Slant-range accuracy assessment for the YaoGan 13

: YaoGan 13 (YG-13) represents the most advanced Chinese synthetic aperture radar satellite currently in use. This paper reports on experiments conducted to assess the slant-range accuracy of YG-13. Error sources in the YG-13 ranging system, such as atmospheric path delay and the internal electronic delay of the instrument were analysed. A real-time atmospheric delay correction model was established to consider both tropospheric and ionospheric delays. Six corner reflectors (CRs) were set up to ensure the accuracy of validation methods. Results showed that pixel location accuracies of up to 0.427 m standard deviation could be achieved. Furthermore, adjustment of the CRs can cause a marginal loss of ranging precision. After eliminating this error, the ranging accuracy was improved to 0.162 m. For YG-13, a single frequency GPS receiver is used and the orbital accuracy is the biggest factor restricting its slant-range accuracy. Results show that the YG-13 slant-range can achieve decimetre-level accuracy. YG-13 provides convenience in terms of access to control points and target locations that does not depend on ground equipment.


Introduction
Synthetic aperture radar (SAR) is an effective microwave sensor with the capacity to work during the day and night under any weather conditions [1]. It can capture high resolution images of large areas, and thus plays an important role in Earth observations. In the past, SAR images were used merely for their 2D imaging ability, while the inherently good geolocation accuracy of SAR systems was not fully exploited by the remote sensing community. For example, the pixel location accuracy requirements of Chinese SAR images were low (∼250 m) for many years.
However, applications of SAR systems are expanding. In the 21st century, many SAR satellites have been launched globally. Their high geometric accuracy is a result of extensive calibration work [2]. In particular, TerraSAR-X pixel location accuracies of up to 2.6 cm standard deviation can be achieved following a single calibration, which is the best ranging accuracy reported for spaceborne radar amplitude images to date [3].
The Chinese YaoGan 13 (YG-13) mission was launched in November 2015, equipped with a next-generation high-resolution SAR X-band sensor, with a resolution of up to 0.5 m. The launch provided China with the ability to acquire high-resolution SAR images globally. YG-13 includes several improvements as compared to previous Chinese SAR satellites, including: (i) a new sliding-spot imaging mode which provides higher image resolution; (ii) the ability to image on both the left and right sides facilitating more flexible data acquisition; and (iii) improvement in the measuring accuracy of the instrument.
As space-borne SAR image resolution increases, the influence of the ranging accuracy on the geometric and radiometric quality of the SAR image is becoming increasingly important [4]. In this paper, we focus on the ranging accuracy of YG-13. The following sections highlight that there are many error sources affecting the accuracy of slant-range measurement. We demonstrate that, using corner reflector (CR) measurements, decimetre-level ranging accuracy for YG-13 can be achieved. Although the ranging accuracy of YG-13 is lower than that of TerraSAR-X, it is in accordance with its theoretical precision.

Methodology
The SAR imaging geometry is represented in Fig. 1. The slantrange r between the target on the ground and the antenna phase centre can be calculated from its range pixel position in the image by; where r 0 is the slant-range of the first range gate which is determined by the radar pulse propagation time, i is the range pixel coordinate of the target in the image, c is the propagation velocity of microwaves in the atmosphere, and f s is the sampling frequency of the pulse. As Fig. 1 and (1)

Instrument internal electronic delay
The slant-range of the first range gate r 0 is obtained by the propagation time of radar signal. Therefore, the internal electronic delay of the instrument affects the slant-range accuracy. The internal electronic delay of the instrument is related to the bandwidth and pulsewidth of the radar signal. If the radar signal has the same bandwidth and pulsewidth, the internal electronic delay of the instrument is a fixed value. The slant-range delay can be corrected by precisely measuring the internal electronic delay of the instrument prior to satellite launch (Table 1).

Propagation errors
As the refractive index of the atmosphere is not uniform, the radar signal encounters group delay in both the ionosphere and troposphere, known as atmospheric path delay [5,6]. The one-way atmospheric path delay may be estimated by; where ΔL Z is the zenith delay and θ is the incident angle [7][8][9].
The ΔL Z consists of two parts; the ionosphere zenith delay ΔL iono and troposphere zenith delay ΔL trop . The troposphere zenith delay can be modelled well if the altitude, pressure, and water vapor content are known [10][11][12][13]. Troposphere zenith delay ΔL trop is given by: where n(z) is the refractive index along the zenith direction, k 1 (λ) P d /T z d −1 is the delay caused by dry air, which is composed of oxygen and nitrogen, k 2 (λ) P w /T z w −1 is the delay caused by wet air, which is composed of water vapour and CO2, P d is the pressure of dry air, T is temperature, and z d is the compressibility of dry air. P w is the pressure of wet air and z w is the compressibility of wet air. k 1 (λ) and k 2 (λ) are related to the wavelength of the radar signal. The empirical equations proposed by Owens for k 1 (λ) and k 2 (λ) are as follows: (see (4)) Approximately 90% of the total troposphere zenith delay ΔL trop is caused by dry air (∼2.3 m), and the remainder is caused by wet air. Troposphere group delay correction is estimated using atmospheric data from the National Centers for Environmental Prediction (NCEP) [14].
The ΔL iono is also considered. The velocity of the radar signal passing through the ionosphere is affected by the dispersion of the ionosphere [15,16]. The delay in metres is given by; where f is the carrier frequency and TEC is the vertical total electron content, denoted in units of 10 16 (called TECU). Fig. 2 shows changes in TEC extracted for 24 h a day over the Songshan test field. The TEC values range between 1.5 and 30.3 TECU; the maximum occurring at noon, and the minimum during the night. Zenith delays of 0.648 and 13.090 cm were caused by TEC values of 1.5 and 30.3 TECU, respectively. It is important to note that YG-13 is a low orbit satellite; hence, its images will only pass through a section of the total column of electrons. Considering the YG-13 orbit accuracy of 0.3 m, the difference in the ionosphere zenith delay value caused by the approximate calculation of the ionospheric electron content can be safely ignored.

Orbit accuracy
Orbit accuracy has an effect on the measurement accuracy of slantrange. For YG-13, a single frequency GPS receiver is used to obtain the position of the SAR antenna phase centre. After accurately determining the orbit using single frequency GPS, a 3D accuracy of 0.3 m is achieved for YG-13. In contrast, a dual frequency GPS receiver is used for TerraSAR-X, which provides a much higher 3D accuracy of 4.2 cm [17].

Corner reflector location measurement and pixel coordinate extraction
CRs are often used for the slant-range accuracy validation of SAR images because their locations on the image can be accurately determined. Fig. 3 shows the appearance of a YG-13 CR and its signature on the YG-13 sliding-spot image. The CR appears as a bright target on the SAR image. The centre line of the CR should coincide with the incident direction of the radar wave during radar operation in order to reach the maximum radar cross-section. At this point, the brightest position on the image represents the pixel coordinate of the CR vertex. However, because the SAR image is a two-dimensional discrete signal, the peak of the CR pulse response does not necessarily correspond to the existing pixel signal on the SAR image. Consequently, bilinear interpolation calculation is necessary. The position of the CR in Earth fixed coordinates can be measured with a GPS. Using this method, the 3D position fix accuracy can be within 0.1 m.

Experiment data and explanation
As show in Fig. 4  (4)  Table 2 provides information on the 14 images used in this experiment. Every time the radar operates, the satellite orbit type and incident angle differ; as such, the orientation of the CRs must be adjusted according to the satellite parameters. The peak positions of the CRs were measured on each image using 32 × 32 pixel windows centred at each CR, and bilinear interpolation around the maximum. Using this method, the previously determined theoretical accuracy can be achieved in practice.

Result of experiment and analysis of performance
The range-Doppler model is commonly used for the rigorous positioning of SAR satellites [18]. Image pixel coordinates and the target ground position can be correlated very accurately using three equations: the distance equation, Doppler equation, and earth model equation. The pixel coordinates of the CRs are then subtracted from the expected ideal geometric peak position (without considering the estimated propagation effects annotated in the product), which we refer to as the measured pixel coordinate. Furthermore, when the geometric positions of the CRs are known, we can calculate their pixel coordinates using the range-Doppler model, which we refer to as the calculated pixel coordinate. The difference between the calculated and measured pixel coordinates can be converted to the slant-range error. Additional (one-way) correction due to atmospheric path delay is calculated by considering the zenith delay, incidence angle, and altitude of the CRs. The difference in the atmospheric path delay calculated by using each CR in a scene is within 1 cm; therefore, the atmospheric path delay of the entire scene is calculated by averaging the results. Fig. 5 shows the atmospheric path delay of the 14 experiment images. It is apparent that the atmospheric path delay increases with the incidence angle.
During the YG-13 in-orbit commissioning phase, an unexpectedly high range geolocation error was discovered. Subsequent investigation shed light on the issue and led to the implementation of another necessary timing correction, related to the YG-13 radar signal pulsewidth. The actual pulsewidth of the YG-13 radar system is inconsistent with the nominal pulsewidth. To ensure that the radar signal is not disturbed by noise, the actual pulsewidth is larger than the nominal pulsewidth. As shown in Fig. 6, both ends of the pulse carry useless information. The radar system takes the front edge of the pulse as the transmission time, and determination of the receiving time is related to the pulse peak position and pulsewidth. A computational error for the YG-13 was generated in the calculation process. The slant-range error is given by; where τ act is the actual pulsewidth, τ nom is the nominal pulsewidth, and c is the propagation velocity of microwaves in the atmosphere. For Data A and Data B, the actual pulsewidth is 24.4 μs, while the nominal pulsewidth is 24.64 μs, resulting in a slant-range error of 17.987 m. Based on the previous analysis of slant-range accuracy, the ranging error ΔR for the YG-13 can be calculated using the following formula;   where R s = [x s , y s , z s ] T is the position vector of the phase centre of the YG-13 antenna, R t = [x t , y t , z t ] T is the CR position vector, R near is the near range of the first range gate, N i is the range pixel coordinate of the CR in the image, c is the propagation velocity of microwaves in the atmosphere, f s is the sampling frequency of the pulse, R atmo is atmospheric path delay, and R tr is the internal electronic delay of the instrument. Tables 3 and 4 detail the localisation residuals of CRs and standard deviations for Data A and Data B images, respectively.
Taking full account of multiple error factors, the ranging accuracy of YG-13 is 0.502 and 0.427 m for Data A and Data B images, respectively. Considering a 0.3 m orbital error, the residual range accuracy can still be improved, because other error sources exist.
Tables 5 and 6 provide statistics for the standard deviation of two orbital type images for Data A and Data B images, respectively. Results indicate that the ranging accuracy can be improved by considering the orbit orientation and lookside. For example, the standard deviation of Data A images improved from 0.502 m ( Table 3) to 0.312 and 0.183 m ( Table 5). The same is true for Data B images: ranging accuracy is improved from 0.427 m ( Table 4) to 0.162 and 0.266 m ( Table 6). As the orientation of the CRs needs to be adjusted when the orbital type of the images differs, error is introduced. Thus, the achieved accuracy is better as compared to the orbital accuracy of 0.3 m, indicating that the orbital accuracy may be better than 0.3 m.

Conclusion
In this study, the sources of error in the YG-13 ranging system were analysed. The YG-13 can achieve decimetre-level ranging accuracy after correction for atmospheric path delay and the internal electronic delay of the instrument. Considering the 0.3 m orbital nominal accuracy, our results were close to the theoretical limit. The ranging accuracy of YG-13 is mainly limited by the orbit accuracy determined by a single frequency GPS. Thus, our results prove that the slant-range measurement of a SAR does not use the attitude parameter, and can achieve high precision.
An atmospheric delay correction method using external data was selected. For X-band satellites, the ionospheric delay correction was very small, and atmospheric path delay was mainly influenced by tropospheric delay. Consideration of ionospheric delays can only marginally improve results, thus, we ignored some of the dynamics of the ionosphere. This is acceptable for the Xband but not for C-and L-bands. Furthermore, ionospheric delays need to be considered for centimetre-level ranging accuracy validation.
As the test images comprised two orbit-types (ascending and descending), it was necessary to adjust the CRs, which introduced some errors. For centimetre-level ranging accuracy validation experiments, fixed CRs would be necessary in addition to a series of repeat-pass acquisition images on the same orbit and incidence angle. Decimetre-level ranging accuracy can satisfy the requirement of high precision control points and target positioning. Notwithstanding, there is still scope for improvement to centimetre-level precision. With centimetre-level ranging accuracy, absolute measurements of volcanoes and glaciers are possible without the use of ground equipment and SAR interferometry.