Virtual Telescope for X-Ray Observations

Selected by NASA for an Astrophysics Science SmallSat study, The Virtual Telescope for X-Ray Observations (VTXO) is a small satellite mission being developed by NASA’s Goddard Space Flight Center (GSFC) and New Mexico State University (NMSU). VTXO will perform X-ray observations with an angular resolution around 50 milliarcseconds, an order of magnitude better than is achievable by current state of the art X-ray telescopes. VTXO’s fine angular resolution enables measuring the environments closer to the central engines in compact X-ray sources. This resolution will be achieved by the use of Phased Fresnel Lenses (PFLs) optics which provide near diffraction-limited imaging in the X-ray band. However, PFLs require long focal lengths in order to realize their imaging performance, for VTXO this dictates that the telescope’s optics and the camera will have a separation of 1 km. As it is not realistic to build a structure this large in space, the solution being adapted for VTXO is to place the camera, and the optics on two separate spacecraft and fly them in formation with the necessary spacing. This requires centimeter level control, and sub-millimeter level knowledge of the two spacecraft’s relative transverse position. This paper will present VTXO’s current baseline, with particular emphasis on the mission’s flight dynamics design

Attitude Control Optimization of a Virtual Telescope for X-ray Observations

In this paper, a novel approach is investigated for the attitude control of two satellites acting as a virtual telescope. The Virtual Telescope for X-ray Observations (VTXO) is a mission exploiting two 6U-CubeSats operating in precision formation. The goal of the VTXO project is to develop a space-based, X-ray imaging telescope with high angular resolution precision. In this scheme, one CubeSat carries a diffractive lens and the other one carries an imaging device to support a focal length of 100 m. In this mission, the attitude control algorithms are required to keep the two spacecrafts in alignment with the Crab Nebula observations. To meet this goal, the attitude measurements from the gyros and the star trackers are used in an extended Kalman filter, for a robust hybrid controller. Due to limited energy and the requirement of high accuracy, the energy and accuracy of attitude control is optimized for this mission

Trajectory Optimization for the Virtual Telescope for X-Ray Observations

The Virtual Telescope for X-Ray Observations (VTXO) is a long focal length telescope which promises to provide orders of magnitude improvement in angular resolution in the X-ray band. VTXO will include a Phased Fresnel Lens (PFL), which provides nearly diffraction-limited imaging, with a 1 km focal length. The PFL is carried by the Optics Spacecraft, which flies in a formation with the Detector Spacecraft, approximating a rigid telescope body. In order to maintain the formation requirements, while pointing the telescope axis at the desired astronomical targets, one spacecraft will be traveling on a non-natural trajectory, requiring the vehicle to maneuver regularly to maintain the telescope pointing. If care is not taken in the trajectory design, these paths result in large propellant consumption. However, there is an opportunity to optimize trajectories when re-arranging the formation between different astronomical targets. This paper presents an optimization scheme for re-pointing the telescope, utilizing a non-traditional path-based cost function to solve the propellant optimal trajectory. The resulting trajectories show a factor of four improvement in propellant consumption compared to the baseline. The optimization techniques developed for VTXO are applicable to orbits ranging from low-Earth orbit, to highly eccentric Earth orbits, and Lagrange point orbits

Hybrid Attitude Control of a Two-CubeSat Virtual Telescope in a Highly Elliptical Orbit

The Virtual telescope for X-ray observation (VTXO) is a mission exploiting two 6U-CubeSats operating in precision formation. The goal of the VTXO research is to develop a space-based, X-ray imaging telescope with sub-arcsecond angular resolution. In the scheme, one CubeSat carries a diffractive lens and the other one carries an imaging device to support focal lengths from 100m to 1 km. In this mission, the Guidance, navigation and control (GN&C) algorithms are required to keep the two spacecraft in alignment while collecting data. In the VTXO mission, we have three major phases including the open-loop formation phase, the development phase, and the scientific phase. In the open-loop formation phase, no attitude control is performed and the two satellites pass the perigee to achieve the development phase. In the next phase, the development phase, the coarse pre-attitude control is performed to provide enough attitude determination for the scientific phase. In the scientific phase, the precision attitude control takes place. In this phase, the two satellites point at the Crab Nebula or the Sun. This phase takes place in the apogee since there is more time in the apogee, comparing to the other parts of the orbit, and the two satellites move more slowly, which results in a more precise attitude control. In this paper, attitude control is exploited based on the quaternion model of the two satellites. In this model, the gravitational and the atmospheric drag perturbations are considered. In the attitude control design of the system, the noises of different sensors, including the astrometric sensor, the IMU sensor, and the star tracker, are considered and the navigation part of the control system uses a filter to approximate the relative velocity and position of the two satellites based on the noisy data from the sensors. In the attitude control system, each phase has to be stable and the duration of each phase has to be designed based on the stability of each phase, the stability of the whole system and the desired sub-arcsecond angular resolution in the scientific phase with all the noises and the perturbations in the system. Considering all the previously mentioned criteria involved in the attitude control deign and the three different phases in the attitude control, hybrid control techniques are investigated in this paper for the attitude control design, due to the fact that hybrid control has the capacity to satisfy the given criteria and can include different stages in control

Relative Navigation Schemes for Formation Flying of Satellites

This paper will present a survey of relative navigation methods that can be adapted to the Virtual Telescope for X-ray Observations (VTXO) project. VTXO is a collaboration between educational institutions (NMSU, UNM) and NASA GSFC and supports NASA’s Science Technology Mission Directorate (STMD) and Science Mission Directorate (SMD). The VTXO mission is a sub-arcsecond resolution X-ray telescope that will utilize two CubeSats flying in formation. The two CubeSats will carry a lens and camera mounted on a leader and a follower, respectively. The main objective of the mission is to investigate technologies that will enable a full Virtual Telescope space mission. This mission will require very precise alignment and determination (sub-arcsecond to milli-arcsecond) to enable imaging at a higher quality than currently available. This will be made possible through relative navigation methods that enable formation flying of the CubeSats. Formation flying consists of satellites, in a constellation, that maneuver around or maintain a position relative to one another. Formation flight utilizes principles of relative navigation to resolve position and velocity telemetry relative to both an inertial frame and two or more satellites in the constellation. High precision alignment requirements call for precise knowledge of both spacecraft’s position relative to one another. In the case of a pair of satellites, a leader and follower scheme is used. The absolute position and velocity with respect to an inertial frame is determined for each vehicle using GPS, radar or other techniques that will be discussed. The relative position with respect to each spacecraft can then be resolved and corrections can be made to the follower’s attitude to align itself with respect to the leader. The technology enabled by formation flight enables smaller spacecraft to perform complex science missions such as interferometry, stereographic imaging, telescope-occulter imaging, and others. A technology driver in the development of the science for relative navigation and formation flying is the need for autonomy. As deep space exploration interest grows, the need for autonomous relative navigation systems also expands. Systems such as GPS and NASA’s DSN work well for near earth missions but do not satisfy the precision requirements needed for autonomous formation flying in deep space. The insight gained by this survey will provide valuable information for the VTXO mission where bilateral communication between the CubeSats is required for alignment. The survey of relative navigation systems will examine both developed and state-of-the-art techniques: GPS tracking, Deep Space Network (DSN), Ground station to satellite Doppler, X-ray pulsars, and others. These systems will be categorized based on the mission altitude, their nominal performance at relative distance, and their applicability to Small Satellites. These technologies will be analyzed with the context of how they can be leveraged for use on the VTXO mission

VTXO: The Virtual Telescope for X-ray Observations

The Virtual Telescope for X-ray Observations (VTXO) will use lightweight Phase Frensel Lenses (PFLs) in a virtual X-ray telescope with 1 km focal length and with nearly 50 milli-arc second angular resolution. Laboratory characterization of PFLs have demonstrated near diffraction-limited angular resolution in the X-ray band, but they require long focal lengths to achieve this quality of imaging. VTXO is formed by using precision formation flying of two SmallSats: a smaller, 6U OpticsSat that houses the PFLs and navigation beacons while a larger, ESPA-class DetectorSat contains an X-ray camera, a charged-particle radiation monitor, a precision star tracker, and the propulsion for the formation flying. The baseline flight dynamics uses a highly-elliptical supersynchronous geostationary transfer orbit to allow the inertial formation to form and hold around the 90,000 km apogee for 10 hours of the 32.5-hour orbit with nearly a year mission lifetime. The guidance, navigation, and control (GN&C) for the formation flying uses standard CubeSat avionics packages, a precision star tracker, imaging beacons on the OpticsSat, and a radio ranging system that also serves as an inter-satellite communication link. VTXO’s fine angular resolution enables measuring the environments nearly an order of magnitude closer to the central engines of bright compact X-ray sources compared to the current state of the art. This X-ray imaging capability allows for the study of the effects of dust scattering nearer to the central objects such as Cyg X-3 and GX 5-1, for the search for jet structure nearer to the compact object in X-ray novae such as Cyg X-1and GRS 1915+105, and for the search for structure in the termination shock of in the Crab pulsar wind nebula. In this paper, the VTXO science performance, SmallSat and instrument designs, and mission description is described. The VTXO development was supported as one of the selected 2018 NASA Astrophysics SmallSat Study (AS3) missions

Mode identification using stochastic hybrid models with applications to conflict detection and resolution

Most models of aircraft trajectories are non-linear and stochastic in nature; and their internal parameters are often poorly defined. The ability to model, simulate and analyze realistic air traffic management conflict detection scenarios in a scalable, composable, multi-aircraft fashion is an extremely difficult endeavor. Accurate techniques for aircraft mode detection are critical in order to enable the precise projection of aircraft conflicts, and for the enactment of altitude separation resolution strategies. Conflict detection is an inherently probabilistic endeavor; our ability to detect conflicts in a timely and accurate manner over a fixed time horizon is traded off against the increased human workload created by false alarms that is, situations that would not develop into an actual conflict, or would resolve naturally in the appropriate time horizon-thereby introducing a measure of probabilistic uncertainty in any decision aid fashioned to assist air traffic controllers. The interaction of the continuous dynamics of the aircraft, used for prediction purposes, with the discrete conflict detection logic gives rise to the hybrid nature of the overall system. The introduction of the probabilistic element, common to decision alerting and aiding devices, places the conflict detection and resolution problem in the domain of probabilistic hybrid phenomena. A hidden Markov model (HMM) has two stochastic components: a finite-state Markov chain and a finite set of output probability distributions. In other words an unobservable stochastic process (hidden) that can only be observed through another set of stochastic processes that generate the sequence of observations. The problem of self separation in distributed air traffic management reduces to the ability of aircraft to communicate state information to neighboring aircraft, as well as model the evolution of aircraft trajectories between communications, in the presence of probabilistic uncertain dynamics as well as partially observable and uncertain data. We introduce the Hybrid Hidden Markov Modeling (HHMM) formalism to enable the prediction of the stochastic aircraft states (and thus, potential conflicts), by combining elements of the probabilistic timed input output automaton and the partially observable Markov decision process frameworks, along with the novel addition of a Markovian scheduler to remove the non-deterministic elements arising from the enabling of several actions simultaneously. Comparisons of aircraft in level, climbing/descending and turning flight are performed, and unknown flight track data is evaluated probabilistically against the tuned model in order to assess the effectiveness of the model in detecting the switch between multiple flight modes for a given aircraft. This also allows for the generation of probabilistic distribution over the execution traces of the hybrid hidden Markov model, which then enables the prediction of the states of aircraft based on partially observable and uncertain data. Based on the composition properties of the HHMM, we study a decentralized air traffic system where aircraft are moving along streams and can perform cruise, accelerate, climb and turn maneuvers.We develop a common decentralized policy for conflict avoidance with spatially distributed agents (aircraft in the sky) and assure its safety properties via correctness proofs