SPECTRANET-SO(3): Learning Satellite Orientation from Optical Spectra by Implicitly Modeling Mutually Exclusive Probability Distributions on The Rotation Manifold

In the space domain, remotely measuring the rotational state of a spacecraft provides critical information for assessing its operational health. For the large family of space assets that lie in regions of space too distant to resolve spatial features with ground sensors, measurement of the energy spectrum of reflected sunlight has shown recent promise in probing their material and spatial properties. In this work, we explore the utility of using the recently proposed Implicit-PDF network to implicitly learn challenging probability distributions associated with satellite orientations using only raw optical spectra as input. Originally designed for computer vision applications, we detail how the Implicit-PDF architecture can be applied directly to spectra and further extended to a broad class of signal inputs. We discuss key aspects to improving performance and demonstrate the generalizability of the implicit framework by showing how a single network can efficiently learn mutually exclusive probability distributions over multiple satellite classes without meaningful performance loss.¹

1. INTRODUCTION

While orbital trajectories define the motion of the center of the mass, as we seek to complete the kinematic specification of all man-made space objects orbiting Earth, we must also measure the additional degrees of freedom regarding the motion about the center of mass. For the many assets in Geosynchronous Earth Orbit (GEO), measuring the rotational state of satellites using ground-based sensors becomes infeasible with traditional focal plane imaging techniques due to the limited resolving power of even the largest telescopes [1]. Recent application of spectroscopy – an optical modality long used by astronomers to probe the properties of the most distant objects in the universe – has shown promising utility for non-resolved object characterization [2]. By measuring the energy spectrum of photons emitted from the sun and reflected off satellites, one is able to capture rich information related to an object’s atomic material properties, surface normals, and sun-object-sensor reflection geometry (cf. Fig. 1). As the object of interest rotates, ground-based spectrometers sample different points associated with the angular reflectance distribution function. With a sufficient number of spectral measurements, in principle one may construct a mapping from spectra to ro-tation. Given the complex geometry of man-made space objects, the dependence of spectral intensity at a given wavelength on rotation angle is highly non-linear and analytically non-tractable; however, cast as a supervised machine learning problem, and given a network with proper inductive biases and sufficient capacity, it is possible to learn the underlying mapping [3].