f f cos cosθθ ' 16 2 , and f is the electromagnetic frequency. wherewhere K = 40.28 m3 /sm23,/sthe unit forforTEC 2, the unit TECisis10 1016 electrons/m electrons/m2, and f is the electromagnetic frequency. K = 40.28 FromFrom Equation (5), (5), we we cancan seesee that delay isisrelated relatedtotothethe TEC content Equation thatthe theionospheric ionospheric delay TEC content and and the the electromagnetic frequency. electromagnetic frequency.

H = 450 km Target

P'

θ

SAR '

θ

P

Single ionosphere

O Figure 1. Schematic diagram of single-layer ionosphere model interpolation. Figure 1. Schematic diagram of single-layer ionosphere model interpolation.

Global Ionosphere Maps (GIM) in the Ionosphere Exchange (IONEX) format are provided by

Global Ionosphere (GIM) in the Ionosphere Exchange (IONEX) format areone provided the European CentreMaps for Orbit Determination (CODE) every day. From UTC zero to 24, global by ionospheric TEC map is acquired every two hours, so 12 maps are From produced every However, the European Centre for Orbit Determination (CODE) every day. UTC zeroday. to 24, one global starting TEC from map 19 October 2014, there aretwo 24 maps eachsoday, with intervals of one hour. The GIMHowever, grid ionospheric is acquired every hours, 12 maps are produced every day. partition intervals are 5° in longitude, and 2.5° in latitude. The longitude range is from −180° W to grid starting from 19 October 2014, there are 24 maps each day, with intervals of one hour. The GIM 180° E, and the latitude range is from 87.5°S to −87.5°N, so there are, in total, 5183 grid points. To partition intervals are 5◦ in longitude, and 2.5◦ in latitude. The longitude range is from −180◦ W obtain a specific point-of-time delay, three steps are needed, as follows. to 180◦ E, and the latitude range is from 87.5◦ S to −87.5◦ N, so there are, in total, 5183 grid points. First, the global TEC content map is obtained from the IONEX file, and the TEC content is To obtain a specific point-of-time delay, three steps are needed, as follows. calculated using linear interpolation from the grid points near the puncture point. Second, after the First, the global TECthe content is obtained from the IONEX and the TEC interpolation in space, bilinearmap interpolation in time is carried out at thefile, corresponding time content point. is calculated using linear interpolation from the grid points near the puncture point. Second, after the Third, after obtaining the TEC in the vertical direction of the corresponding time point of the puncture interpolation in space, the bilinear interpolation in time is carried out at the corresponding time point, the ionospheric delay value of the radar signal along the propagation path is calculated bypoint. an appropriate mapping function.direction of the corresponding time point of the puncture Third,selecting after obtaining the TEC in the vertical point, the ionospheric delay value of the radar signal along the propagation path is calculated by 3. Geometric Calibration of Spaceborne selecting an appropriate mapping function.SAR The core of the spaceborne SAR calibration algorithm is to calculate the geometric calibration

3. Geometric Calibration of Spaceborne SAR parameters of the spaceborne SAR system based on the offset between the pixel coordinates obtained directly from SAR image and the pixel coordinates calculated by a rigorous imaging geometry model.

The core of the spaceborne SAR calibration algorithm is to calculate the geometric calibration This approach can improve the positioning accuracy of a spaceborne SAR system without control parameters of the spaceborne SAR system based on the offset between the pixel coordinates obtained points. directly from SAR image and the pixel coordinates calculated by a rigorous imaging geometry model. approach can improve the positioning 3.1.This Geometric Calibration Model for Spaceborne SAR accuracy of a spaceborne SAR system without control points. The transmission and reception of SAR signals are realized on time scales, including fast time (range) and slow time (azimuth). The two-dimensional time errors, which are the main error sources 3.1. Geometric Calibration Model for Spaceborne SAR of spaceborne SAR, mainly affect the geometric positioning error of the SAR image in the range and azimuth direction. Thus, the geometric calibration model for spaceborne SAR is constructed as fast time The transmission and reception of SAR signals are realized on time scales, including

(range) and slow time (azimuth). The two-dimensional time errors, which are the main error sources of spaceborne SAR, mainly affect the geometric positioning error of the SAR image in the range and azimuth direction. Thus, the geometric calibration model for spaceborne SAR is constructed as   t f = t f 0 + tdelay + ∆t f + 

ts = (ts0 + ∆ts ) +

y−1 f pr f

x−1 fs

(6)


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where tf and ts are, respectively, the fast time in range and slow time in azimuth; tf0 and ts0 are, respectively, the measured value of the starting time in range and azimuth; tdelay is the atmospheric propagation delay time; ∆tf and ∆ts are the system delay time errors; fs is the sampling frequency, fprf is the pulse repetition frequency; x and y are pixel coordinates. The delay time error ∆tf is the system time-delay generated by the radar signal through each device of the SAR system. The system time delay can be obtained by calibration of the ground laboratory, but it will be affected by the tiny change in the load device that occurs with the satellite launching. However, tf is also affected by the atmospheric propagation delay due to the radar signal crossing the atmosphere to reach the ground and returning to the atmosphere from the ground. The propagation delay of the radar signal is mainly related to the local atmospheric pressure, temperature, water vapor content, ionospheric electron density, and radar signal frequency. Therefore, the propagation delay error is a systematic error related to the satellite imaging angle and imaging time. The system delay time error ∆ts is mainly caused by the error of the system time control unit. The system time control unit, which has a certain degree of time accuracy and a certain recording frequency, is used to record the time of all events. Therefore, it affects the accuracy of the start time in the azimuth. The starting time of the satellite record is the receiving time of the radar signal. However, the radar signal of a SAR satellite is transmitted and received in continuous motion. The equivalent SAR imaging time is the intermediate time between the transmitting and receiving time [20]. Therefore, it should be compensated for as ts0 = t0s0 −

N/ f pr f + tsample_delay 2

(7)

where t0s0 is the echo receiving time recorded on the satellite, N is the number of times the radar signal is transmitted from the transmitter to the receiver, and tsample_delay is the sample time delay in the satellite record. The Range Doppler (RD) model is a rigorous imaging geometry model for spaceborne SAR that establishes a close relationship between the object coordinate and the image coordinate as [21]  q 2 2 2   R = X − X + Y − Y + Z − Z = t f 0 + tdelay + ( ) ( ) ( )  t s t s t s  2 f D = − λR ( Rs − Rt ) · (Vs − Vt )   Xt2 + Yt2 Z2   + t =1 R2e

x−1 fs

×c (8)

R2p

where Rs = [Xs Yx Zs ]T and Vs are the orbit vector data of the SAR satellite in WGS84; Rt = [Xt Yt Zt ]T and Vt are the position vector data and velocity vector data of the target point in WGS84; fD is the Doppler centroid frequency; λ is the radar wavelength; R is the slant range, X is the column number of the target point in SAR image, and c is the speed of light; Re is the mean equatorial radius and R p = (1 − 1/ f ) Re is the polar radius with a flattening factor f = 298.255. The track vector data recorded on the satellite are collected at equal time intervals. In the actual calculation, the orbit vector data of the SAR satellite should be fit by a polynomial and interpolated according to the corresponding azimuth time [22–25]. The mathematical relationship between the ground point coordinates and the azimuth time and the range can be established based on the indirect positioning algorithm of the RD positioning model [26,27]. The azimuth time and slant range correspond to the line and column numbers of the SAR image. Therefore, if there are many control points in the SAR image, the correction value of the starting time in azimuth and range can be accurately calculated by least squares adjustment. The geometric calibration accuracy of spaceborne SAR is mainly affected by the satellite position error, the random error of the SAR system delay, the dispersion of the SAR antenna, the position error of the corner reflector, and the propagation delay model error. The satellite position accuracy can be improved by high-precision orbit determination data processing technology. The random error of a


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SAR system is mainly controlled by the design organization of the satellite payload. The dispersion error of the SAR antenna is dependent on the precision control by the design organization of the satellite payload, and requires precise compensation by ionosphere delay modeling. Because of the problem of low installation accuracy and poor stability for traditional artificial corner reflectors, automatic corner reflectors installed in geometric calibration fields are conducive to improving the positioning accuracy of control points. System analysis and accurate modeling of atmospheric propagation delay can improve the computational accuracy of the atmospheric propagation delay of SAR signals. 3.2. Geometric Calibration Scheme and Calculation Geometric calibration is mainly used to calibrate the fixed deviation in the same working conditions as spaceborne SAR, and requires analysis of the relationship between the operating state of the spaceborne SAR system and the geometric calibration parameters, in order to determine a reasonable calibration scheme. The classical geometric calibration schemes all take into account the ascending and descending modes, left and right side looks, and different beam positions. However, these considerations are not the main factors that affect the calibration parameters of the physical properties of the SAR signal. In addition, the current spaceborne SAR systems have dozens or even hundreds of beam positions. It is not realistic to calibrate every beam position. From the point of view of radar signal characteristics, the accuracy of range measurement depends on the bandwidth of the radar signal. Therefore, the bandwidth is the basic measurement of range accuracy [28]. At the same time, the pulse width affects the accuracy of the range measurement. The pulse signal is transmitted from the generator to the antenna, and the echo signal is relayed from the antenna to the data sampler. In this process, a delay is produced as the radar signal passes through the various components of the signal channel. The difference in this time delay is mainly affected by pulse-width and bandwidth of the radar signal. In summary, the pulse-width and bandwidth of the radar signal affect the system time delay error of spaceborne SAR. Therefore, it is necessary to adopt different pulse-width and bandwidth combination schemes for high-precision geometric calibration. The geometric calibration model for spaceborne SAR can be expressed as follows [29]:  h i  Fx = t f − t f 0 + tdelay + ∆t f + x − 1 = 0 i fs h y−1  =0 Fy = ts − (ts0 + ∆ts ) + f

(9)

pr f

The error equation for Equation (9) is V = Bx − l  where B = 

∂Fx ∂∆t f ∂Fy ∂∆t f

∂Fx ∂∆ts ∂Fy ∂∆ts

 , x =

h

d∆t f

d∆ts

iT

(10) "

,l=

− Fx0 − Fy0

# .

The main treatment scheme (as shown in Figure 2) in the multi-mode hybrid geometric calibration method for spaceborne SAR, considering the atmospheric propagation delay, is as follows: 1.

Determine the geometric calibration scheme considering the pulse-width and bandwidth, and obtain SAR image data and control point data. According to analysis of the error sources that affect the calibration accuracy of spaceborne SAR, the geometric calibration scheme is established by considering the pulse-width and bandwidth of the radar signal. On the basis of the corresponding relationship between the beam position number and the combination of pulse-width and bandwidth, the beam position numbers are classified, and the imaging task planning for calibration and verification field area is carried out according to the classification of the beam position numbers. Then, according to the imaging task of the SAR satellite, the normal direction of automatic corner reflector is adjusted by remote control, in order to carry out a series of satellite ground synchronous experiments. The original SAR data and auxiliary parameter files

the corresponding relationship between the beam position number and the combination of pulse-width and bandwidth, the beam position numbers are classified, and the imaging task planning for calibration and verification field area is carried out according to the classification of the beam position numbers. Then, according to the imaging task of the SAR satellite, the Remotenormal Sens. 2017, 9, 464 7 of 19 direction of automatic corner reflector is adjusted by remote control, in order to carry out a series of satellite ground synchronous experiments. The original SAR data and auxiliary parameter files are collected. The image coordinates of the control points are obtained by are collected. The image coordinates of the control points are obtained by accurately extracting accurately extracting the corner reflector points of the SAR image, and corrected using the the corner reflector points of the SAR image, and corrected using the calculated solid earth tides. calculated solid earth tides. 2. Calculate the atmospheric propagation delay point by point. According to the NCEP global 2. Calculate the atmospheric propagation delay point by point. According to the NCEP global atmospheric parameters updated every six hours and the global TEC data provided by CODE, atmospheric parameters updated every six hours and the global TEC data provided by CODE, the correction values for the atmospheric propagation delay are calculated from the antenna the correction values for the atmospheric propagation delay are calculated from the antenna phase center to each ground control point, in order to eliminate the influence of atmospheric phase center to each ground control point, in order to eliminate the influence of atmospheric propagation delay point by point. propagation delay point by point. 3. Solve for the geometric calibration parameters. Based on precise satellite orbit data, tf and ts 3. Solve for the geometric calibration parameters. Based on precise satellite orbit data, tf and ts are are calculated by an indirect localization algorithm of an RD location model. Making use of calculated by an indirect localization algorithm of an RD location model. Making use of the offset the offset between the pixel coordinates obtained directly from the SAR image and the pixel between the pixel coordinates obtained directly from the SAR image and the pixel coordinates coordinates calculated by a rigorous imaging geometry model, geometric calibration parameters calculated by a rigorous imaging geometry model, geometric calibration parameters are are calculated using Equations (9) and (10). calculated using Equations (9) and (10). 4. Accuracy verification verification and and evaluation. evaluation. Accuracy Accuracy verification verification and and evaluation evaluation of of the the geometric 4. Accuracy geometric calibration is carried out using SAR images of the verification field area with calibration is carried out using SAR images of the verification field area with ground ground control control points. points. Determine the geometric calibration scheme considering the pulse-width and bandwidth

Obtain image data and control point data

Calculate the atmospheric propagation delay

Solve for the geometric calibration parameters

Accuracy verification and evaluation

Figure 2. Flowchart Flowchart of of geometric calibration scheme.

4. Geometric Calibration of Spaceborne SAR 4.1. Experimental Data 4.1.1. YG-13 Data from Spaceborne SAR There are 33 scenes of YG-13 SAR images covering the Songshan calibration field area and 14 scenes of YG-13 SAR images covering the accuracy verification field area. The accuracy verification field areas include Taiyuan, Anping, Xianning, and Tianjin in China. The data were collected from 28 December 2015 to 29 May 2016, in strip-map mode and sliding spotlight mode. In order to analyze the experiments, the SAR images of the calibration field area and verification field area were acquired by left side-looking and right side-looking on the ascending orbit and descending orbit, respectively. Details of the acquired YG-13 SAR images are listed in Table 1, in which C1, C2, C3, C4, C5 and C6 represent the identifiers of pulse-width and bandwidth combinations.


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Table 1. YG-13 data information.

Imaging Mode

Pulse-Width and Bandwidth Combinations

Date of Image

Imaging Area

Number of Images

24.4 µs & 200 MHz (C1)

28 December 2015 to 29 March 2016 28 May 2016 29 May 2016

Songshan Taiyuan Tianjin

11 1 1

24.4 µs & 150 MHz (C2)

29 December 2015 to 2 April 2016 1 June 2016 9 June 2016 10 June 2016 12 June 2016

Songshan Taiyuan Anping Tianjin Xianning

11 1 1 1 1

29.2 µs & 600 MHz (C3)

18 December 2015 to 10 January 2016 21 May 2016 22 May 2016

Songshan Xianning Tianjin

3 1 1

29.2 µs & 512 MHz (C4)

11 December 2015 to 11 January 2016 27 May 2016 4 June 2016

Songshan Xianning Tianjin

4 1 1

24 µs & 300 MHz (C5)

27 February 2016 to 9 April 2016 28 May 2016 4 June 2016

Songshan Tianjin Taiyuan

2 1 1

28 µs & 300 MHz (C6)

14 March 2016 to 24 March 2016 29 May 2016 30 May 2016

Songshan Taiyuan Anping

2 1 1

Strip-map mode

Sliding spotlight mode

The orbital state vector of the SAR satellite is the key factor that affects the geometric location. There are three kinds of orbit data products, including real-time orbit data recorded by GNSS on the satellite, near-real-time preprocessing orbit data and precise orbit data from post-processing. Because of the dependence on external data, the production of precise orbit data, with accuracies better than 0.5 m, generally need to be delayed for one week. Nevertheless, in order to improve the performance of the SAR satellite system, precise orbit data is used for geometric calibration. 4.1.2. Ground Control Points Compared to ordinary scattering targets, the artificial corner reflector forms a strong luminance region in the SAR image. The center of the corner reflector can be accurately identified to provide the desired high-precision coordinates of the control points. The classical method of utilizing artificial corner reflectors requires a large amount of manpower, material, and financial resources, which is not convenient for engineering applications. In order to meet the requirements of different times and different incident angles, a high-accuracy automatic corner reflector that is self-developed, unattended, and controlled remotely SAR. Remote Sens. 2017, 9, 463(as shown in Figure 3) can be used for geometric calibration of spaceborne 9 of 19

Figure Automatic corner Figure 3. 3. Automatic cornerreflector. reflector.

According to imaging width and the ascending and descending mode of YG-13, six automatic corner reflectors were installed in Songshan, Henan Province, as shown in Figure 4. According to the Continuously Operating Reference Stations (CORS) established by network RTK technology in Henan Province, the point measurement accuracy of each corner reflector is at the centimeter level. Because of the different orientations of each corner reflector during each calibration task, the zenith coordinates of each corner reflector are compensated for accurately according to the rotation angle.


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Figure 3. Automatic corner reflector.

According descendingmode modeof ofYG-13, YG-13,six sixautomatic automatic Accordingtotoimaging imagingwidth width and and the the ascending ascending and and descending corner reflectors were installed in Songshan, Henan Province, as shown in Figure 4. According the corner reflectors were installed in Songshan, Henan Province, as shown in Figure 4. According totothe Continuously Reference Stations (CORS) established by network RTK RTK technology in Henan ContinuouslyOperating Operating Reference Stations (CORS) established by network technology in Province, the point measurement accuracy of each corner reflector is at the centimeter level. Because Henan Province, the point measurement accuracy of each corner reflector is at the centimeter level.of the different orientations each cornerofreflector during each calibration task, the zenith coordinates Because of the different of orientations each corner reflector during each calibration task, the zenithof each corner reflector compensated forcompensated accurately according to theaccording rotation angle. In addition, the coordinates of each are corner reflector are for accurately to the rotation angle. zenith coordinates of each corner reflector also reflector correctedare foralso the corrected impact offor solid tides (SET), In addition, the zenith coordinates of eachare corner theearth impact of solid which by the International Earth Rotation Earth Service (IERS)Service Conventions 2003 [30] and earth are tidescalculated (SET), which are calculated by the International Rotation (IERS) Conventions and a small program called [31].toAccording the YG-13 plan, the automatic angleis a 2003 small[30] program called solid.exe [31].solid.exe According the YG-13toplan, the automatic angle reflector reflectorby is remote adjustedcontrol by remote control to efficiency realize high efficiency and fast synchronization between adjusted to realize high and fast synchronization between satellite and satellite and target. This meets the requirements of normalization and fast calibration. target. This meets the requirements of normalization and fast calibration.

Figure4.4.Distribution Distribution of of automatic automatic corner reflectors Figure reflectors in in Songshan Songshanregion. region.

4.2.Experimental ExperimentalResults Resultsand andAnalysis Analysis 4.2. Makinguse useofofYG-13 YG-13data, data,the the following following three three experiments experiments were Making were carried carriedout. out.(1) (1)For Fordifferent different distributions of control points in the same scene, different beam positions, ascending and descending distributions of control points in the same scene, different beam positions, ascending and descending mode, left and right side-looking, and different imaging areas, the influences of atmospheric mode, left and right side-looking, and different imaging areas, the influences of atmospheric propagation delay (including neutral atmospheric delay and ionospheric delay) on the geometric propagation delay (including neutral atmospheric delay and ionospheric delay) on the geometric calibration accuracy are respectively analyzed. (2) Geometric calibration and accuracy evaluation of YG-13 are carried out using the multimode hybrid geometric calibration method for spaceborne SAR (considering atmospheric propagation delay) proposed in this paper. (3) Based on the geometric calibration results of YG-13 without considering the pulse-width and bandwidth of the radar signal, and analysis of broadband and the effects of the geometric calibration accuracy, the effectiveness of the proposed method is verified. The influence of pulse-width and bandwidth on the accuracy of geometric calibration is analyzed, and the effectiveness of the proposed method is then verified.

4.2.1. Impact Analysis of Atmospheric Propagation Delay According to the NCEP atmosphere data and CODE ionospheric data from 2012 to 2016, atmospheric propagation delay corrections of radar signals, including the neutral atmospheric delay and ionospheric delay, are calculated using the atmospheric propagation delay model in order to analyze the influence of atmospheric delay at different times on the accuracy of the geometric calibration.

According to the NCEP atmosphere data and CODE ionospheric data from 2012 to 2016, atmospheric propagation delay corrections of radar signals, including the neutral atmospheric delay and ionospheric delay, are calculated using the atmospheric propagation delay model in order to analyze the influence of atmospheric delay at different times on the accuracy of the geometric Remote Sens. 2017, 9, 464 10 of 19 calibration. Atmospheric Delay Delay Accuracy Analysis of Neutral Atmospheric calculated using the following two The atmospheric propagation delay of the radar signal is calculated methods. (1) (1) Based Based on on the ground point as the interpolation point, the zenith delay of the point is obtained, then the delay along the the propagation propagation path path is is calculated calculated by by aa mapping mapping function. function. (2) The interpolation points points are areacquired acquiredininthe thesignal signalpropagation propagationdirection direction height intervals interpolation atat height intervals of of 200200 mm upup to to 20 atmospheric propagation delays of these points are calculated in range the range of m, 200and m, 20 km.km. TheThe atmospheric propagation delays of these points are calculated in the of 200 andcumulatively are cumulatively to calculate thedelay total value delay in value in thepropagation signal propagation direction. are used used to calculate the total the signal direction. Finally, Finally, delay differences between the two are methods are compared. results the delay the delaythe differences between the two methods compared. The resultsThe of the delayofdifferences differences between2016 1 January May 2016days) (up to 132 days)inare shown between 1 January and 112016 Mayand 201611(up to 132 are shown Figure 5. in Figure 5.

Figure 5. 5. Accuracy of atmospheric atmospheric correction correction model. model. Figure Accuracy analysis analysis of

The figure figure shows shows that that the the atmospheric atmospheric propagation propagation delay delay differences differences calculated calculated by by the the two two The methods are are all all less less than than 22 mm. methods mm. The The error error of of this this magnitude magnitude is is negligible negligible for for the the geometric geometric positioning positioning accuracy. Therefore, the method used to solve for the atmospheric propagation delay correction is accuracy. Therefore, the method used to solve for the atmospheric propagation delay correction reliable. is reliable. Atmospheric Propagation Propagation Delay Delay for for the the Same Same Scene Scene and and Different DifferentGround GroundPoints Points Atmospheric In the the same same scene, scene, the the two two main main factors factors that that affect affect the the propagation propagation delay delay are are elevation elevation and and In incidence angle. Atmospheric pressure is different at different heights, and affects the delay in the incidence angle. Atmospheric pressure is different at different heights, and affects the delay in the zenith direction. direction. The in the the mapping mapping function function is is caused caused by by different different incident incident angles, angles, and and zenith The difference difference in affects the the delay delay along along the the signal signal propagation propagation path. path. In order to to analyze analyze the the influence influence of of terrain terrain and and affects In order distribution range range of of points points on on the the atmospheric atmospheric propagation propagation delay delay in in aa scene, scene, the the YG-13 YG-13 data data for for the the distribution ◦ Songshan region asas experimental data. In order to analyze the Songshan region and and aa43° 43 incidence incidenceangle, angle,were wereused used experimental data. In order to analyze effects of the incidence angle, ground points were regularly sampled at intervals of 150 m up to the effects of the incidence angle, ground points were regularly sampled at intervals of 150 m up 20 to km,km, in in thethe same azimuth. that the 20 same azimuth.Assuming Assuming thatthe theelevation elevationofofeach eachsampling samplingpoint point isis the the same, same, the atmospheric propagation delay of each sampling point is calculated, as shown in Figure 6. In order to analyze the impact of elevation, using the same sampled points, the elevation of each sampled point is valued equally at elevation intervals of 100 m from an altitude of −400 m to 8900 m. These elevations correspond to the highest land elevation in the world, Mount Zhumulangma at 8848.43 m, and the lowest, the Dead Sea at −392 m. The propagation delay for each sampling point at different elevations is calculated, as shown in Figure 7. Figure 6 shows that at the same height, the atmospheric propagation delay increases gradually from the near range to the far range, and the delay variation is less than 0.04 m in the SAR image of 20 km width. At the same range, the atmospheric propagation delay decreases with increased elevation, and the delay decreases by about 0.02–0.04 m when the elevation increases 100 m. In the same scene, the influence of elevation on atmospheric propagation delay is greater than that of the incident angle. When the elevation is increased by 100 m, the atmospheric pressure is reduced to about 10 mbar. However, the puncture point for calculating the ionosphere delay is almost not affected, so the

fromthe thenear nearrange rangeto tothe thefar farrange, range,and andthe thedelay delayvariation variationisisless lessthan than0.04 0.04m min inthe theSAR SARimage imageof of from 20 km km width. width. At At the the same same range, range, the the atmospheric atmospheric propagation propagation delay delay decreases decreases with with increased increased 20 elevation, and and the the delay delay decreases decreases by by about about 0.02–0.04 0.02–0.04 m m when when the the elevation elevation increases increases 100 100 m. m. In In the the elevation, same scene, scene, the the influence influence of of elevation elevation on on atmospheric atmospheric propagation propagation delay delay isis greater greater than than that that of of the the same incident angle. When the elevation is increased by 100 m, the atmospheric pressure is reduced to incident the elevation is increased by 100 m, the atmospheric pressure is reduced Remote Sens.angle. 2017, 9,When 464 11 of to 19 about 10 mbar. However, the puncture point for calculating the ionosphere delay is almost not about 10 mbar. However, the puncture point for calculating the ionosphere delay is almost not affected, so so the the change change in in elevation elevation mainly mainly affects affects the the neutral neutral atmospheric atmospheric delay. delay. In In particular, particular, for for affected, change in elevation mainly affects the neutral atmospheric delay. In particular, for elevation changes elevation changes less than 200 m, such as on plains and in hilly areas, the change in atmospheric elevation changes less than 200 m, such as on plains and in hilly areas, the change in atmospheric less than 200 delay m, such as on plains areas, the change inwidth. atmospheric propagation delay is propagation delay less than 0.08and min ininaahilly standard scene of20 20km km width. Forelevation elevation changes more propagation isisless than 0.08 m standard scene of For changes more less 0.08 m in standard scene of 20the kmchange width.in For elevation changes moredelay thanisis 500 m, such thanthan 500m, m,such such asain in mountain regions, the change in atmospheric propagation delay atleast least 0.1 than 500 as mountain regions, atmospheric propagation at 0.1 as in mountain regions, the change in atmospheric propagation delay is at least 0.1 m in a standard m in a standard scene of 20 km width. For elevation changes between 1000 m and 2000 m, as in high m in a standard scene of 20 km width. For elevation changes between 1000 m and 2000 m, as in high scene of 20regions, km width. elevation changes between 1000 mdelay and 2000 as in high mountain regions, mountain regions, theFor change inatmospheric atmospheric propagation delay atm, least between 0.4m mand and 0.8m m mountain the change in propagation isisat least between 0.4 0.8 the change in atmospheric propagation delay is at least between 0.4 m and 0.8 m in a standard scene in a standard scene of 20 km width. Therefore, the geometric correction method for spaceborne SAR, in a standard scene of 20 km width. Therefore, the geometric correction method for spaceborne SAR, of 20 km width. Therefore, the geometric correction method spaceborne SAR, the with a corrected with corrected atmospheric propagation delay for for each for point can improve improve the accuracy accuracy by with aa corrected atmospheric propagation delay each point can by atmospheric propagation delay for each point can improve the accuracy by centimeters at least. centimetersat at least. centimeters least.

Figure6.6.Same Sameheight heightand anddifferent differentranges. ranges. Figure

Figure7.7.Same Samerange rangeand anddifferent differentheights. heights. Figure

Atmospheric Propagation Delay for the Same Scene and Different Beam Positions The influence of different beam positions on geometric calibration mainly involves the difference in the atmospheric propagation delay. Aiming at the same target point in the same scene, the neutral atmospheric delay, ionospheric delay, and total atmospheric propagation delay for eight beam positions were calculated for the period from 2012 to 2016 (5 years), as shown in Figure 8.

Atmospheric Propagation Delay for the Same Scene and Different Beam Positions The influence of different beam positions on geometric calibration mainly involves the difference in the atmospheric propagation delay. Aiming at the same target point in the same scene, the neutral atmospheric delay, ionospheric delay, and total atmospheric propagation delay for eight beam Remote Sens. 2017, 9, 464 12 of 19 positions were calculated for the period from 2012 to 2016 (5 years), as shown in Figure 8.

(a)

(b)

(c) Figure 8. Influence of different beam positions on atmospheric propagation delay. (a) Neutral Figure 8. Influence of different beam positions on atmospheric propagation delay. (a) Neutral atmospheric delay; (b) Ionospheric delay; (c) Total atmospheric propagation delay. atmospheric delay; (b) Ionospheric delay; (c) Total atmospheric propagation delay.

Figure 8 shows that the atmospheric propagation delay of the radar signal, including the neutral atmospheric delay and ionospheric delay, increases with increasing beam position number. The change in trend of the neutral atmospheric delay with time is relatively smooth. The neutral atmospheric delay is about 2–5 m, and the maximum variation is about 0.1 m. In an entire year, the neutral atmospheric


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Figure 8 shows that the atmospheric propagation delay of the radar signal, including the neutral 13 of 19 atmospheric delay and ionospheric delay, increases with increasing beam position number. The change in trend of the neutral atmospheric delay with time is relatively smooth. The neutral atmospheric delay is about than 2–5 m,inand the maximum variation is about 0.1 m. In anwith entire year, delay in summer is smaller winter. The variation in ionospheric delay time is the more neutral atmospheric delay in summer is smaller than in winter. The variation in ionospheric delay obvious. The ionospheric delay, which is about 0.01–0.2 m, in April and May of every year is the with time is more obvious. The ionospheric delay, which is about 0.01–0.2 m, in April and May of largest. However, the variation in ionospheric delay is rarely affected by the beam position, and the every year is the largest. However, the variation in ionospheric delay is rarely affected by the beam maximum difference in the delay is 0.056 m. In addition, the ionospheric delay in 2016 is smaller. position, and the maximum difference in the delay is 0.056 m. In addition, the ionospheric delay in The trend variation in atmospheric propagation delay, which is obviously larger with increasing beam 2016 is smaller. The trend variation in atmospheric propagation delay, which is obviously larger with position number, is relatively stable. The maximum difference in delay between the beam positions increasing beam position number, is relatively stable. The maximum difference in delay between the can reach about 2.7 m. beam positions can reach about 2.7 m. Remote Sens. 2017, 9, 464

Atmospheric Propagation Delay of the Same Scene, Ascending and Descending Mode, Left and Atmospheric Propagation Delay of the Same Scene, Ascending and Descending Mode, Left and Right Side-Looking Right Side-Looking For the same scene and the same beam position, the influences of the ascending and descending For the same scene and the same beam position, the influences of the ascending and descending modes and left and right side looks on geometric calibration are mainly due to the two SAR satellites modes and left and right side looks on geometric calibration are mainly due to the two SAR satellites on both sides of the imaging area, which causes the atmospheric propagation delay to be different for on both sides of the imaging area, which causes the atmospheric propagation delay to be different different propagation paths. paths. Figures 9 and 910and show difference in atmospheric propagation delay of for different propagation Figures 10 the show the difference in atmospheric propagation ascending and descending modes with the same W108 beam position for left and right side-lookings, delay of ascending and descending modes with the same W108 beam position for left and right sidewith similarwith W023 and W025 positions 2012from to 2016 years) inyears) the Songshan region. lookings, similar W023 beam and W025 beam from positions 2012(five to 2016 (five in the Songshan Figures 9 and 10 show that the difference between the atmospheric propagation delay in ascending region. and descending aboutthat 0–0.38 and the between differencethe between the atmospheric Figures 9 modes and 10isshow the m, difference atmospheric propagationpropagation delay in delays for leftand anddescending right side-lookings about0–0.38 0.023–0.043 ascending modes is isabout m, andm. the difference between the atmospheric The delay delays difference variation of the former is larger than that of them.latter. When the SAR images propagation for left and right side-lookings is about 0.023–0.043 The delay variation of the former is larger than that ofmode the latter. the SAR images of the same area difference are acquired in descending mode and ascending withWhen the same side-looking, the same are on acquired in descending and ascending mode with the same side-looking, theofsatellite is area located the opposite side of mode the target area at two instantaneous imaging moments. satellite located on the the opposite side the target in area two instantaneous imaging moments. Thethe larger the is beam position, greater theofdifference theationosphere delay calculated by the two The larger the beam position, greater the difference in the ionosphere delay calculated by the two probable puncture points. The the neutral atmospheric delay difference between the two instantaneous probable puncture points. The neutral atmospheric delay difference between the two instantaneous imaging moments is small, since the neutral atmospheric delay is calculated using the zenith direction. imagingthe moments is Figure small, 9,since theare neutral atmospheric delaythe is atmospheric calculated using the zenith Therefore, results in which the differences between propagation delay direction. Therefore, the results in Figure 9, which are the differences between the atmospheric in ascending and descending modes, are mainly affected by the difference of ionospheric delay, and propagation delay in ascending and descending modes, are mainly affected by the difference of are similar to the trend of Figure 8b. ionospheric delay, and are similar to the trend of Figure 8b. The results of delay difference in Figure 10, which are the differences between the atmospheric The results of delay difference in Figure 10, which are the differences between the atmospheric propagation delay in left and right side-lookings, are calculated for the case of a small beam position, propagation delay in left and right side-lookings, are calculated for the case of a small beam position, and are relatively stable at about 0.03 m. Because the difference in atmospheric propagation delay is and are relatively stable at about 0.03 m. Because the difference in atmospheric propagation delay is relatively small, the different delays may be caused by the definition of the satellite orbit, which is relatively small, the different delays may be caused by the definition of the satellite orbit, which is usually determined for antenna isisoutside outsidethe thecenter centerofofmass. mass. usually determined forthe thecenter centerofofmass, mass,while while the the SAR SAR antenna

Figure 9. Descending and right side-looking (W108) and ascending and right side-looking (W108). Figure 9. Descending and right side-looking (W108) and ascending and right side-looking (W108).


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Figure 10. Descending and right side-looking (W025) and descending and left side-looking (W023). Figure 10. Descending and right side-looking (W025) and descending and left side-looking (W023). Figure 10. Descending and right side-looking (W025) and descending and left side-looking (W023).

Atmospheric Propagation Delay of Different Scenes and the Same Beam Position Atmospheric Scenes and andthe theSame SameBeam BeamPosition Position AtmosphericPropagation PropagationDelay Delay of of Different Different Scenes For the same beam position, ascending and descending modes, and left and right side-lookings, For beam ascending and anddescending descendingmodes, modes,and and left and right side-lookings, Forthe thesame same beamposition, position, left and right side-lookings, the influence of different scenes onascending atmospheric propagation delay is analyzed from 2012 to 2016 (five the influence of different scenes on atmospheric propagation delay is analyzed from 2012 to 2016 (five the influence of different scenes on atmospheric propagation delay is analyzed from 2012 to 2016 (five years), as shown in Figure 11. years), as shown in Figure 11. years), as shown in Figure 11. The Figure 11 shows that the atmospheric propagation delay for different scenes is about 0.05– The TheFigure Figure1111shows showsthat thatthe theatmospheric atmosphericpropagation propagationdelay delayfor fordifferent differentscenes scenesisisabout about0.05–0.35 0.05– 0.35 m. The change in the atmospheric propagation delay increases with increasing beam position m.0.35 Them. change in the atmospheric propagation delay delay increases with increasing beam beam position number, The change in the atmospheric propagation increases with increasing position number, and the maximum difference in delay can reach 0.341 m. number, and the maximum in delay reach and the maximum differencedifference in delay can reachcan 0.341 m. 0.341 m.

Figure11. 11. Atmospheric Atmospheric propagation different scenes. Figure propagationdelay delaydifference differencefor for Figure 11. Atmospheric propagation delay difference for different different scenes. scenes.

4.2.2. Parameter Calculation and Accuracy Evaluation 4.2.2. Parameter Calculation and Accuracy Evaluation First, the geometric calibration parameters (the start time in azimuth and the initial slant range First, the and thethe initial slant range in the geometric geometriccalibration calibrationparameters parameters(the (thestart starttime timeininazimuth azimuth and initial slant range in range) are calculated based on sample data from the calibration field in Songshan. Then, based on range) are calculated based on sample data from the calibration field in Songshan. Then, based on the inthe range) are calculated based on sample from thestarting calibration field in Songshan. Then,oblique based on calibration results of multiple times data (i.e., azimuth time, distance to the initial calibration results of multiple times times (i.e., azimuth startingstarting time, distance to the initial oblique distance) the calibration results of multiple (i.e., azimuth time, distance to the initial oblique distance) and the atmospheric delay correction information of the SAR image, the geometric and the atmospheric delay correction information of the SAR image, the geometric parameters of the distance) andof the atmospheric delay correction information thethe SAR image, the geometric parameters the SAR image to be verified are accounted for. Afterofthat, image will be processed SAR image to verified areFinally, accounted for. After that, theaccuracy image will be validation processed from echo data parameters of be the SAR image to bethe verified are accounted for. After that, the image will be processed from raw echo data again. geometric location of the data israw evaluated. again. Finally, the geometric location accuracy of the validation data is evaluated. from raw echo data again. Finally, the geometric location accuracy of the validation data is evaluated. Using the geometric calibration method for spaceborne SAR proposed in this paper, the Using calibration the geometric calibration method for spaceborne proposed in this paper, geometric parameters for 22 scenes of YG-13 SAR imagesSAR acquired by stripmap mode withthe geometric calibration parameters for scenes SAR images acquired byare stripmap calibration parameters for 2222 scenes of of YG-13 images acquired by stripmap modemode with two pulse-width and bandwidth combinations in YG-13 the SAR Songshan calibration field calculated. with two pulse-width and combinations in Songshan calibration fieldare are calculated. calculated. Thepulse-width variation trends thebandwidth parameters with time are in Figurescalibration 12 and 13. field two andin bandwidth combinations in shown thethe Songshan The variation trends trends in in the the parameters parameters with with time time are are shown shown in in Figures Figures12 12and and13. 13.

Remote Sens. 2017, 9, 464 Remote Sens. 2017, 9, 463

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(a)

(b) Figure correction value in in azimuth. (a) 24.4 µs and 200 200 MHz; (b) Figure 12. 12. Variation Variationtrend trendofofstarting startingtime time correction value azimuth. (a) 24.4 µs and MHz; 24.4 µs and 150 150 MHz. (b) 24.4 µs and MHz.

As can be seen from Figure 12, there are positive and negative values of starting time correction As can be seen from Figure 12, there are positive and negative values of starting time correction in azimuth, and the variation in starting time in azimuth is less than 0.2 ms. It is obvious that there is in azimuth, and the variation in starting time in azimuth is less than 0.2 ms. It is obvious that there no systematic error in the azimuth starting time. Moreover, Figure 13 shows that the variation in is no systematic error in the azimuth starting time. Moreover, Figure 13 shows that the variation in starting range is less than 2 m, and the standard deviations of the slant range correction are 0.6094 m starting range is less than 2 m, and the standard deviations of the slant range correction are 0.6094 m and 0.6088 m. It is clear that the variation trend of the geometric calibration parameters is stable. and 0.6088 m. It is clear that the variation trend of the geometric calibration parameters is stable. According to the geometric calibration parameters of each pulse-width and bandwidth According to the geometric calibration parameters of each pulse-width and bandwidth combination mode, the reimaging of SAR images to be verified is performed by compensating for the combination mode, the reimaging of SAR images to be verified is performed by compensating for the geometric parameters. The geometric positioning accuracies after calibration are as shown in Table 2. geometric parameters. The geometric positioning accuracies after calibration are as shown in Table 2. Table 2 shows that the geometric positioning accuracy of the stripmap mode is better than 3 m Table 2 shows that the geometric positioning accuracy of the stripmap mode is better than 3 m after calibration, and the geometric positioning accuracy of the sliding spotlight mode is better than after calibration, and the geometric positioning accuracy of the sliding spotlight mode is better than 1.5 m after calibration. 1.5 m after calibration. The geometric positioning accuracy is mainly affected by the accuracy of the geometric The geometric positioning accuracy is mainly affected by the accuracy of the geometric calibration, calibration, target point selection, satellite orbit, and atmospheric delay correction. The results shown target point selection, satellite orbit, and atmospheric delay correction. The results shown in Figure 12 in Figure 12 indicate that the azimuth calibration accuracy is better than 0.15 ms, which is mainly indicate that the azimuth calibration accuracy is better than 0.15 ms, which is mainly equivalent to equivalent to 1.2 m positioning accuracy in azimuth. Figure 13 indicates that the calibration accuracy 1.2 m positioning accuracy in azimuth. Figure 13 indicates that the calibration accuracy of the slant of the slant range is better than 0.7 m. Thus, the two-dimensional accuracy of the geometric calibration range is better than 0.7 m. Thus, the two-dimensional accuracy of the geometric calibration is about is about 1.4 m. Generally speaking, the accuracy of the target point selection is about 0.5 pixels. In 1.4 m. Generally speaking, the accuracy of the target point selection is about 0.5 pixels. In other words, other words, the accuracy of the target point selection is about 0.8 m in stripmap mode and about 0.3 the accuracy of the target point selection is about 0.8 m in stripmap mode and about 0.3 m in sliding m in sliding spotlight mode. As a result of using precise orbit data in the geometric calibration, the spotlight mode. As a result of using precise orbit data in the geometric calibration, the accuracy of accuracy of the satellite orbit is better than 0.5 m. Compared with the atmospheric propagation delay correction model of TerraSAR-X, the accuracy of the atmospheric propagation delay correction used


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the satellite orbit is better than 0.5 m. Compared with the atmospheric propagation delay correction model of TerraSAR-X, the accuracy of the atmospheric propagation delay correction used in this study is better than 0.2 m. To sum up, the geometric positioning accuracy in stripmap mode should be about Remote 9, 463 of 19 2.9 m, andSens. that2017, in sliding spotlight mode should be about 2.4 m. Therefore, the results given16in Table 2 are reasonable. in this study is better than 0.2 m. To sum up, the geometric positioning accuracy in stripmap mode should be about 2.9 m, and that in sliding spotlight mode should be about 2.4 m. Therefore, the results Table 2. Comparison of geometric positioning accuracy before and after compensating for geometric given in Table 2 are reasonable. calibration parameters. Table 2. Comparison of geometric positioning accuracy before and after compensating for geometric

Imaging Pulse-Width and calibrationBandwidth parameters. Mode Combination

Imaging Mode

Pulse-Width and Bandwidth Combination 24.4 µs & 200 MHz 24.4 µs & 200 MHz

Strip-map mode

Strip-map mode

24.4 µs & 150 MHz

24.4 µs & 150 MHz

29.2 µs & 600 MHz 29.2 µs & 600 MHz

Sliding spotlight Sliding mode spotlight

mode

29.2 µs & 512 MHz 29.2 µs & 512 MHz

28 µs & 300 MHz 28 µs & 300 MHz

24 µs µs & 24 & 300 300 MHz MHz

Imaging Date and Area

Imaging Date 28 May 2016 and Area Taiyuan 28 29 May May 2016 2016 Taiyuan Tianjin 29 May 2016 1 June 2016 Tianjin Taiyuan 1 June 2016 9 Taiyuan June 2016 Anping 9 June 2016 10 Anping June 2016 10 Tianjin June 2016 12 Tianjin June 2016 12Xianning June 2016 21Xianning May 2016 21Xianning May 2016 22Xianning May 2016 22 Tianjin May 2016 Tianjin 27 May 2016 27Xianning May 2016 Xianning 4 June 2016 4 June 2016 Tianjin Tianjin 29 May 2016 29 May 2016 Taiyuan Taiyuan 30 May 2016 2016 30 May Anping Anping 28 May May 2016 2016 28 Tianjin Tianjin

4 June 2016 Taiyuan

Calibration Before Calibration After Before Before After After Before Before After After Before Before After After Before Before After After Before After Before After Before After Before Before After After Before Before After After Before Before After After Before Before After After Before Before After After Before Before After After Before Before After After Before Before After After

(a) Figure 13. Cont.

Azimuth (Pixel)

Azimuth 2.483 (Pixel) 2.482 2.483 0.528 2.482 0.528 0.528 2.883 0.528 2.882 2.883 1.609 2.882 1.609 1.609 1.330 1.609 1.330 1.330 1.330 0.703 0.704 0.703 0.704 4.018 4.018 4.021 4.021 4.685 4.685 4.685 4.685 1.365 1.365 1.365 1.365 3.717 3.717 3.716 3.716 2.143 2.143 2.133 2.133 1.100 1.100 1.100 1.100 0.357 0.357 0.342 0.342 1.659 1.659 1.661 1.661

Range (Pixel)

Range 24.871 (Pixel) 0.513 24.871 24.733 0.513 0.714 24.733 14.729 0.714 1.428 14.729 15.561 1.428 0.347 15.561 16.979 0.347 0.883 16.979 0.883 17.052 1.100 17.052 1.100 78.510 78.510 5.246 5.246 82.899 82.899 4.545 4.545 55.105 55.105 3.718 3.718 59.625 59.625 1.486 1.486 43.396 43.396 1.812 1.812 39.698 39.698 1.533 1.533 33.836 33.836 1.471 1.471 34.427 34.427 0.332 0.332

2-D Error

(Pixel) (m) 24.9952-D Error 15.085 (Pixel) 2.329 (m) 2.534 24.995 15.085 24.739 14.837 2.534 0.878 2.329 0.888 24.739 14.837 15.009 12.873 0.888 0.878 3.217 2.932 15.009 12.873 15.644 3.217 13.421 2.932 1.646 1.615 15.644 13.421 17.031 1.646 14.594 1.615 1.596 17.031 1.536 14.594 1.596 14.620 1.536 17.066 1.306 17.066 1.347 14.620 1.306 16.828 1.347 78.613 78.613 1.346 16.828 6.610 6.610 17.772 1.346 83.032 83.032 1.301 17.772 6.528 6.528 1.301 55.122 13.769 55.122 0.971 13.769 3.961 3.961 0.971 59.741 14.916 59.741 14.916 4.002 0.890 4.002 0.890 43.449 18.599 43.449 18.599 2.799 1.056 2.799 1.056 39.714 17.006 39.714 17.006 1.887 1.319 1.887 1.319 33.838 33.838 14.491 14.491 1.510 1.510 0.640 0.640 34.467 14.755 14.755 34.467 1.694 1.694 0.598 0.598


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(b) Figure 13. Variation trend of starting slant range correction value in range. (a) 24.4 µs and 200 MHz; (b) 24.4 µs and 150 MHz.

(b)

4.2.3. Impact Analysis of Pulse-Width and Bandwidth Combinations Figure 13. Variation trend of starting slant range correction value in range. (a) 24.4 µs and 200 MHz; are differences the system time delays with value different pulse-width bandwidth Figure There 13. Variation trend of in starting slant range correction in range. (a) 24.4and µs and 200 MHz; (b) 24.4 µs and 150 MHz. combinations. In order to verify the necessity of the geometric calibration scheme proposed in this (b) 24.4 µs and 150 MHz. paper, a series of mutual calibration–compensation experiments is carried out using different pulse4.2.3. Impact Analysis of Pulse-Width and Bandwidth Combinations width and bandwidth combinations. The experimental results are shown in Figure 14, where, the 4.2.3. Impact Analysis of Pulse-Widthand and Bandwidth Combinations legend the pulse-width bandwidth combinations for verification. Thererepresents are differences in the system time delays with different pulse-width and bandwidth 14 the geometric calibration results are better when the combinations usedbandwidth combinations. Inshows orderthat toin verify the necessity the geometric calibration scheme proposed inforthis There Figure are differences the system timeofdelays with different pulse-width and calibration and verification are identical. In other experiments words, betterisgeometric calibration results pulseare paper, a series of mutual calibration–compensation carried out using different combinations. In order to verify the necessity of the geometric calibration scheme proposed in obtained using the method proposedThe in experimental this paper. It can be seen from the comparison that thethe width and bandwidth combinations. results are shown in Figure 14, where, this paper, a series of mutual calibration–compensation experiments is carried out using different geometric calibration results of and YG-13 withoutcombinations considering the pulse-width and bandwidth legend represents the pulse-width bandwidth for verification. pulse-width and bandwidth combinations. The experimental results are showntoinconsider Figure the 14, where, combination are worse than those of the proposed method. Therefore, it is necessary Figure 14 shows that the geometric calibration results are better when the combinations used for the legend represents the pulse-width and bandwidth combinations forcalibration verification. pulse-width and bandwidth combination of radar signals in the geometric scheme.

calibration and verification are identical. In other words, better geometric calibration results are obtained using the method proposed in this paper. It can be seen from the comparison that the geometric calibration results of YG-13 without considering the pulse-width and bandwidth combination are worse than those of the proposed method. Therefore, it is necessary to consider the pulse-width and bandwidth combination of radar signals in the geometric calibration scheme.

Comparison results calibration based on different and pulse-width bandwidth Figure Figure 14. 14. Comparison resultsof geometric of geometric calibration based pulse-width on different and combinations. bandwidth combinations.

5. Conclusions

Figure 14 shows that the geometric calibration results are better when the combinations used In this paper, a multimode hybrid geometric calibration method of Spaceborne SAR considering for calibration andpropagation verification are identical. In other words, better geometric calibration results atmospheric delay is proposed. The effectiveness of the proposed method was verified Figure 14. Comparison results of geometric calibration based on different pulse-width and bandwidth are obtained using the method paper. propagation It can be seen the comparison that by a series of experiments. Theproposed influence ofin thethis atmospheric delayfrom and pulse-width and combinations. the geometric calibration results of YG-13 without considering the pulse-width and bandwidth combination are worse than those of the proposed method. Therefore, it is necessary to consider 5. Conclusions the pulse-width and bandwidth combination of radar signals in the geometric calibration scheme. In this paper, a multimode hybrid geometric calibration method of Spaceborne SAR considering atmospheric 5. Conclusions propagation delay is proposed. The effectiveness of the proposed method was verified by a series of experiments. The influence of the atmospheric propagation delay and pulse-width and

In this paper, a multimode hybrid geometric calibration method of Spaceborne SAR considering atmospheric propagation delay is proposed. The effectiveness of the proposed method was verified by a series of experiments. The influence of the atmospheric propagation delay and pulse-width and bandwidth combination on the accuracy of geometric calibration was analyzed in detail. The geometric


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positioning accuracy of YG-13 was evaluated using the proposed method. Through analysis and verification, the following conclusions were obtained: 1. 2.

3.

The atmospheric propagation delay is the main factor that affects the accuracy of geometric calibration, and can be in the range of meters. Based on the geometric calibration method proposed in this paper, the calibration accuracy of the slant range for YG-13 is better than 0.7 m of standard deviation. Without considering the effect of altitude error, the geometric positioning accuracy in stripmap mode without control points is better than 3 m after calibration, and that in sliding spotlight mode is better than 1.5 m. It is necessary to consider the pulse-width and bandwidth combination for the geometric calibration scheme proposed in this paper.

The method proposed in this paper is suitable for low earth orbit mono-SAR satellites. The radar signal of a medium and geosynchronous earth orbit SAR satellite will be affected by complex ionosphere phenomena, such as ionospheric scintillation. The imaging geometry of multistatic SAR is different from that of mono-SAR. In future research, the geometric calibration method will be applied to medium and geosynchronous earth orbit, multistatic SAR satellites. Acknowledgments: This work was supported by, Key research and development program of Ministry of science and technology (2016YFB0500801), National Natural Science Foundation of China (Grant No. 91538106, Grant No. 41501503, 41601490, Grant No. 41501383), China Postdoctoral Science Foundation (Grant No. 2015M582276), Hubei Provincial Natural Science Foundation of China (Grant No. 2015CFB330), Open Research Fund of State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing (Grant No. 15E02), Open Research Fund of State Key Laboratory of Geo-information Engineering (Grant No. SKLGIE2015-Z-3-1), Fundamental Research Funds for the Central University (Grant No. 2042016kf0163). The authors also thank the anonymous reviews for their constructive comments and suggestions. We would like to thank Editage [www.editage.cn] for English language editing. Author Contributions: Guo Zhang, Ruishan Zhao, Mingjun Deng, and Fan Yang conceived and designed the experiments; Ruishan Zhao, Mingjun Deng, Zhenwei Chen, and Yuzhi Zheng performed the experiments; Ruishan Zhao and Zhenwei Chen analyzed the data; Ruishan Zhao wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

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