Selected FDF White Papers

Transiting Exoplanet Survey Satellite (TESS) Flight Dynamics Commissioning Results and Experiences
The Transiting Exoplanet Survey Satellite (TESS) will perform the first-ever spaceborne all-sky exoplanet transit survey and is the first primary-mission application of a lunar-resonant orbit. Launched on April 18, 2018, TESS completed a two-month commissioning phase consisting of three phasing loops followed by a lunar flyby and a final maneuver to achieve resonance. During the mission orbit, no further station-keeping maneuvers are planned or required. NASA Goddard Space Flight Center is performing flight dynamics operations for the mission. This paper covers the design, implementation, and results from TESS commissioning, including the projected performance of the final mission orbit.

Preliminary Analysis of Ground-Based Orbit Determination Accuracy for the Wide Field Infrared Survey Telescope (WFIRST)
The Wide Field Infrared Survey Telescope is a 2.4-meter telescope planned for launch to the Sun-Earth L2 point in 2026. This paper details a preliminary study of the achievable accuracy for WFIRST from ground-based orbit determination routines. The analysis here is divided into two segments. First, a linear covariance analysis of early mission and routine operations provides an estimate of the tracking schedule required to meet mission requirements. Second, a simulated operations” scenario gives insight into the expected behavior of a daily Extended Kalman Filter orbit estimate over the first mission year given a variety of potential momentum unloading schemes.

Filter Tuning Using the Chi-Squared Statistic
This paper examines the use of the Chi-square statistic as a means of evaluating filter performance. The goal of the process is to characterize the filter performance in the metric of covariance realism. The Chi-squared statistic is the value calculated to determine the realism of a covariance based on the prediction accuracy and the covariance values at a given point in time. Once calculated, it is the distribution of this statistic that provides insight on the accuracy of the covariance. The process of tuning an Extended Kalman Filter (EKF) for Aqua and Aura support is described, including examination of the measurement errors of available observation types, and methods of dealing with potentially volatile atmospheric drag modeling. Predictive accuracy and the distribution of the Chi-squared statistic, calculated from EKF solutions, are assessed.

Orbit Determination for the Lunar Reconnaissance Orbiter Using an Extended Kalman Filter
Orbit determination (OD) analysis results are presented for the Lunar Reconnaissance Orbiter (LRO) using a commercially available Extended Kalman Filter, Analytical Graphics’ Orbit Determination Tool Kit (ODTK). Process noise models for lunar gravity and solar radiation pressure (SRP) are described and OD results employing the models are presented. Definitive accuracy using ODTK meets mission requirements and is better than that achieved using the operational LRO OD tool, the Goddard Trajectory Determination System (GTDS). Results demonstrate that a Vasicek stochastic model produces better estimates of the coefficient of solar radiation pressure than a Gauss-Markov model, and prediction accuracy using a Vasicek model meets mission requirements over the analysis span. Modeling the effect of antenna motion on range-rate tracking considerably improves residuals and filter-smoother consistency. Inclusion of off-axis SRP process noise and generalized process noise improves filter performance for both definitive and predicted accuracy. Definitive accuracy from the smoother is better than achieved using GTDS and is close to that achieved by precision OD methods used to generate definitive science orbits. Use of a multi-plate dynamic spacecraft area model with ODTK’s force model plugin capability provides additional improvements in predicted accuracy.

Orbit Determination Accuracy Analysis of the Magnetospheric Multiscale Mission During Perigee Raise
The Goddard Space Flight Center (GSFC) Flight Dynamics Facility (FDF) will provide orbit determination and prediction support for the Magnetospheric Multiscale (MMS) mission during the missions commissioning period. The spacecraft will launch into a highly elliptical Earth orbit in 2015. Starting approximately four days after launch, a series of five large perigee-raising maneuvers will be executed near apogee on a nearly every-other-orbit cadence. This perigee-raise operations concept requires a high-accuracy estimate of the orbital state within one orbit following the maneuver for performance evaluation and a high-accuracy orbit prediction to correctly plan and execute the next maneuver in the sequence. During early mission design, a linear covariance analysis method was used to study orbit determination and prediction accuracy for this perigee-raising campaign. This paper provides a higher fidelity Monte Carlo analysis using the operational COTS extended Kalman filter implementation that was performed to validate the linear covariance analysis estimates and to better characterize orbit determination performance for actively maneuvering spacecraft in a highly elliptical orbit. The study finds that the COTS extended Kalman filter tool converges on accurate definitive orbit solutions quickly, but prediction accuracy through orbits with very low altitude perigees is degraded by the unpredictability of atmospheric density variation.

Lunar Reconnaissance Orbiter Orbit Determination Accuracy Analysis
LRO definitive and predictive accuracy requirements were easily met in the nominal mission orbit, using the LP150Q lunar gravity model. center dot Accuracy of the LP150Q model is poorer in the extended mission elliptical orbit. center dot Later lunar gravity models, in particular GSFC-GRAIL-270, improve OD accuracy in the extended mission. center dot Implementation of a constrained plane when the orbit is within 45 degrees of the Earth-Moon line improves cross-track accuracy. center dot Prediction accuracy is still challenged during full-Sun periods due to coarse spacecraft area modeling – Implementation of a multi-plate area model with definitive attitude input can eliminate prediction violations. – The FDF is evaluating using analytic and predicted attitude modeling to improve full-Sun prediction accuracy. center dot Comparison of FDF ephemeris file to high-precision ephemeris files provides gross confirmation that overlap compares properly assess orbit accuracy.

Improving Fermi Orbit Determination and Prediction in an Uncertain Atmospheric Drag Environment
Orbit determination and prediction of the Fermi Gamma-ray Space Telescope trajectory is strongly impacted by the unpredictability and variability of atmospheric density and the spacecraft’s ballistic coefficient. Operationally, Global Positioning System point solutions are processed with an extended Kalman filter for orbit determination, and predictions are generated for conjunction assessment with secondary objects. When these predictions are compared to Joint Space Operations Center radar-based solutions, the close approach distance between the two predictions can greatly differ ahead of the conjunction. This work explores strategies for improving prediction accuracy and helps to explain the prediction disparities. Namely, a tuning analysis is performed to determine atmospheric drag modeling and filter parameters that can improve orbit determination as well as prediction accuracy. A 45% improvement in three-day prediction accuracy is realized by tuning the ballistic coefficient and atmospheric density stochastic models, measurement frequency, and other modeling and filter parameters.

Lunar Reconnaissance Orbiter Orbit Determination Accuracy Analysis
Results from operational OD produced by the NASA Goddard Flight Dynamics Facility for the LRO nominal and extended mission are presented. During the LRO nominal mission, when LRO flew in a low circular orbit, orbit determination requirements were met nearly 100% of the time. When the extended mission began, LRO returned to a more elliptical frozen orbit where gravity and other modeling errors caused numerous violations of mission accuracy requirements. Prediction accuracy is particularly challenged during periods when LRO is in full-Sun. A series of improvements to LRO orbit determination are presented, including implementation of new lunar gravity models, improved spacecraft solar radiation pressure modeling using a dynamic multi-plate area model, a shorter orbit determination arc length, and a constrained plane method for estimation. The analysis presented in this paper shows that updated lunar gravity models improved accuracy in the frozen orbit, and a multiplate dynamic area model improves prediction accuracy during full-Sun orbit periods. Implementation of a 36-hour tracking data arc and plane constraints during edge-on orbit geometry also provide benefits. A comparison of the operational solutions to precision orbit determination solutions shows agreement on a 100- to 250-meter level in definitive accuracy.