A Semi-Rigorous Sensor Model for Precision Geometric Processing of Mini-Rf Bistatic Radar Images of the Moon

Abstract

ABSTRACT:The spaceborne synthetic aperture radar (SAR) instruments known as Mini-RF were designed to image shadowed areas of the lunar poles and assay the presence of ice deposits by quantitative polarimetry. We have developed radargrammetric processing techniques to enhance the value of these observations by removing spacecraft ephemeris errors and distortions caused by topographic parallax so the polarimetry can be compared with other data sets. Here we report on the extension of this capability from monostatic imaging (signal transmitted and received on the same spacecraft) to bistatic (transmission from Earth and reception on the spacecraft) which provides a unique opportunity to measure radar scattering at nonzero phase angles. In either case our radargrammetric sensor models first reconstruct the observed range and Doppler frequency from recorded image coordinates, then determine the ground location with a corrected trajectory on a more detailed topographic surface. The essential difference for bistatic radar is that range and Doppler shift depend on the transmitter as well as receiver trajectory. Incidental differences include the preparation of the images in a different (map projected) coordinate system and use of "squint" (i.e., imaging at nonzero rather than zero Doppler shift) to achieve the desired phase angle. Our approach to the problem is to reconstruct the time-of-observation, range, and Doppler shift of the image pixel by pixel in terms of rigorous geometric optics, then fit these functions with low-order polynomials accurate to a small fraction of a pixel. Range and Doppler estimated by using these polynomials can then be georeferenced rigorously on a new surface with an updated trajectory. This "semi-rigorous" approach (based on rigorous physics but involving fitting functions) speeds the calculation and avoids the need to manage both the original and adjusted trajectory data. We demonstrate the improvement in registration of the bistatic images for Cabeus crater, where the LCROSS spacecraft impacted in 2009, and describe plans to precision-register the entire Mini-RF bistatic data collection.

WITHDRAWN: Optical Satellite Sensor and Positioning Accuracy Assessment for The Hongqi-H9 Wide-Range Satellite in Different Terrains

“…Generally, satellite images can be used to evaluate the geometric positioning accuracy by using two approaches [18]. In the first approach, high-performance sensor structures and parameters can be used to realize the geometric transformation from the image space to the ground space [19][20][21][22]. The second approach is based on the use of a rational function model (RFM), which exploits the constraints between different images [23][24][25].…”

A Semi-Rigorous Sensor Model for Precision Geometric Processing of Mini-Rf Bistatic Radar Images of the Moon

“…Bistatic products delivered to the NASA Planetary Data System (PDS) to date use a grid referenced to the spacecraft trajectory in a complex way; companion files were provided to give the latitude and longitude of each pixel. A first step toward precision geometric processing of the bistatic images (Kirk et al, 2014) was to regenerate them in the Oblique Cylindrical projection used for monostatic Level 2 products. The result is very similar visually, but latitude-longitude coordinates can now be calculated by a simple set of map projection equations (Reid, 2010), vastly simplifying the subsequent analysis.…”

“…The image labels contain the coefficients of polynomials that can be used to convert sample number to range. Our initial model of the geometry of the bistatic observations (Kirk et al, 2014) went astray by following this monostatic example too closely.…”

“…Here, we describe our approach to processing bistatic observations, in which a signal transmitted from Earth is received on board the spacecraft (Patterson et al, 2016). These observations are of tremendous scientific interest as part of the overall Mini-RF program of searching for ice deposits at the lunar poles (Kirk et al, 2014;Spudis et al, 2009) because the variation of signal strength with the phase angle between transmitter and receiver may distinguish between coherent backscatter in ice (Hapke and Blewett, 1991) and diffuse scattering by blocky surfaces (Nelson et al, 2000). By controlling and rectifying these observations we enable the quantitative analysis of radar-scattering properties on a pointby-point basis with the more extensive monostatic radar images and other remote sensing data such as optical and thermal images and altimetry on a pixel-by-pixel basis.…”