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Tensor Network Space-Time Spectral Collocation Method for Time-Dependent Convection-Diffusion-Reaction Equations

Emerging tensor network techniques for solutions of partial differential equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultra-fast numerical solutions of high-dimensional problems. Here, we introduce a Tensor Train (TT) Chebyshev spectral collocation method, in both space and time, for the solution of the time-dependent convection-diffusion-reaction (CDR) equation with inhomogeneous boundary conditions, in Cartesian geometry. Previous methods for numerical solution of time-dependent PDEs often used finite difference for time, and a spectral scheme for the spatial dimensions, which led to a slow linear convergence. Spectral collocation space-time methods show exponential convergence; however, for realistic problems they need to solve large four-dimensional systems. We overcome this difficulty by using a TT approach, as its complexity only grows linearly with the number of dimensions. We show that our TT space-time Chebyshev spectral collocation method converges exponentially, when the solution of the CDR is smooth, and demonstrate that it leads to a very high compression of linear operators from terabytes to kilobytes in TT-format, and a speedup of tens of thousands of times when compared to a full-grid space-time spectral method. These advantages allow us to obtain the solutions at much higher resolutions.

97 MATHEMATICS AND COMPUTING↗

Flexible User Radio for Lunar Missions

NASA’s Artemis program and other lunar exploration and development programs are planning over 40 lunar missions before 2030. Lunar missions, both crewed and uncrewed, include orbiters, landers, rovers, and surface stations. All these missions require communications with Earth, either via Direct to Earth (DTE) links or through relays in lunar orbit. Multiple DTE options are available among existing and planned ground stations: Deep Space Network (DSN), European Space Agency, and others. Relay options include the planned Lunar Gateway, LunaNet compliant relays, and some lunar landers propose to launch dedicated orbiters. The dilemma for lunar system designers is to identify a communication link which meets mission requirements but does not have issues of limited access (e.g. DSN is in high demand supporting deep space missions with high priority and some with inflexible schedules), system impacts (high power Radio Frequency (RF) for DTE links), cost (dedicated relay), or operational date. To avoid this difficult decision, a Flexible Radio for Lunar Missions is proposed, which will enable system designs to proceed prior to any final decision on the communication network to be used, by enabling compatibility with any of multiple DTE or orbital relay communication systems. The Flexible Radio will support the necessary frequency, bandwidth, modulation, and power requirements to interoperate with the majority of known or planned DTE or relay systems, and can be designed into a lunar mission without prior knowledge of which link will ultimately be used. Furthermore, the link being used can be changed as needed during the mission, in near real time. The Flexible Radio design will leverage work already completed at NASA in the areas of Wideband RF, Software Defined Radio, Adaptive Coding and Modulation, and Phased Array antennas. The Flexible Radio requires sufficient bandwidth to cover the allocated frequencies for both the operation of links in cislunar space and for space-to-Earth links; the flexibility to support multiple modulations, data rates, and coding schemes; the ability to identify available relays, detect and recognize the signals of those relays, and adapt its own frequency, modulation, symbol rate, and code rate to operate with the detected relay (or DTE station); and finally, it requires appropriate software to support network configuration and interoperability with the detected network. The Flexible Radio can be designed in a sufficiently small, lightweight, and low-power package to be used in a wide variety of lunar systems. The initial implementation, as proposed, will focus on the Ka-band, supporting up to 2 GHz bandwidth around the 27 GHz frequency for return links, and 23 GHz for forward links. Other frequency bands are under consideration for future configurations. The software defined modem will support OQPSK, BPSK, and NASA-defined modulations which also support two-way ranging with data. For near-real time adaptation, the Flexible Radio will scan the sky for available relays, using a phased array antenna with Adaptive/Cognitive Communications. It will then configure for network interoperability supporting DTN and other protocol options. The Flexible Radio will support scheduled connections and on-demand use when available.

Lunar Space Communications↗

Flexible User Radio for Lunar Missions

NASA’s Artemis program and other lunar exploration and development programs are planning over 40 lunar missions before 2030. Lunar missions, both crewed and uncrewed, include orbiters, landers, rovers, and surface stations. All these missions require communications with Earth, either via Direct to Earth (DTE) links or through relays in lunar orbit. Multiple DTE options are available among existing and planned ground stations: Deep Space Network (DSN), European Space Agency, and others. Relay options include the planned Lunar Gateway, LunaNet compliant relays, and some lunar landers propose to launch dedicated orbiters. The dilemma for lunar system designers is to identify a communication link which meets mission requirements but does not have issues of limited access (e.g. DSN is in high demand supporting deep space missions with high priority and some with inflexible schedules), system impacts (high power Radio Frequency (RF) for DTE links), cost (dedicated relay), or operational date. To avoid this difficult decision, a Flexible Radio for Lunar Missions is proposed, which will enable system designs to proceed prior to any final decision on the communication network to be used, by enabling compatibility with any of multiple DTE or orbital relay communication systems. The Flexible Radio will support the necessary frequency, bandwidth, modulation, and power requirements to interoperate with the majority of known or planned DTE or relay systems, and can be designed into a lunar mission without prior knowledge of which link will ultimately be used. Furthermore, the link being used can be changed as needed during the mission, in near real time. The Flexible Radio design will leverage work already completed at NASA in the areas of Wideband RF, Software Defined Radio, Adaptive Coding and Modulation, and Phased Array antennas. The Flexible Radio requires sufficient bandwidth to cover the allocated frequencies for both the operation of links in cislunar space and for space-to-Earth links; the flexibility to support multiple modulations, data rates, and coding schemes; the ability to identify available relays, detect and recognize the signals of those relays, and adapt its own frequency, modulation, symbol rate, and code rate to operate with the detected relay (or DTE station); and finally, it requires appropriate software to support network configuration and interoperability with the detected network. The Flexible Radio can be designed in a sufficiently small, lightweight, and low-power package to be used in a wide variety of lunar systems. The initial implementation, as proposed, will focus on the Ka-band, supporting up to 2 GHz bandwidth around the 27 GHz frequency for return links, and 23 GHz for forward links. Other frequency bands are under consideration for future configurations. The software defined modem will support OQPSK, BPSK, and NASA-defined modulations which also support two-way ranging with data. For near-real time adaptation, the Flexible Radio will scan the sky for available relays, using a phased array antenna with Adaptive/Cognitive Communications. It will then configure for network interoperability supporting DTN and other protocol options. The Flexible Radio will support scheduled connections and on-demand use when available.

Lunar Space Communications↗

Telecommunications and data acquisition systems support for the Viking 1975 mission to Mars, volume 5

The support provided by the Deep Space Network to the Viking Project from 1 June 1978 to 30 April 1980 is described. The project was supported by the worldwide network of Deep Space Stations with 26- and 64-meter-diameter antennas, together with a ground communications system, for the transmission of commands, telemetry, radio metric data, and operational instructions between the stations and the network operation control center in Pasadena, California. Assistance was substantially less than in the previous phases of the Viking Project in order to provide adequate support to the Pioneer and Voyager Projects.

Larkin, W. E.↗

Orbit Determination Error Analysis Results for the Triana Sun-Earth L2 Libration Point Mission

Using the NASA Goddard Space Flight Center's Orbit Determination Error Analysis System (ODEAS), orbit determination error analysis results are presented for all phases of the Triana Sun-Earth L1 libration point mission and for the science data collection phase of a future Sun-Earth L2 libration point mission. The Triana spacecraft was nominally to be released by the Space Shuttle in a low Earth orbit, and this analysis focuses on that scenario. From the release orbit a transfer trajectory insertion (TTI) maneuver performed using a solid stage would increase the velocity be approximately 3.1 km/sec sending Triana on a direct trajectory to its mission orbit. The Triana mission orbit is a Sun-Earth L1 Lissajous orbit with a Sun-Earth-vehicle (SEV) angle between 4.0 and 15.0 degrees, which would be achieved after a Lissajous orbit insertion (LOI) maneuver at approximately launch plus 6 months. Because Triana was to be launched by the Space Shuttle, TTI could potentially occur over a 16 orbit range from low Earth orbit. This analysis was performed assuming TTI was performed from a low Earth orbit with an inclination of 28.5 degrees and assuming support from a combination of three Deep Space Network (DSN) stations, Goldstone, Canberra, and Madrid and four commercial Universal Space Network (USN) stations, Alaska, Hawaii, Perth, and Santiago. These ground stations would provide coherent two-way range and range rate tracking data usable for orbit determination. Larger range and range rate errors were assumed for the USN stations. Nominally, DSN support would end at TTI+144 hours assuming there were no USN problems. Post-TTI coverage for a range of TTI longitudes for a given nominal trajectory case were analyzed. The orbit determination error analysis after the first correction maneuver would be generally applicable to any libration point mission utilizing a direct trajectory.

Marr, G.↗

A Journey with MOM

In late 2013, the Indian Space Research Organization (ISRO) launched its "Mars Orbiter Mission" (MOM). ISRO engaged NASA's Jet Propulsion Laboratory (JPL) for navigation services to support ISRO's objectives of MOM achieving and maintaining Mars orbit. The navigation support included planning, documentation, testing, orbit determination, maneuver design /analysis, and tracking data analysis. Several of MOM's attributes had an impact on navigation processes, e.g., S -band telecommunications, Earth Orbit Phase maneuvers, and frequent angular momentum desaturation s (AMDs). The primary source of tracking data was NASA/ JPL's Deep Space Network (DSN); JPL also conducted a performance assessment of Indian Deep Space Network (IDSN) tracking data. Planning for the Mars Orbit Insertion (MOI) was complicated by a pressure regulator failure that created uncertainty regarding MOM's main engine and raised potential planetary protection issues. A successful main engine test late on approach resolved these issues; it was quickly followed by a successful MOI on 24-September - 2014 at 02:00 UTC. Less than a month later, Comet Siding Spring's Mars flyby necessitated plans to minimize potential spacecraft damage. At the time of this writing, MOM's orbital operations continue, and plans to extend JPL 's support are in progress. This paper covers the JPL 's support of MOM through the Comet Siding Spring event.

Mars orbiter↗

Juno Gravity Science: Preparing for Data Collection at Jupiter

One of the primary goals of the Juno mission is to investigate Jupiter’s interior by mapping its gravitational field with the gravity science instrument. The Juno spacecraft has two radio science components that comprise the gravity science instrument: the X-band telecommunications system for a X-up/X-down link and a Ka-band Translator for a Ka-up/Ka-down link. The Deep Space Network’s DSS-25 beam waveguide antenna at the Goldstone Deep Space Communications Complex in California provides the X- and Ka-band uplink alongside an Advanced Water Vapor Radiometer to calibrate tropospheric effects. X-band and Ka-band downlink data are collected with both open-loop and closed-loop receivers located at the complex. Utilization of Ka-band provides scientific benefit to the Doppler measurements, but also adds operational challenges. Pointing of the uplink and downlink Ka-band signals requires additional systems to be calibrated and operated by the Deep Space Network; and the higher frequency of Ka-band means the signal dynamics are increased by a factor of four over X-band signals. Due to the spacecraft’s elliptical orbit and 4000 kilometer perijove altitude, it accelerates at an extreme rate as it approaches Jupiter, inducing large dynamic ranges in Doppler range of approximately 6 MHz over 3 hours at Ka-band. After the installation of a new Ka-band transmitter at DSS-25 for Juno was completed in 2015, end-to-end testing was conducted to ensure readiness for operations at Jupiter and provide an initial assessment of the performance. Cruise testing was conducted in the same operational configuration that the system will be used in during perijove passes. Processed open-loop data yielded uncalibrated Doppler residuals of 1.9 mHz at X-band and 6.0 mHz at Ka-band with 5-second compression time. Conduction of these tests has prepared the instrument and the operations team for science data collection during the science phase of the mission.

Buccino, Dustin↗

Mixed Integer Programming and Heuristic Scheduling for Space Communication Networks

In this paper, we propose to solve the constrained optimization problem in two phases. The first phase uses heuristic methods such as the ant colony method, particle swarming optimization, and genetic algorithm to seek a near optimal solution among a list of feasible initial populations. The final optimal solution can be found by using the solution of the first phase as the initial condition to the SQP algorithm. We demonstrate the above problem formulation and optimization schemes with a large-scale network that includes the DSN ground stations and a number of spacecraft of deep space missions.

Communication Network Scheduling↗

Communications protocols for a fault tolerant, integrated local area network for Space Station applications

The evolutionary growth of the Space Station and the diverse activities onboard are expected to require a hierarchy of integrated,local area networks capable of supporting data, voice and video communications. In addition, fault tolerant network operation is necessary to protect communications between critical systems attached to the net and to relieve the valuable human resources onboard Space Station of day-to-day data system repair tasks. An experimental, local area network is being developed which will serve as a testbed for investigating candidate algorithms and technologies for a fault tolerant, integrated network. The establishment of a set of rules or protocols which govern communications on the net is essential to obtain orderly and reliable operation. A hierarchy of protocols for the experimental network is presented and procedures for data and control communications are described.

Meredith, B. D.↗

NASA directory of observation station locations, volume 1

Geodetic information for NASA tracking stations and for observation stations cooperating in NASA geodetic satellite programs is presented. A Geodetic Data Sheet is provided for each station, giving the position of the station and describing briefly how it was established. Geodetic positions and geocentric coordinates of these stations are tabulated on local or major geodetic datums and on selected world geodetic systems. The principal tracking facilities used by NASA, including the Spaceflight Tracking and Data Network, the Deep Space Network, and several large radio telescopes are discussed. Positions of these facilities are tabulated on their local or national datums, the Mercury Spheroid 1960, the Modified Mercury Datum 1968, and the Spaceflight Tracking and Data Network System. Observation stations in the NASA Geodetic Satellites Program are included along with stations participating in the National Geodetic Satellite Program. Positions of these facilities are given on local or preferred major datums, and on the Modified Mercury Datum 1968.

Source record↗

Microwave spectrum compatibility in planetary research

The paper presents an overview of solar system exploration, basic functions of the Deep Space Network (DSN), deep space microwave links, space research compatibility problems, and DSN's interference susceptibility. To maintain the operational integrity of competing radio systems using the microwave spectrum, the technology must extend to make possible the shared use of the spectral ranges without the ill effects of interferences. Suggestions are given which are only examples of many possible techniques that can eliminate or reduce interferences.

Siegmeth, A. J.↗

Networks consolidation program

Progress in the networks consolidations program (NCP) to combine the resources of the two NASA ground spacecraft tracking networks (the Deep Space Network, operated by JPL, and the ground spaceflight tracking and data network, operated by Goddard) into one consolidated network is reported. Management, design, and implementation activities occurring between August 1981 and April 1982 are addressed, with special emphasis on planning and budgeting activities.

Yeater, M. L.↗

The Telecommunications and Data Acquisition Report

Archival reports on developments in programs managed by JPL's Office of Telecommunications and Data Acquisition (TDA) are provided. Activities of the Deep Space Network (DSN) in space communications, radio navigation, radio science, and ground-based radio astronomy are reported. Also included are the plans, supporting research and technology, implementation and operations for the Ground Communications Facility (GCF). In geodynamics, the publication reports on the application of radio interferometry at microwave frequencies for geodynamic measurements. In the search for extraterrestrial intelligence (SETI), it reports on implementation and operations for searching the microwave spectrum.

Posner, E. C.↗

Asynchronous transfer mode link performance over ground networks

The results of an experiment to determine the feasibility of using asynchronous transfer mode (ATM) technology to support advanced spacecraft missions that require high-rate ground communications and, in particular, full-motion video are reported. Potential nodes in such a ground network include Deep Space Network (DSN) antenna stations, the Jet Propulsion Laboratory, and a set of national and international end users. The experiment simulated a lunar microrover, lunar lander, the DSN ground communications system, and distributed science users. The users were equipped with video-capable workstations. A key feature was an optical fiber link between two high-performance workstations equipped with ATM interfaces. Video was also transmitted through JPL's institutional network to a user 8 km from the experiment. Variations in video depending on the networks and computers were observed, the results are reported.

Chow, E. T.↗

Determining noise temperatures in beam waveguide systems

A new 34-m research and development antenna was fabricated and tested as a precursor to introducing beam waveguide (BWG) antennas and Ka-band (32 GHz) frequencies into the NASA/JPL Deep Space Network. For deep space use, system noise temperature is a critical parameter. There are thought to be two major contributors to noise temperature in a BWG system: the spillover past the mirrors, and the conductivity loss in the walls. However, to date, there are no generally accepted methods for computing noise temperatures in a beam waveguide system. An extensive measurement program was undertaken to determine noise temperatures in such a system along with a correspondent effort in analytic prediction. Utilizing a very sensitive radiometer, noise temperature measurements were made at the Cassegrain focus, an intermediate focal point, and the focal point in the basement pedestal room. Several different horn diameters were used to simulate different amounts of spillover past the mirrors. Two analytic procedures were developed for computing noise temperature, one utilizing circular waveguide modes and the other a semiempirical approach. The results of both prediction methods are compared to the experimental data.

Imbriale, W.↗

Determining Noise Temperatures in Beamwaveguide Systems

A new 34-meter research and development antenna was fabricated and tested as a precursor to introducing beamwaveguide antennas and Ka-band frequencies into the NASA/JPL Deep Space Network. For deep space use, system noise temperature is a critical parameter. There are thought to be two major contributors to noise temperature in a BWG system: the spillover past the mirrors and the conductivity loss in the walls. However, to date, there are no generally accepted methods for computing noise temperatures in a beamwaveguide system. An extensive measurement program was undertaken to determine noise temperatures in such a system along with a correspondent effort in analytic prediction. Utilizing a very sensitive radiometer, noise temperature measurements were made at the cassegrain focus, an intermediate focal point, and the focal point in the basement pedestal room...

Imbriale, W.↗

Orbit Determination of Spacecraft in Earth-Moon L1 and L2 Libration Point Orbits

The ARTEMIS mission, part of the THEMIS extended mission, is the first to fly spacecraft in the Earth-Moon Lissajous regions. In 2009, two of the five THEMIS spacecraft were redeployed from Earth-centered orbits to arrive in Earth-Moon Lissajous orbits in late 2010. Starting in August 2010, the ARTEMIS P1 spacecraft executed numerous stationkeeping maneuvers, initially maintaining a lunar L2 Lissajous orbit before transitioning into a lunar L1 orbit. The ARTEMIS P2 spacecraft entered a L1 Lissajous orbit in October 2010. In April 2011, both ARTEMIS spacecraft will suspend Lissajous stationkeeping and will be maneuvered into lunar orbits. The success of the ARTEMIS mission has allowed the science team to gather unprecedented magnetospheric measurements in the lunar Lissajous regions. In order to effectively perform lunar Lissajous stationkeeping maneuvers, the ARTEMIS operations team has provided orbit determination solutions with typical accuracies on the order of 0.1 km in position and 0.1 cm/s in velocity. The ARTEMIS team utilizes the Goddard Trajectory Determination System (GTDS), using a batch least squares method, to process range and Doppler tracking measurements from the NASA Deep Space Network (DSN), Berkeley Ground Station (BGS), Merritt Island (MILA) station, and United Space Network (USN). The team has also investigated processing of the same tracking data measurements using the Orbit Determination Tool Kit (ODTK) software, which uses an extended Kalman filter and recursive smoother to estimate the orbit. The orbit determination results from each of these methods will be presented and we will discuss the advantages and disadvantages associated with using each method in the lunar Lissajous regions. Orbit determination accuracy is dependent on both the quality and quantity of tracking measurements, fidelity of the orbit force models, and the estimation techniques used. Prior to Lissajous operations, the team determined the appropriate quantity of tracking measurements that would be needed to meet the required orbit determination accuracies. Analysts used the Orbit Determination Error Analysis System (ODEAS) to perform covariance analyses using various tracking data schedules. From this analysis, it was determined that 3.5 hours of DSN TRK-2-34 range and Doppler tracking data every other day would suffice to meet the predictive orbit knowledge accuracies in the Lissajous region. The results of this analysis are presented. Both GTDS and ODTK have high-fidelity environmental orbit force models that allow for very accurate orbit estimation in the lunar Lissajous regime. These models include solar radiation pressure, Earth and Moon gravity models, third body gravitational effects from the Sun, and to a lesser extent third body gravitational effects from Jupiter, Venus, Saturn, and Mars. Increased position and velocity uncertainties following each maneuver, due to small execution performance errors, requires that several days of post-maneuver tracking data be processed to converge on an accurate post-maneuver orbit solution. The effects of maneuvers on orbit determination accuracy will be presented, including a comparison of the batch least squares technique to the extended Kalman filter/smoother technique. We will present the maneuver calibration results derived from processing post-maneuver tracking data. A dominant error in the orbit estimation process is the uncertainty in solar radiation pressure and the resultant force on the spacecraft. An estimation of this value can include many related factors, such as the uncertainty in spacecraft reflectivity and surface area which is a function of spacecraft orientation (spin-axis attitude), uncertainty in spacecraft wet mass, and potential seasonal variability due to the changing direction of the Sun line relative to the Earth-Moon Lissajous reference frame. In addition, each spacecraft occasionally enters into Earth or Moon penumbra or umbra and these shadow crossings reduche solar radiation force for several hours. The effects of these events on orbit determination accuracy will be presented. In order to plan for upcoming stationkeeping maneuvers, the maneuver planning team must take the current orbit estimate, propagate it forward to the planned maneuver time, and determine the optimal maneuver to maintain the Lissajous orbit for one or more revolutions. The propagation is performed using a Runge-Kutta 7/8 integrator and typically the position and velocity uncertainty increases with propagation time, increasing the overall uncertainty of the orbit state at the maneuver execution time. The effect of orbit knowledge uncertainty on stationkeeping operations will be presented.

Woodard, Mark↗