EI+FWI Method for Reconstructing Interior Structure of Asteroid Using Lander-to-Orbiter Bistatic Radar System

EI+FWI Method for Reconstructing Interior Structure of Asteroid Using Lander-to-Orbiter Bistatic Radar System

 

Jian Deng¹,Wlodek Kofman^2,3, Pei-min Zhu¹, Alain Herique ²,Ruidong Liu⁴, Shi Zheng⁴

 

¹ China University of Geoscience AQ:5 (CUG), Wuhan 430074, China (e-mail: dengjian_cug@126.com).

²  CNRS, CNES, IPAG, Université Grenoble Alpes, 38000 Grenoble, France, wlodek.kofman@univ-grenoble-alpes.fr).

³  Centrum Badan KosmicznychPolskiej Akademii Nauk (CBK PAN), 00-716 Warsaw, Poland (e-mail:

⁴ China Academy of Space Technology, Xi’an Branch, Xi’an 710100, China (e-mail: shizheng_xjtu@163.com).

 

 

Since the missions to asteroids including Dawn, Hayabusa2 [2 - 4],  OSIRIS-Rex [5] and so on, we had accumulated some preliminary knowledge on the surface structure and components of asteroids. But the internal structure which is the key to understanding and modeling asteroid accretion and evolution history is still fairly unknown and has never been measured accurately for any asteroid. In view of this, China National Space Administration (CNSA) is actively preparing a mission named “Zhenghe” [6] aiming to reveal the inner structure of Asteroid 2016HO3. Consequently, study on radar tomography for imaging the interior of asteroids is becoming one of the most in-demand technologies.

The conventional radar tomography is usually based on ray tracing method (RTM), which utilizes only a small portion of the signal information and is unable to generate complete results especially under the acquisition geometry of limited data density. To get the accurate dielectric permittivity distribution within the asteroid, full waveform inversion (FWI) [7] which utilizes the whole information (including time, amplitude and phase) of the signal, is proposed as a promising method which could be applied in the future asteroid interior detection missions.

Despite the high resolution, FWI is a highly nonlinear and ill-posed inverse problem which is sensitive to inaccuracies of the starting model especially when bandwidth is limited. Because of the bandwidth limitation, the range-compressed radar signal with carrier oscillates rapidly in the time domain, which makes the object function of FWI contains numerous local minimums. Thus, it is hard for FWI to converge to the global minimum of model space without an accurate initial model. Concerning this problem, we propose the envelope inversion (EI) [8], which is more robust to the choice of initial model because the time-domain envelope signal is in the baseband frequency range and varies slower than the range-compressed signal with carrier, as a supplement to FWI to recover the inner permittivity distribution of asteroid. The conventional FWI compares in the object function complete wave forms, while EI compares the time-domain envelope between the synthesized and observed signal.

It has been discussed that asteroid radar tomography could be performed in different observation geometries, such as monostatic orbiter, bistatic orbiters and lander-to-orbiter system, and our work mainly focuses on the bistatic lander-to-orbiter scenario. Such analogous scenario (Fig. 1) has been applied in the CONSERT (Comet Nucleus Sounding Experiment by radio wave transmission) [9] mission to the Comet 67P/CG.

Fig. 1.  Lander-to-orbiter configuration. This artistic view is based on CONSERT/Rosetta

In our work, the effects of initial model, noise level and carrier-frequency on FWI and EI algorithm for asteroid tomography are analyzed based on 2D numerical experiments [8],. The 2D numerical experiments shows that the EI+FWI combination, where EI serves to define the initial model for FWI, constrained by total variation regularization, has good potential for asteroid tomography. Based on EI+FWI strategy, a series of 3D numerical experiments are conducted to test the influence of orbital measurement density and landing site on the tomography. The synthetic asteroid model and the observation geometry are presented in Fig. 2.

The 3D numerical experiments demonstrate that, if the signal is less contaminated by noise, EI+FWI has the ability to reconstruct the interior structure with a sufficient accuracy even under a sparse observation (like only 20 orbital measurement points); but if the signal is highly contaminated by noise, dense observation will be indispensable to ensure the reconstruction accuracy. Besides, the results also indicate that the single lander system has the potential to reveal the interior of asteroid, but the landing site could have a significant influence on the tomography. The partial results of the 3D experiments are shown as Fig. 3.

Fig. 2. (a) 3D synthetic asteroid model, the model contains 3 anomalies (red) embedded in the background (green),  the anomalies and the background is 4 and 3, respectively. (b) Schematic illustration of spiral observation geometry, it contains 480 measurement points (blue dots), and the angle θ is between the rotation axis and the line defined by the lander and the barycenter of the asteroid

Fig. 3.  EI+FWI reconstructions under the spiral observation illustrated in Fig. 2(b). (a) and (b) present the reconstructions without noise and with the SNR= –10dB (before the processing of range compressing the BPSK signal), respectively. The inversions are started with a homogenous asteroid of which the  (i.e. 10% lower than the background of true model).  

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[8], J. Deng,et al., “EI + FWI Method for Reconstructing Interior Structure of Asteroid Using Lander-to-Orbiter Bistatic Radar System”  IEEE TGRS in press

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