Engineering topics

Carpenter, J. Russell

Publications and source records attributed to Carpenter, J. Russell.

At least 37 records · Page 2

NASA NTRS2012

Statistical Orbit Determination using the Particle Filter for Incorporating Non-Gaussian Uncertainties

The tracking of space objects requires frequent and accurate monitoring for collision avoidance. As even collision events with very low probability are important, accurate prediction of collisions require the representation of the full probability density function (PDF) of the random orbit state. Through representing the full PDF of the orbit state for orbit maintenance and collision avoidance, we can take advantage of the statistical information present in the heavy tailed distributions, more accurately representing the orbit states with low probability. The classical methods of orbit determination (i.e. Kalman Filter and its derivatives) provide state estimates based on only the second moments of the state and measurement errors that are captured by assuming a Gaussian distribution. Although the measurement errors can be accurately assumed to have a Gaussian distribution, errors with a non-Gaussian distribution could arise during propagation between observations. Moreover, unmodeled dynamics in the orbit model could introduce non-Gaussian errors into the process noise. A Particle Filter (PF) is proposed as a nonlinear filtering technique that is capable of propagating and estimating a more complete representation of the state distribution as an accurate approximation of a full PDF. The PF uses Monte Carlo runs to generate particles that approximate the full PDF representation. The PF is applied in the estimation and propagation of a highly eccentric orbit and the results are compared to the Extended Kalman Filter and Splitting Gaussian Mixture algorithms to demonstrate its proficiency.

Mashiku, Alinda↗

NASA NTRS2012

Linear Covariance Analysis and Epoch State Estimators

This paper extends in two directions the results of prior work on generalized linear covariance analysis of both batch least-squares and sequential estimators. The first is an improved treatment of process noise in the batch, or epoch state, estimator with an epoch time that may be later than some or all of the measurements in the batch. The second is to account for process noise in specifying the gains in the epoch state estimator. We establish the conditions under which the latter estimator is equivalent to the Kalman filter.

Markley, F. Landis↗

NASA NTRS2011

Sensitivity of Magnetospheric Multi-Scale (MMS) Mission Naviation Accuracy to Major Error Sources

The Magnetospheric Multiscale (MMS) mission consists of four satellites flying in formation in highly elliptical orbits about the Earth, with a primary objective of studying magnetic reconnection. The baseline navigation concept is independent estimation of each spacecraft state using GPS pseudorange measurements referenced to an Ultra Stable Oscillator (USO) with accelerometer measurements included during maneuvers. MMS state estimation is performed onboard each spacecraft using the Goddard Enhanced Onboard Navigation System (GEONS), which is embedded in the Navigator GPS receiver. This paper describes the sensitivity of MMS navigation performance to two major error sources: USO clock errors and thrust acceleration knowledge errors.

Olson, Corwin↗

NASA NTRS2010

Sequential Probability Ratio Test for Collision Avoidance Maneuver Decisions

When facing a conjunction between space objects, decision makers must chose whether to maneuver for collision avoidance or not. We apply a well-known decision procedure, the sequential probability ratio test, to this problem. We propose two approaches to the problem solution, one based on a frequentist method, and the other on a Bayesian method. The frequentist method does not require any prior knowledge concerning the conjunction, while the Bayesian method assumes knowledge of prior probability densities. Our results show that both methods achieve desired missed detection rates, but the frequentist method's false alarm performance is inferior to the Bayesian method's

Carpenter, J. Russell↗

NASA NTRS2010

Guidance and Navigation for Rendezvous and Proximity Operations with a Non-Cooperative Spacecraft at Geosynchronous Orbit

The feasibility and benefits of various spacecraft servicing concepts are currently being assessed, and all require that the servicer spacecraft perform rendezvous, proximity, and capture operations with the target spacecraft to be serviced. Many high-value spacecraft, which would be logical targets for servicing from an economic point of view, are located in geosynchronous orbit, a regime in which autonomous rendezvous and capture operations are not commonplace. Furthermore, existing GEO spacecraft were not designed to be serviced. Most do not have cooperative relative navigation sensors or docking features, and some servicing applications, such as de-orbiting of a non-functional spacecraft, entail rendezvous and capture with a spacecraft that may be non-functional or un-controlled. Several of these challenges have been explored via the design of a notional mission in which a nonfunctional satellite in geosynchronous orbit is captured by a servicer spacecraft and boosted into super-synchronous orbit for safe disposal. A strategy for autonomous rendezvous, proximity operations, and capture is developed, and the Orbit Determination Toolbox (ODTBX) is used to perform a relative navigation simulation to assess the feasibility of performing the rendezvous using a combination of angles-only and range measurements. Additionally, a method for designing efficient orbital rendezvous sequences for multiple target spacecraft is utilized to examine the capabilities of a servicer spacecraft to service multiple targets during the course of a single mission.

Barbee, Brent William↗

NASA NTRS2008

Generalized Linear Covariance Analysis

We review and extend in two directions the results of prior work on generalized covariance analysis methods. This prior work allowed for partitioning of the state space into "solve-for" and "consider" parameters, allowed for differences between the formal values and the true values of the measurement noise, process noise, and a priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and a priori solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator s anchor time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the "variance sandpile" and the "sensitivity mosaic," and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.

Carpenter, J. Russell↗

NASA NTRS2007

A Concept for In-space, System-level Validation of Spacecraft Precision Formation Flying

A number of international space agencies and organizations, to include the National Aeronautics and Space Administration (NASA), the European Space Agency (ESA), and the Centre National d'Etudes Spatiales (CNES), to name a few, have embraced the concept of spacecraft formation flying to revolutionize the capabilities of astronomy and Earth remote sensing from space. The concept has been around well over a decade and a wide array of technologies and capabilities have been developed to enable multiple spacecraft to collaborate in a highly-coupled manner as would be required for a formation flying mission. Furthermore, many relevant capabilities for formation flying have been demonstrated in the area of rendezvous and docking, loosely-controlled formations, and in missions with collaborating spacecraft with very precise metrology. .However, in considering the case of precision formation flying (PFF), i.e, when the relative geometry of multiple vehicles must be controlled on-board in a continuous and precise manner, there have been several missions proposed, but the realization in space has not yet occurred due to a range of issues. This paper will briefly examine those issues and present a concept for demonstrating a core capability for performing PFF, necessary for virtually any PFF mission concept, that will help to overcome the problems encountered in prior attempts and help to allay the risks to enable future PFF science missions.

Leitner, Jesse↗

NASA NTRS2007

Non-Parametric Collision Probability for Low-Velocity Encounters

An implicit, but not necessarily obvious, assumption in all of the current techniques for assessing satellite collision probability is that the relative position uncertainty is perfectly correlated in time. If there is any mis-modeling of the dynamics in the propagation of the relative position error covariance matrix, time-wise de-correlation of the uncertainty will increase the probability of collision over a given time interval. The paper gives some examples that illustrate this point. This paper argues that, for the present, Monte Carlo analysis is the best available tool for handling low-velocity encounters, and suggests some techniques for addressing the issues just described. One proposal is for the use of a non-parametric technique that is widely used in actuarial and medical studies. The other suggestion is that accurate process noise models be used in the Monte Carlo trials to which the non-parametric estimate is applied. A further contribution of this paper is a description of how the time-wise decorrelation of uncertainty increases the probability of collision.

Carpenter, J. Russell↗

NASA NTRS2005

Hardware in-the-Loop Demonstration of Real-Time Orbit Determination in High Earth Orbits

This paper presents results from a study conducted at Goddard Space Flight Center (GSFC) to assess the real-time orbit determination accuracy of GPS-based navigation in a number of different high Earth orbital regimes. Measurements collected from a GPS receiver (connected to a GPS radio frequency (RF) signal simulator) were processed in a navigation filter in real-time, and resulting errors in the estimated states were assessed. For the most challenging orbit simulated, a 12 hour Molniya orbit with an apogee of approximately 39,000 km, mean total position and velocity errors were approximately 7 meters and 3 mm/s respectively. The study also makes direct comparisons between the results from the above hardware in-the-loop tests and results obtained by processing GPS measurements generated from software simulations. Care was taken to use the same models and assumptions in the generation of both the real-time and software simulated measurements, in order that the real-time data could be used to help validate the assumptions and models used in the software simulations. The study makes use of the unique capabilities of the Formation Flying Test Bed at GSFC, which provides a capability to interface with different GPS receivers and to produce real-time, filtered orbit solutions even when less than four satellites are visible. The result is a powerful tool for assessing onboard navigation performance in a wide range of orbital regimes, and a test-bed for developing software and procedures for use in real spacecraft applications.

Moreau, Michael↗

NASA NTRS2004

Conservative Analytical Collision Probabilities for Orbital Formation Flying

The literature offers a number of approximations for analytically and/or efficiently computing the probability of collision between two space objects. However, only one of these techniques is a completely analytical approximation that is suitable for use in the preliminary design phase, when it is more important to quickly analyze a large segment of the trade space than it is to precisely compute collision probabilities. Unfortunately, among the types of formations that one might consider, some combine a range of conditions for which this analytical method is less suitable. This work proposes a simple, conservative approximation that produces reasonable upper bounds on the collision probability in such conditions. Although its estimates are much too conservative under other conditions, such conditions are typically well suited for use of the existing method.

Carpenter, J. Russell↗

NASA NTRS2004

Libration Point Navigation Concepts Supporting Exploration Vision

Farquhar described several libration point navigation concepts that would appear to support NASA s current exploration vision. One concept is a Lunar Relay Satellite operating in the vicinity of Earth-Moon L2, providing Earth-to-lunar far-side and long- range surface-to-surface navigation and communications capability. Reference [ 1] lists several advantages of such a system in comparison to a lunar orbiting relay satellite constellation. Among these are one or two vs. many satellites for coverage, simplified acquisition and tracking due to very low relative motion, much longer contact times, and simpler antenna pointing. An obvious additional advantage of such a system is that uninterrupted links to Earth avoid performing critical maneuvers "in the blind." Another concept described is the use of Earth-Moon L1 for lunar orbit rendezvous, rather than low lunar orbit as was done for Apollo. This rendezvous technique would avoid large plane change and high fuel cost associated with high latitude landing sites and long stay times. Earth-Moon L1 also offers unconstrained launch windows from the lunar surface. Farquhar claims this technique requires only slightly higher fuel cost than low lunar orbit rendezvous for short-stay equatorial landings. Farquhar also describes an Interplanetary Transportation System that would use libration points as terminals for an interplanetary shuttle. This approach would offer increased operational flexibility in terms of launch windows, rendezvous, aborts, etc. in comparison to elliptical orbit transfers. More recently, other works including Folta[3] and Howell[4] have shown that patching together unstable trajectories departing Earth-Moon libration points with stable trajectories approaching planetary libration points may also offer lower overall fuel costs than elliptical orbit transfers. Another concept Farquhar described was a Deep Space Relay at Earth-Moon IA and/or L5 that would serve as a high data rate optical navigation and communications relay satellite. The advantages in comparison to a geosynchronous relay are minimal Earth occultation, distance from large noise sources on Earth, easier pointing due to smaller relative velocity, and a large baseline for interferometry if both L4 and L5 are used.

Carpenter, J. Russell↗

NASA NTRS2004

Navigation Accuracy Guidelines for Orbital Formation Flying

Some simple guidelines based on the accuracy in determining a satellite formation s semi-major axis differences are useful in making preliminary assessments of the navigation accuracy needed to support such missions. These guidelines are valid for any elliptical orbit, regardless of eccentricity. Although maneuvers required for formation establishment, reconfiguration, and station-keeping require accurate prediction of the state estimate to the maneuver time, and hence are directly affected by errors in all the orbital elements, experience has shown that determination of orbit plane orientation and orbit shape to acceptable levels is less challenging than the determination of orbital period or semi-major axis. Furthermore, any differences among the member s semi-major axes are undesirable for a satellite formation, since it will lead to differential along-track drift due to period differences. Since inevitable navigation errors prevent these differences from ever being zero, one may use the guidelines this paper presents to determine how much drift will result from a given relative navigation accuracy, or conversely what navigation accuracy is required to limit drift to a given rate. Since the guidelines do not account for non-two-body perturbations, they may be viewed as useful preliminary design tools, rather than as the basis for mission navigation requirements, which should be based on detailed analysis of the mission configuration, including all relevant sources of uncertainty.

Carpenter, J. Russell↗

NASA NTRS2004

Lunar Navigation with Libration Point Orbiters and GPS

NASA is currently studying a Vision for Space Exploration based on spiral development of robotic and piloted missions to the moon and Mars, but research into how to perform such missions has continued ever since the first era of lunar exploration. One area of study that a number of researchers have pursued is libration point navigation and communication relay concepts. These concepts would appear to support many of NASA's current requirements for navigation and communications coverage for human and robotic spacecraft operating in lunar space and beyond. In trading libration point concepts against other options, designers must consider issues such as the number of spacecraft, required to provide coverage, insertion and stationkeeping costs, power and data rate requirements, frequency allocations, and many others. The libration points, along with a typical cis-lunar trajectory, are equilibrium locations for an infinitesimal mass in the rotating coordinate system that follows the motion of two massive bodies in circular orbits with respect to their common barycenter. There are three co-linear points along the line connecting the massive bodies: between the bodies, beyond the secondary body, and beyond the primary body. The relative distances of these points along the line connecting the bodies depend on the mass ratios. There are also two points that form equilateral triangles with the massive bodies. Ideally, motion in the neighborhood of the co-linear points is unstable, while motion near the equilibrium points is stable. However, in the real world, the motions are highly perturbed so that a satellite will require stationkeeping maneuvers.

Carpenter, J. Russell↗

NASA NTRS2004

Conservative Analytical Collision Probability for Design of Orbital Formations

Carpenter, J. Russell↗

NASA NTRS2004

Libration Point Navigation Concepts Supporting the Vision for Space Exploration

This work examines the autonomous navigation accuracy achievable for a lunar exploration trajectory from a translunar libration point lunar navigation relay satellite, augmented by signals from the Global Positioning System (GPS). We also provide a brief analysis comparing the libration point relay to lunar orbit relay architectures, and discuss some issues of GPS usage for cis-lunar trajectories.

Carpenter, J. Russell↗

NASA NTRS2003

Benchmark Problems for Spacecraft Formation Flying Missions

To provide high-level focus to distributed space system flight dynamics and control research, several benchmark problems are suggested. These problems are not specific to any current or proposed mission, but instead are intended to capture high-level features that would be generic to many similar missions.

Carpenter, J. Russell↗

NASA NTRS2003

Benchmark Problems for Space Mission Formation Flying

To provide a high-level focus to distributed space system flight dynamics and control research, several benchmark problems are suggested for space mission formation flying. The problems cover formation flying in low altitude, near-circular Earth orbit, high altitude, highly elliptical Earth orbits, and large amplitude lissajous trajectories about co-linear libration points of the Sun-Earth/Moon system. These problems are not specific to any current or proposed mission, but instead are intended to capture high-level features that would be generic to many similar missions that are of interest to various agencies.

Carpenter, J. Russell↗

NASA NTRS2003

Navigation Guidelines for Orbital Formation Flying Missions

Some simple guidelines based on the accuracy in determining a satellite formation's semi-major axis differences are useful in making preliminary assessments of the navigation accuracy needed to support such missions. These guidelines are valid for any elliptical orbit, regardless of eccentricity. Although maneuvers required for formation establishment, reconfiguration, and station-keeping require accurate prediction of the state estimate to the maneuver time, and hence are directly affected by errors in all the orbital elements, experience has shown that determination of orbit plane orientation and orbit shape to acceptable levels is less challenging than the determination of orbital period or semi-major axis. Furthermore, any differences among the member's semi-major axis are undesirable for a satellite formation, since it will lead to differential along-track drift due to period differences. Since inevitable navigation errors prevent these differences from ever being zero, one may use the guidelines this paper presents to determine how much drift will result from a given relative navigation accuracy, or vice versa. Since the guidelines do not account for non-two-body perturbations, they may be viewed as useful preliminary design tools, rather than as the basis for mission navigation requirements, which should be based on detailed analysis of the mission configuration, including all relevant sources of uncertainty.

Carpenter, J. Russell↗