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Orbit Determination Support for the Microwave Anisotropy Probe (MAP)

THe microwave Anisotropy Probe (MAP) ia the second Medium Class Explorer (MIDEX) mission of the National Aeronautics and Space Administration (NASA). The main goal of the MAP observatory is to measure the temperature fluctuations, known as anisotropy, of the cosmic microwave background (CBG) radiation over the entire sky and to produce a map of the CMB anisotropies with an angular resolution of approximately 3 degrees. MAP was launched from the Cape Canaveral Air Force Station Complex 17 aboard a Delta II 7425-10 expendable launch vehicle at exactly 19:46:46.183 UTC on June 30, 20001. The spacecraft receiver a nominal direct insertion by the Delta expendable launch vehicle into a 185-km circular orbit with a 28.7 deg. inclination. MAP was than maneuvered into a sequence of phasing loops designed to set up a lunar gravity-assisted acceleration of the spacecraft onto a transfer trajectory to a lissajous orbit about the Earth-Sun L2 Lagrange point, about 1.5 million km from Earth. The science mission minimum lifetime is two years of observations at L2 with a desired lifetime of 4 years. The MAP transfer orbit consisted of 3.5 phasing loops.The MAP trajectory schematic all the way through L2 is shown. The first loop had a period of 7 days, the second and third loops were 10 days long, and the last half loop was 5 days. The periselene (i.e., lunar encounter or swingby) took place approximately 30 days after launch. After the periselene, the spacecraft cruised for approximately 60 days before it arrived in the vicinity of the L2 libration point. Two mid-course correction (MCC) maneuvers were performed to refine MAP's post-launch trajectory-one after periselene and one prior to arrival at vicinity of L2. Now that MAP is at its operational L2 lissajous orbit, the MAP satellite is commanded to perform occasional station-keeping (SK) maneuvers in order to maintain its orbit around L2. Because of its complex orbital characteristics, the mission provided a unique challenge to orbit determination (OD) support in many orbital regimes.

Truong, Son H.↗

An Overview of Trajectory Design Operations for the Microwave Anisotropy Probe (MAP) Mission

The main science objective of the Microwave Anisotropy Probe (MAP) mission is to produce an accurate full-sky map of the cosmic microwave background temperature fluctuations - anisotropy. MAP will collect these measurements from a lissajous orbit about the Sun-Earth/Moon L2 Lagrange Point. The NASA Goddard Space Flight Center (GSFC) Flight Dynamics Analysis Branch provided mission analysis, maneuver planning and maneuver calibration for the MAP spacecraft. This paper will provide an overview of the MAP trajectory design, a summary of the maneuvers executed. Differences from the pre-launch nominal plan will also be discussed. During the MAP phasing loops, MAP performed three calibration maneuvers in order to characterize the performance of the primary sets of thrusters - +X, +Z, and -Z. The calibration maneuvers were designed to minimize their impact on the trajectory. Four maneuvers were performed to set up the gravity assist of the Moon - required to propel MAP out to its orbit about L2. These maneuvers were performed at the three phasing loop perigees and at 18 hours after the final perigee. It became necessary to alter some of the perigee maneuvers in order to shape the gravity assist. This shaping was done to help meet some mission goals. In particular, the gravity assist was changed slightly in order to remove lunar shadows in both the cruise out to L2 and in the first revolution about L2. This amounted to a change in the phasing loop AV of less than 1 m/s. After the gravity assist, two mid-course correction (MCC) maneuvers were performed in order to fine-tune the trajectory. MCC1 was used to clean up and errors which resulted from the gravity assist. MCC2 was performed in order to mitigate a large stationkeeping maneuver following a crucial instrument calibration period during the cruise phase. MAP executed it's first stationkeeping maneuver in January 16th and is ready for a second calibration period during late Winter / early Spring. Further information concerning subsequent stationkeeping maneuver will be added as they become available.

Cuevas, Osvaldo O.↗

Using Solar Radiation Pressure to Control L2 Orbits

The main perturbations at the Sun-Earth Lagrange points L1 and L2 are from solar radiation pressure (SRP), the Moon and the planets. Traditional approaches to trajectory design for Lagrange-point orbits use maneuvers every few months to correct for these perturbations. The gravitational effects of the Moon and the planets are small and periodic. However, they cannot be neglected because small perturbations in the direction of the unstable eigenvector are enough to cause exponential growth within a few months. The main effect of a constant SRP is to shift the center of the orbit by a small distance. For spacecraft with large sun-shields like the Microwave Anisotropy Probe (MAP) and the Next Generation Space Telescope (NGST), the SRP effect is larger than all other perturbations and depends mostly on spacecraft attitude. Small variations in the spacecraft attitude are large enough to excite or control the exponential eigenvector. A closed-loop linear controller based on the SRP variations would eliminate one of the largest errors to the orbit and provide a continuous acceleration for use in controlling other disturbances. It is possible to design reference trajectories that account for the periodic lunar and planetary perturbations and still satisfy mission requirements. When such trajectories are used the acceleration required to control the unstable eigenvector is well within the capabilities of a continuous linear controller. Initial estimates show that by using attitude control it should be possible to minimize and even eliminate thruster maneuvers for station keeping.

Tene, Noam↗

Orbit Determination Support for the Microwave Anisotropy Probe (MAP)

The Microwave Anisotropy Probe (MAP) is a Medium Class Explorers (MIDEX) mission produced in partnership between Goddard Space Flight Center (GSFC) and Princeton University. The main science objective of the MAP mission is to produce an accurate full-sky map of the cosmic microwave background temperature fluctuations anisotropy. MAP was launched from the Cape Canaveral Air Force Station Complex 17 aboard a Delta II 7425-10 expendable launch vehicle at exactly 19:46:46.183 UTC on June 30, 2001. The spacecraft received a nominal direct insertion by the Delta into a 185 km circular orbit. MAP was then maneuvered into a sequence of phasing loops designed to set up a lunar swingby (gravity-assisted acceleration) of the spacecraft onto a transfer trajectory to a Lissajous orbit about the Earth-Sun L2 point. The mission duration is approximately 27 months with 3 to 4 months of transfer time to the final mission orbit about L2. The MAP transfer orbit consisted of 3.5 phasing loops: the first loop has a 7-day period, the second and third loops have a 9-day period, and the last half loop has a 4-day period as illustrated in Figure 1, which also indicates the placement of maneuvers. A Pfinal correction maneuver was performed 18 hours after the last perigee to more closely achieve the targeted lissajous orbit. The lunar encounter or swingby took place approximately 30 days after launch. After the lunar encounter, the spacecraft will cruise for approximately 120 days before it arrives at L2. A Mid-Course Correction (MCC) maneuver was executed seven days after the swingby to further refine the trajectory. Once the MAP satellite is injected into the L2 Lissajous orbit, it will perform occasional stationkeeping maneuvers to maintain the Lissajous orbit for a minimum of two years (and a goal of four years). Because of its complex orbital characteristics, the mission provided a unique challenge to orbit determination (OD) support in many orbital regimes. Extensive trajectory error covariance analysis was performed to predict ephemeris accuracy for the OD process using a Bayesian least-squares technique. The orbit determination error analysis is essential for maneuver planning and maneuver recovery study. Several tracking scenarios were investigated for each phase of the mission. This paper provides a summary of the premission trajectory covariance error analysis, as well as actual real-time OD results. The use and impact of the various tracking stations, systems, and measurements will be discussed. Details of the operational OD support and the inferred OD accuracy will be presented, and the results will be compared to the premission covariance analysis, In addition, there will be a discussion of the challenges presented to OD support including delta-Vs at apogee as well as perigee, and effects due to spacecraft attitude mode, in light of their implications to the OD accuracy and covariance analysis.

Truong, Son H.↗

Mars Science Laboratory Cruise Propulsion Maneuvering Operations

Mars Science Laboratory "Curiosity" is NASA's most recent mission to Mars, launched in November 2011, and landed in August 2012. It is a subcompact car-sized nuclear powered rover designed for a long duration mission, with an extensive suite of science instruments. Entry, descent and landing used a unique "skycrane" concept. This report describes the propulsive maneuvering operations during cruise from Earth to Mars, to control attitudes and to target the vehicle for entry. The propulsion subsystem, mission operations, and flight performance are discussed. All trajectory control maneuvers were well within accuracy requirements, and all turns and spin corrections were nominal.

Baker, Raymond S.↗

Mission Analysis Program for Solar Electric Propulsion (MAPSEP). Volume 2: User's manual for earth orbital MAPSEP

The trajectory simulation mode (SIMSEP) requires the namelist SIMSEP to follow TRAJ. The SIMSEP contains parameters which describe the scope of the simulation, expected dynamic errors, and cumulative statistics from previous SIMSEP runs. Following SIMSEP are a set of GUID namelists, one for each guidance correction maneuver. The GUID describes the strategy, knowledge or estimation uncertainties and cumulative statistics for that particular maneuver. The trajectory display mode (REFSEP) requires only the namelist TRAJ followed by scheduling cards, similar to those used in GODSEP. The fixed field schedule cards define: types of data displayed, span of interest, and frequency of printout. For those users who can vary the amount of blank common storage in their runs, a guideline to estimate the total MAPSEP core requirements is given. Blank common length is related directly to the dimension of the dynamic state (NDIM) used in transition matrix (STM) computation, and, the total augmented (knowledge) state (NAUG). The values of program and blank common must be added to compute the total decimal core for a CDC 6500. Other operating systems must scale these requirements appropriately.

Source record↗

Performance Impacts to the NASA Artemis II Trajectory Correction Burn Placement

As NASA embarks to return humans to the lunar vicinity with the upcoming Artemis II mission, the selected free return trajectory taking the crew to the Moon in the Orion spacecraft is impacted by the execution of small trajectory correction burns to ensure the spacecraft stays on course for a successful return to Earth. The placement of these nominally zero translational maneuvers must account for the crew schedule, navigation tracking constraints, spacecraft venting, thermal and communication requirements, and a host of other programmatic factors. Understanding the influence the placement of these periodic burn corrections have on the integrated GN\&C performance can provide valuable insight to mission controllers and trajectory planning processes to untangle the complex trade space considered for both baseline and contingency scenarios. This sensitivity information can also be utilized to facilitate the optimized placement of these burns. This paper utilizes several techniques to systematically generate the performance impacts to the NASA Artemis II trajectory correction burn placement and demonstrate how to derive optimized locations that make the system robust to crew activity, maneuver execution errors, navigation uncertainty, orbit insertion errors, disturbance accelerations, and other system limitations.

GN&C↗

Optimized Trajectory Correction Burn Placement for the NASA Artemis II Mission

The NASA Artemis II mission represents the first time humans plan to return to the lunar vicinity in over 50 years with a crew traveling to the Moon in the Orion spacecraft on a free return trajectory. This first crewed mission of the Artemis program will evaluate human-rated elements of Orion in preparation to sending astronauts to the lunar surface. The selected free-return cislunar trajectory profile that is reminiscent of the Apollo 8 mission that nominally requires no additional translational burns following the trans-lunar injection (TLI) burn. Due to crew activity, maneuver execution errors, navigation uncertainty, orbit insertion errors, disturbance accelerations, and other system limitations; periodic trajectory corrections burns are necessary to ensure proper entry interface (EI) conditions are satisfied for a safe return to Earth. Robust trajectory optimization techniques are utilized to determine the optimized placements for the Artemis II trajectory correction burns that accounts for the crew schedule, both the primary and backup navigation systems, targeting strategies and burn plan configurations, spacecraft venting, thruster selection, and the integrated GN&C performance.

Linear Covariance Analysis↗

The Maneuver Planning Process for the Microwave Anisotropy Probe (MAP) Mission

The Microwave Anisotropy Probe (MAP) was successfully launched from Kennedy Space Center's Eastern Range on June 30, 2001. MAP will measure the cosmic microwave background as a follow up to NASA's Cosmic Background Explorer (COBE) mission from the early 1990's. MAP will take advantage of its mission orbit about the Sun-Earth/Moon L2 Lagrangian point to produce results with higher resolution, sensitivity, and accuracy than COBE. A strategy comprising highly eccentric phasing loops with a lunar gravity assist was utilized to provide a zero-cost insertion into a lissajous orbit about L2. Maneuvers were executed at the phasing loop perigees to correct for launch vehicle errors and to target the lunar gravity assist so that a suitable orbit at L2 was achieved. This paper will discuss the maneuver planning process for designing, verifying, and executing MAP's maneuvers. A discussion of the tools and how they interacted will also be included. The maneuver planning process was iterative and crossed several disciplines, including trajectory design, attitude control, propulsion, power, thermal, communications, and ground planning. Several commercial, off-the-shelf (COTS) packages were used to design the maneuvers. STK/Astrogator was used as the trajectory design tool. All maneuvers were designed in Astrogator to ensure that the Moon was met at the correct time and orientation to provide the energy needed to achieve an orbit about L2. The Mathworks Matlab product was used to develop a tool for generating command quaternions. The command quaternion table (CQT) was used to drive the attitude during the perigee maneuvers. The MatrixX toolset, originally written by Integrated Systems, Inc., now distributed by Mathworks, was used to create HiFi, a high fidelity simulator of the MAP attitude control system. HiFi was used to test the CQT and to make sure that all attitude requirements were met during the maneuver. In addition, all ACS data plotting and output were generated in MatrixX. A final test used FlatSat, a real-time hardware-in-the-loop simulator, which used identical MAP flight code to simulate operations on the spacecraft. Simulations in FlatSat allowed the MAP team to verify maneuver commands, timing, and spacecraft configuration before the commands were sent up to the spacecraft for execution. The MAP maneuver team successfully pieced together all of these COTS tools for designing MAP's maneuvers and MAP is now collecting data at L2.

Mesarch, Michael A.↗

Autonomous navigation - The ARMMS concept

A conceptual design is outlined for the navigation subsystem of the Autonomous Redundancy and Maintenance Management Subsystem (ARMMS). The principal function of this navigation subsystem is to maintain the spacecraft over a specified equatorial longitude to within + or - 3 deg. In addition, the navigation subsystem must detect and correct internal faults. It comprises elements for a navigation executive and for orbit determination, trajectory, maneuver planning, and maneuver command. Each of these elements is described. The navigation subsystem is to be used in the DSCS III spacecraft.

Wood, L. J.↗

Halo orbit station keeping for International Sun-Earth Explorer-C /ISEE-C/

The ISEE-C spacecraft must be kept close to an unstable 'halo' orbit with a series of discrete orbital maneuvers set at intervals at least one month apart. A numerical algorithm has been developed to compute a velocity correction at any point on the trajectory which will minimize the distance between the satellite orbit and the nominal halo path. This algorithm is used to generate a number of station keeping histories with fixed time intervals between maneuvers to ascertain bounds on fuel cost, tightness of fit to nominal path and expected duration between thrust applications. The difference between a third order analytic representation of the halo orbit and a numerically improved nominal path as a reference orbit in the station keeping scheme is investigated as well as the distinction between a tight control and a loose control. A simulation of an operational approach to station keeping is also presented which shows that intermittant propulsive maneuvers can be used to control the spacecraft with very modest fuel expenditure.

Heuberger, H.↗

James Webb Space Telescope Initial Mid-Course Correction Monte Carlo Implementation using Task Parallelism

The James Webb Space Telescope will be launched into a highly elliptical orbit that does not possess sufficient energy to achieve a proper Sun-Earth L2 libration point orbit. Three mid-course correction (MCC) maneuvers are planned to rectify the energy deficit: MCC-1a, MCC-1b, and MCC-2. To validate the propellant budget and trajectory design methods, a set of Monte Carlo analyses that incorporate MCC maneuver modeling and execution are employed. The first analysis focuses on the effects of launch vehicle injection errors on the magnitude of MCC-1a. The second on the spread of potential V based on the performance of the propulsion system as applied to all three MCC maneuvers. The final highlights the slight, but notable, contribution of the attitude thrusters during each MCC maneuver. Given the possible variations in these three scenarios, the trajectory design methods are determined to be robust to errors in the modeling of the flight system.

Libration Point Orbit↗

James Webb Space Telescope Initial Mid-Course Correction Monte Carlo Implementation using Task Parallelism

The James Webb Space Telescope will be launched into a highly elliptical orbit that does not possess sufficient energy to achieve a proper Sun-Earth/Moon L2 libration point orbit. Three mid-course correction (MCC) maneuvers are planned to rectify the energy deficit: MCC-1a, MCC-1b, and MCC-2. To validate the propellant budget and trajectory design methods, a set of Monte Carlo analyses that incorporate MCC maneuver modeling and execution are employed. The first analysis focuses on the effects of launch vehicle injection errors on the magnitude of MCC-1a. The second on the spread of potential V based on the performance of the propulsion system as applied to all three MCC maneuvers. The final highlights the slight, but notable, contribution of the attitude thrusters during each MCC maneuver. Given the possible variations in these three scenarios, the trajectory design methods are determined to be robust to errors in the modeling of the flight system.

James Webb Space Telescope↗

JUNO navigation for Jupiter orbit insertion

Juno arrived at Jupiter on 05 July 2016 UTC, achieving orbit with the execution of the Jupiter Orbit Insertion (JOI) maneuver. Thanks to a dynamically wellbehaved spacecraft, the delivery of Juno to JOI was done largely with only a maneuver to setup and Earth gravity assist (EGA), an EGA, an EGA clean-up maneuver, and a JOI targeting maneuver. During the last several weeks of the approach to JOI, the dominant uncertainties in the predicted trajectory were from the Jupiter barycenter ephemeris. In this paper, we discuss the maneuver and orbit determination (OD) strategy for successfully arriving at JOI, the the challenges of calculating a correction to the Jupiter barycenter ephemeris using only radiometric data types, and how the ephemeris estimates during approach to JOI compare to a post-JOI trajectory reconstruction.

Takahashi, Yu↗

Nozomi Cis-Lunar Phase Orbit Determination

Japan's Institute of Space and Astronautical Science (ISAS) launched Nozomi, its first mission to the planet Mars using the newly developed M-V launch vehicle on July 3, 1998. Scientific objectives of the mission are to study the structure and dynamics of the Martian upper atmosphere and its interaction with the solar wind. Nozomi is a cooperative mission between ISAS and the National Aeronautics and Space Administration (NASA). The NASA contribution includes navigation and tracking services provided by the Jet Propulsion Laboratory (JPL). The spacecraft also serves as an engineering demonstration of basic technology for planetary exploration. One of the new technologies was a unique trajectory, developed by ISAS, which used solar gravitational perturbations at the weak stability boundary as an aid to achieve an Earth-Mars transfer orbit. This trajectory saves approximately 120 m/s of Delta V compared to direct hyperbolic insertion and is considered an enabling technology for the mission. Nozomi was the first spacecraft to employ this trajectory and provided on-orbit validation of the technique. The trajectory was achieved by initially placing the spacecraft in a highly elliptical cis-lunar phasing orbit. Six maneuvers were performed during this period to correct injection errors and target an outbound lunar swingby in September 1998. The gravity assist from the lunar swingby raised apogee to the vicinity of the weak stability boundary. After three more targeting maneuvers, Nozomi performed an inbound lunar swingby followed immediately by a powered Earth swingby in late December 1998. A 420 m/s Trans Mars Insertion (TMI) burn at the final Earth periapsis was intended to place the spacecraft on a heliocentric trajectory leading to Mars orbit insertion in October 1999. Orbit determination for Nozomi is performed in parallel by both ISAS and the Multi-Mission Navigation (MMNAV) group at JPL. This was an advantage for the mission because each group would generate solutions based on data collected from their respective tracking networks. Spacecraft events, such as sequence uplinks and maneuvers, were generally scheduled during passes at the Usuda tracking station in Japan. As a result, maneuver design and reconstruction was derived from MMNAV solutions based on JPL tracking data obtained immediately prior to or following maneuvers. Data was also exchanged between ISAS and MMNAV so orbit determination could be performed on joint data sets in support of critical targeting late in the cis-lunar phase. In this paper, information regarding the MMNAV orbit determination effort for the first six months of the mission is presented. The spacecraft trajectory is characterized first, followed by a discussion of the orbit determination estimation procedure and models. Results from selected orbit solutions are presented and compared against reconstructed trajectories. One area of emphasis in this paper is orbit determination in the vicinity of the weak stability boundary. Precise navigation was necessary to target the second lunar swingby and the powered Earth swingby. Delivery accuracy of 150 m was required for these critical encounters, but a number of factors contributed to the general degradation of orbit determination accuracy. This included the fact that the spacecraft was at apogee, at a range of 1.7 million km and moving at less than I km/sec perpendicular to the line of sight. Nozomi was also close to zero degrees declination where there are known limitations on orbit determination performance. Finally, S-band tracking data was acquired through the Nozomi backup low gain antenna. This antenna is offset from the axis of this spin stabilized spacecraft and superimposed large signatures in the Doppler and range data. These difficulties were overcome by combining long data arcs, spanning several maneuvers, with a high fidelity solar pressure model. The model included a physically accurate representation of the spacecraft structure and a high time resolution orientation model. Observation modeling included the removal of the spin induced Doppler bias, spin signature and per pass correction of range calibration errors applied for data leading up to critical events. As a result, all orbit determination goals were met. A second area of emphasis in this paper is the JPL tracking and orbit determination effort in support of the TMI maneuver. TMI occurred out of contact with ground stations and the JPL Goldstone tracking complex had the first pass following the bum. As a result, MMNAV had the responsibility to make a rapid assessment of the maneuver performance. MMNAV made the determination that a 100 m/s under bum had occurred and promptly informed ISAS via voice lines. ISAS immediately began preparations for a correction maneuver (TMIc), which had to be performed during the next Usuda pass. The near real time assessment by MMNAV provided accurate antenna frequency and pointing updates for the spacecraft acquisition at Usuda and the close coordination between the two agencies enabled the design and successful execution of the TMc maneuver. Propellant consumption during the correction burn dictated that the mission be redesigned. ISAS developed a new plan which adds 3 full solar orbits, two Earth swingbys and one lunar swingby with arrival at Mars in January 2004. The final Mars orbit will still enable the mission to achieve all of its science objectives.

Ryne, Mark↗

Worst-error analysis of batch filter and sequential filter in navigation problems

This paper proposes a worst-error analysis for dealing with problems of estimation of spacecraft trajectories in deep space missions. Navigation filters in use assume either constant or stochastic (Markov) models for their estimated parameters. When the actual behavior of these parameters does not follow the pattern of the assumed model, the filters sometimes result in very poor performance. To prepare for such pathological cases, the worst errors of both batch and sequential filters are investigated based on the incremental sensitivity studies of these filters. By finding critical switching instances of non-gravitational accelerations, intensive tracking can be carried out around those instances. Also the worst errors in the target plane provide a measure in assignment of the propellant budget for trajectory corrections. Thus the worst-error study presents useful information as well as practical criteria in establishing the maneuver and tracking strategy of spacecraft's missions.

Nishimura, T.↗

Robust Cislunar Trajectory Optimization Via Midcourse Correction and Optical Navigation Scheduling

This paper presents a new approach to optimal trajectory design that considers uncertainties in the system, referred to herein as robust trajectory optimization. This approach assumes an existing reference trajectory and optimizes the locations of midcourse correction burns and utilization of onboard navigation sensors to minimize dispersions in ∆v or final position. Navigation errors, maneuver execution errors, orbit insertion errors, and environmental modeling errors are considered. The application in this paper is cislunar flight with the goal of injecting into a Near-Rectilinear Halo Orbit for rendezvous with a target vehicle. Two complementary optimization problems are proposed. One problem minimizes the total ∆v dispersion subject to a final position dispersion constraint. The other problem minimizes the final position dispersion subject to a total ∆v dispersion constraint. The results from each optimization problem are shown for a complete mission profile.

Linear Covariance Analysis↗

Airdata calibration of a high-performance aircraft for measuring atmospheric wind profiles

The research airdata system of an instrumented F-104 aircraft has been calibrated to measure winds aloft in support of the space shuttle wind measurement investigation at the National Aeronautics and Space Administration Ames Research Center Dryden Flight Research Facility. For this investigation, wind measurement accuracies comparable to those obtained from Jimsphere balloons were desired. This required an airdata calibration more accurate than needed for most aircraft research programs. The F-104 aircraft was equipped with a research pilot-static noseboom with integral angle-of-attack and flank angle-of-attack vanes and a ring-laser-gyro inertial reference unit. Tower fly-bys and radar acceleration-decelerations were used to calibrate Mach number and total temperature. Angle of attack and angle of sideslip were calibrated with a trajectory reconstruction technique using a multiple-state linear Kalman filter. The F-104 aircraft and instrumentation configuration, flight test maneuvers, data corrections, calibration techniques, and resulting calibrations and data repeatability are presented. Recommendations for future airdata systems on aircraft used to measure winds aloft are also given.

Haering, Edward A., Jr.↗