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Landing in the permanently shadowed regions (PSRs) on the Moon requires high-resolution topographic information and accurate navigation. Owing to low Sun elevation angles, there is no direct solar illumination in PSR, making it difficult to acquire high-resolution optical images for terrain relative navigation (TRN). Synthetic aperture radar (SAR) onboard lunar orbiter can acquire the high-resolution digital elevation model (DEM) of PSR with the interference phases from repeat-passes, or alternatively, from multiantenna observations in a single orbit pass. In this article, SAR images from dual-antenna observations obtained in single orbit passes are simulated with two-scale model and Range-Doppler algorithm for the interference phases based on the DEM data from the lunar orbiter laser altimeter (LOLA). Hence, we generate DEMs of PSR in two prominent lunar south polar craters, Shoemaker and Shackleton. After geometric correction, the influence of radar parallax in DEM data are removed. The generated DEM data are used to illustrate the possibility of TRN in PSR with the image-matching algorithm. The slope angle image of the PSR from the generated DEM is taken as the reference image for navigation, while high-resolution slope angle image from LOLA DEM data is taken as the real-time image from the flyer. The speeded-up robust features algorithm matches the feature points in the reference image and real-time image. The location of the matched points determines the position and motion vector of the flyer. The simulation proves the DEM data from InSAR can provide detailed topographic information and can be used for navigation in regions of permanent shadows.

In China's Chang'e 7 mission, a miniflyer will be carried for in-situ water ice measurement in permanently shadowed regions (PSRs) around the lunar south pole. The extreme cold environment within PSRs causes serious challenges for the safety of the miniflyer. Predication of temperatures in PSR is critical for designing the internal heating system and the heat source capacity. Conducting in-situ detection mission in relatively warm temperature can reduce the threat of the cold environment and save energy to maintain a suitable operation temperature for payloads. Since the polar-orbiting satellite lunar reconnaissance orbiter passes over the same location in the polar region with intervals of about a month, the temporally continuous observation is unavailable. Simulation is necessary to determine the temporally continuous temperatures of PSR during the mission. In this article, a numerical model of the temperatures in PSR is presented. The ray tracing approach is used to calculate the shadowing effect of terrain on scattered sunlight and thermal radiation. The PSR temperatures are simulated with the one-dimensional heat conduction equation. Simulated temperatures are compared with Diviner data for validation. The spatial and temporal temperature distributions of PSRs in crater Shackleton, which is the preferred landing site for the Chang'e 7 mission, are simulated from 2026 to 2028. The simulated temperature in high temporal resolution of one Earth hour can be applied to analyzing diurnal and seasonal temperatures in PSRs and is helpful for thermal management and design of the internal heating system. The time windows with relatively warm temperature in PSR at regions with slope angles less than 5° are recommended to save energy and reduce the hazards of the extremely cold environment.

In China's Tianwen-2 mission, a dual-frequency radar will be carried out to detect the asteroid 2016 HO3. The dual-frequency radar can acquire the information of the asteroid's surface and internal structure. There are few studies about the radar detection of the asteroid 2016 HO3 and it is unclear what information can be acquired from the radar images. In this article, the radar images of the asteroid under nadir and oblique observations are simulated with the two-scale model of the Kirchhoff approximation/small-perturbation method. The radar images at 900 and 150 MHz are simulated to study the backscattering from the asteroid's surface and the detectability of the internal structure in the asteroid. The influences of the asteroid characteristics, such as the shape, surface roughness, internally embedded object, and the loss tangent of the media, on the radar images and the detectability of internal structure are discussed under nadir and oblique observations. The simulations provide a reference for future data analysis in the Tianwen-2 mission.

Excluding rough areas with surface rocks and craters is critical for the safety of landing missions, such as China’s Chang’e-7 mission, in the permanently shadowed region (PSR) of the lunar south pole. Binned digital elevation model (DEM) data can describe the undulating surface, but the DEM data can hardly detect surface rocks because of median-averaging. High-resolution images from a synthetic aperture radar (SAR) can be used to map discrete rocks and small craters according to their strong backscattering. This study utilizes the You Only Look Once version 7 (YOLOv7) tool to detect varying-sized craters in SAR images. It also employs the Markov random field (MRF) algorithm to identify surface rocks, which are usually difficult to detect in DEM data. The results are validated by optical images and DEM data in non-PSR. With the assistance of the DEM data, regions with slopes larger than 10° are excluded. YOLOv7 and MRF are applied to detect craters and rocky surfaces and exclude regions with steep slopes in the PSRs of craters Shoemaker, Slater, and Shackleton, respectively. This study proves SAR images are feasible in the selection of landing sites in the PSRs for future missions.

The need for accurate modeling of the ionosphere plays an important role in the global navigation satellite system (GNSS) positioning. The traditional multilayer VTEC model without prior has been used for modeling the ionospheric delay error. However, it is assumed that the electron density of the ionosphere is compressed into multiple thin layers at fixed heights in the lack of capturing ionospheric physics. In this article, the data enhancement method by virtual observations is proposed to build the constrained multilayer VTEC model to capture physical features from empirical ionospheric models. The extraction methods of physical knowledge have been developed by prior VTEC based on the principal component analysis and model coefficients based on the EBF. The constrained multilayer modeling has been verified based on simulation and real measurement of GNSS data in Yunnan, China, collected from Ground-based GNSS stations by Qianxun on November 3, 2021. The receiver DCB error estimated by the multilayer model with prior constraint is significantly lower than that of the single-layer model and the traditional multilayer model. The experimental test shows that the constrained multilayer model achieves the accuracy of $0.5 \,\rm {TECU}$ for the independent reference station. The dSTEC of the proposed two multilayer models are significantly lower than those of the single-layer model for low elevation angles, and the RMSE of dSTEC is reduced by 63$\%$ with the cutoff elevation angle of $10^{\circ }$. The spatial distribution of the multilayer VTEC model shows consistency with the tomography model to verify vertical feature-capturing capability. Compared with the undifferenced and uncombined precise point positioning without ionospheric constraint, the multilayer-constrained model based on the test data improves the convergence time approximately by 36.55% and 18.78% in the horizontal (H) and up (U) directions, respectively. These results demonstrate that the proposed multilayer models not only improve ionospheric delay estimation precision but also can obtain the VTEC distribution capturing the physical characteristics of the ionosphere. The proposed multilayer models may be valuable for the ionospheric delay modeling of satellite navigation systems under harsh variable ionospheric conditions.

Dual-frequency synthetic aperture radar (DFSAR) onboard Chandrayaan-2 and Mini-RF onboard Lunar Reconnaissance Orbiter have acquired fully polarized and compact polarized SAR data of the lunar surface. However, there are few numerical simulations of lunar SAR images. Here, a fully polarized SAR images simulation method of lunar rough surfaces is presented. Scatterings from lunar surfaces are numerically simulated with the Kirchhoff approximation and small perturbation model. The Range Doppler algorithm is used to produce the SAR images. SAR images of lunar craters are simulated and compared with the DFSAR and Mini-RF data. The influence of co-polarization ratio $\sigma _{\text{HH}}^0/\sigma _{\text{VV}}^0$ on its relative phase are analyzed and validated with simulation and data. The enhanced polarized scatterings from undulating topography is simulated and validated with Mini-RF data at S-band and optical image of the crater Galilei E. Due to small incidence angles and radar parallax, strong backscattering caused by rocks at the crater wall facing away from the radar occupies more pixels in range direction in DFSAR images than Mini-RF images. DFSAR dual-frequency images of Apollo 17 landing site are specifically analyzed with assistances of simulations, optical images and high-resolution digital terrain model. Dual-frequency SAR images from Chandrayaan-2 reveal different geologic units of lunar surface, which are invisible in optical images. In addition, the inversion of orientation angles is analyzed as well. The simulation and analysis in this paper will be helpful in lunar SAR data interpretation.

Data of fully polarimetric synthetic aperture radar onboard Chandrayaan-2 make it feasible to analyze the geometric and physical properties of the lunar soil layer. A specific mission of Chandrayaan-2 is to investigate if there is water–ice in the regolith of the permanently shadowed region (PSR). Volatile substances are likely to accumulate in the ancient regolith media. Volumetric scattering of the regolith media might indicate specific characteristics of the regolith. Scattering from surface, rocks should be excluded. Such flat regions are difficult to identify in the digital elevation model. In this article, Chandrayaan-2 full-pol data at L-band are used for this purpose. The co-pol and cross-pol scattering coefficients and decomposition parameters, such as H, $\alpha $, degree of polarization, and circular polarization ratio of lunar surface, are studied. High-order scattering from rough surface is numerically simulated and analyzed by the bidirectional analytical ray-tracing code. It is found that rocky rough surface causes high co-pol scatterings. High-order scatterings of the rough surface and volumetric scatterers can enhance cross-pol scattering. Criteria are proposed to select volume scatterings at flat regions at Mare Serenitatis and a PSR crater. Regions with weak co-pol backscattering in a PSR crater at 85.9°N, 111.7°E are classified as flat surface. It is found that a flat region with weak co-pol and high cross-pol terms appears different from surrounding regions. The enhanced cross-pol is likely to be caused by volumetric inhomogeneity in the regolith. This unusual region shows its inhomogeneous soil layer and deserves further study.

We describe the measurement of the brightness temperature of the Moon from space during a total lunar eclipse by using a microwave sounder aboard a weather satellite. Previous observations of lunar eclipses were inconsistent and did not cover the frequency range between 100 and 200 GHz. In this work, we seek to establish a reliable relationship between frequency and drop in brightness temperature during a total eclipse for millimeter wavelengths. For this purpose, we chose the eclipse on 2004 October 28, because it coincided with appearances of the Moon in the deep space view of the Advanced Microwave Sounding Unit-B on NOAA-15. It was therefore possible to measure its disk-integrated radiance at 89, 150, and 183 GHz at 100 minutes intervals. Our observations are, to the best of our knowledge, the only ones between 100 and 200 GHz, and demonstrate the nearly linear dependency on frequency of the maximum relative drop in effective temperature during an eclipse. The slope of this function is m = 0.00114 ± 0.00017 GHz ^−1 in the range 88–300 GHz. The good agreement between the variations of the effective lunar temperature and a new radiative-transfer model suggests that the Moon is suitable as a flux standard for microwave observations with beam sizes larger than 0.5°.

In this paper, the generalized recursive formulations of the finite difference time domain (FDTD) for updating the electric and magnetic fields in the multi-layer anisotropic media are derived with a uniaxial perfectly matched layer. The stability condition of the proposed method is clearly analyzed and verified. Then this method is used to calculate the three-dimensional complex scattering fields in planar multilayered anisotropic microstructures with optical axis perpendicular to the layered interface and the scattering fields of arbitrary shape scatters in the anisotropic layered structures. The electric field induced by the sine dipole source is calculated in the spatial domain and the corresponding spectral domain results are achieved through Fourier transform. The scattering field of composite materials with submillimeter thicknesses used in the industrial engineering is calculated using a terahertz wave with operation frequency of 0.3 THz. Robustness of the derived formulations for the complex uniaxial anisotropic media is verified by comparing with the COMSOL software, which is based on FEM analysis. The comparison of memory and CPU time shows the efficiency of the proposed FDTD method. Finally, the scattering fields of different scatters buried in multilayer anisotropic media are studied. So it is expected to become an effective simulation tool for dealing with complex electromagnetic environment in the future, such as abnormal detection of aircraft coating materials and detection of hidden target and so on.

Numerous radar polarimetry theories and polarimetric synthetic aperture radar (PolSAR) processing methods have been developed. However, the vast majority of SAR images are not fully polarimetric (full-pol). This paper proposes “radar image colorization”to reconstruct a full-pol image from a nonfull-pol image, so that existing PolSAR methods, such as model-based decomposition and unsupervised classification, can be directly applied to the reconstructed full-pol SAR images. It proposes to train a specially designed deep neural network to convert a single polarization gray-scale SAR image to full-pol. It consists of two components: a feature extractor network to extract hierarchical multi-scale spatial features of the grayscale SAR image, followed by a feature translator network to map spatial feature to polarimetric feature with which the polarimetric covariance matrix of each pixel can be reconstructed. Both qualitative and quantitative experiments with real full-pol data are conducted to show the efficacy of the proposed method. The reconstructed full-pol SAR image agrees well with the true full-pol image, not only in the sense of visual similarity but also in the sense of real PolSAR applications, such as target decomposition and terrain classification.

In this work, the numerical steepest descent path (NSDP) method is proposed to compute the highly oscillatory physical optics (PO) scattered fields from the concave surfaces, including both the monostatic and the bistatic cases. Quadratic variations are adopted to approximate the integrands of the PO type integral into the canonical form. Then, on involving the NSDP method, we deform the integration paths of the integrals into several NSDPs on the complex plain, through which the highly oscillatory integrands are converted to exponentially decay integrands. The RCS results of the PO scattered field are calculated and are compared with the high frequency asymptotic (HFA) method and the brute force (BF) method. The results demonstrate that the proposed NSDP method for calculating PO scattered fields from concave surfaces is frequency-independent and error-controllable. Numerical examples are provided to verify the efficiencies of the NSDP method.