ALBERT

Description: Modem orbit determination has mostly been accomplished using Cartesian coordinates. This usage has carried over in recent years to the use of GPS for satellite orbit determination. The unprecedented positioning accuracy of GPS has tended to focus attention more on the system's capability to locate the spacecraft's location at a particular epoch than on its accuracy in determination of the orbit, per se. As is well-known, the latter depends on a coordinated knowledge of position, velocity, and the correlation between their errors. Failure to determine a properly coordinated position/velocity state vector at a given epoch can lead to an epoch state that does not propagate well, and/or may not be usable for the execution of orbit adjustment maneuvers. For the quite common case of near-circular orbits, the degree to which position and velocity estimates are properly coordinated is largely captured by the error in semi-major axis (SMA) they jointly produce. Figure 1 depicts the relationships among radius error, speed error, and their correlation which exist for a typical low altitude Earth orbit. Two familiar consequences are the relationship Figure 1 shows are the following: (1) downrange position error grows at the per orbit rate of 3(pi) times the SMA error; (2) a velocity change imparted to the orbit will have an error of (pi) divided by the orbit period times the SMA error. A less familiar consequence occurs in the problem of initializing the covariance matrix for a sequential orbit determination filter. An initial covariance consistent with orbital dynamics should be used if the covariance is to propagate well. Properly accounting for the SMA error of the initial state in the construction of the initial covariance accomplishes half of this objective, by specifying the partition of the covariance corresponding to down-track position and radial velocity errors. The remainder of the in-plane covariance partition may be specified in terms of the flight path angle error of the initial state. Figure 2 illustrates the effect of properly and not properly initializing a covariance. This figure was produced by propagating the covariance shown on the plot, without process noise, in a circular low Earth orbit whose period is 5828.5 seconds. The upper subplot, in which the proper relationships among position, velocity, and their correlation has been used, shows overall error growth, in terms of the standard deviations of the inertial position coordinates, of about half of the lower subplot, whose initial covariance was based on other considerations.

Description: Goddard Space Flight Center is currently developing advanced spacecraft systems to provide autonomous navigation and control of formation flyers. This paper discusses autonomous relative navigation performance for formations in eccentric, medium, and high-altitude Earth orbits using Global Positioning System (GPS) Standard Positioning Service (SPS) and intersatellite range measurements. The performance of several candidate relative navigation approaches is evaluated. These analyses indicate that the relative navigation accuracy is primarily a function of the frequency of acquisition and tracking of the GPS signals. A relative navigation position accuracy of 0.5 meters root-mean-square (RMS) can be achieved for formations in medium-attitude eccentric orbits that can continuously track at least one GPS signal. A relative navigation position accuracy of better than 75 meters RMS can be achieved for formations in high-altitude eccentric orbits that have sparse tracking of the GPS signals. The addition of round-trip intersatellite range measurements can significantly improve relative navigation accuracy for formations with sparse tracking of the GPS signals.

Description: No abstract available

Description: Flight data from an entry, descent, and landing (EDL) sequence can be used to reconstruct the vehicle's trajectory, aerodynamic coefficients and the atmospheric profile experienced by the vehicle. Past Mars missions have contained instruments that do not provide direct measurement of the freestream atmospheric conditions. Thus, the uncertainties in the atmospheric reconstruction and the aerodynamic database knowledge could not be separated. The upcoming Mars Science Laboratory (MSL) will take measurements of the pressure distribution on the aeroshell forebody during entry and will allow freestream atmospheric conditions to be partially observable. This data provides a mean to separate atmospheric and aerodynamic uncertainties and is part of the MSL EDL Instrumentation (MEDLI) project. Methods to estimate the flight performance statistically using on-board measurements are demonstrated here through the use of simulated Mars data. Different statistical estimators are used to demonstrate which estimator best quantifies the uncertainties in the flight parameters. The techniques demonstrated herein are planned for application to the MSL flight dataset after the spacecraft lands on Mars in August 2012.

Description: Seven studies have been conducted on research in the existence and nature of solutions of the restricted problems of three and four bodies. The details and results of five of these research investigations have already been published, and the latest two studies will be published shortly. A complete bibliography of publications is included in this report. This research has been primarily qualitative and has yielded new information on the behavior of trajectories near the libration points in the Earth-Moon-Sun and Sun-Jupiter-Saturn systems, and on the existence of periodic trajectories about the libration points of the circular and elliptical restricted four-body models. We have also implemented Birkhoff's normalization process for conservative and nonconservative Hamiltonian systems with equilibrium points. This makes available a technique for analyzing stability properties of certain nonlinear dynamical systems, and we have applied this technique to the circular and elliptical restricted three-body models. A related study was also conducted to determine the feasibility of using cislunar periodic trajectories for various space missions. Preliminary results suggest that this concept is attractive for space flight safety operations in cislunar space. Results of this research will be of interest to mathematicians, particularly those working in ordinary differential equations, dynamical systems and celestial mechanics; to astronomers; and to space guidance and mission analysts.

Description: We propose a filter bank consisting of an ordinary current-state extended Kalman filter, and two similar but constrained filters: one is constrained by a null hypothesis that the miss distance between two conjuncting spacecraft is inside their combined hard body radius at the predicted time of closest approach, and one is constrained by an alternative complementary hypothesis. The unconstrained filter is the basis of an initial screening for close approaches of interest. Once the initial screening detects a possibly risky conjunction, the unconstrained filter also governs measurement editing for all three filters, and predicts the time of closest approach. The constrained filters operate only when conjunctions of interest occur. The computed likelihoods of the innovations of the two constrained filters form a ratio for a Wald sequential probability ratio test. The Wald test guides risk mitigation maneuver decisions based on explicit false alarm and missed detection criteria. Since only current-state Kalman filtering is required to compute the innovations for the likelihood ratio, the present approach does not require the mapping of probability density forward to the time of closest approach. Instead, the hard-body constraint manifold is mapped to the filter update time by applying a sigma-point transformation to a projection function. Although many projectors are available, we choose one based on Lambert-style differential correction of the current-state velocity. We have tested our method using a scenario based on the Magnetospheric Multi-Scale mission, scheduled for launch in late 2014. This mission involves formation flight in highly elliptical orbits of four spinning spacecraft equipped with antennas extending 120 meters tip-to-tip. Eccentricities range from 0.82 to 0.91, and close approaches generally occur in the vicinity of perigee, where rapid changes in geometry may occur. Testing the method using two 12,000-case Monte Carlo simulations, we found the method achieved a missed detection rate of 0.1%, and a false alarm rate of 2%.

Description: This paper summarizes the results of processing GPS data from the AMSAT Phase 3D (AP3) satellite for real-time navigation and post-processed orbit determination experiments. AP3 was launched into a geostationary transfer orbit (GTO) on November 16, 2000 from Kourou, French Guiana, and then was maneuvered into its HEO over the next several months. It carries two Trimble TANS Vector GPS receivers for signal reception at apogee and at perigee. Its spin stabilization mode currently makes it favorable to track GPS satellites from the backside of the constellation while at perigee, and to track GPS satellites from below while at perigee. To date, the experiment has demonstrated that it is feasible to use GPS for navigation and orbit determination in HEO, which will be of great benefit to planned and proposed missions that will utilize such orbits for science observations. It has also shown that there are many important operational considerations to take into account. For example, GPS signals can be tracked above the constellation at altitudes as high as 58000 km, but sufficient amplification of those weak signals is needed. Moreover, GPS receivers can track up to 4 GPS satellites at perigee while moving as fast as 9.8 km/sec, but unless the receiver can maintain lock on the signals long enough, point solutions will be difficult to generate. The spin stabilization of AP3, for example, appears to cause signal levels to fluctuate as other antennas on the satellite block the signals. As a result, its TANS Vectors have been unable to lock on to the GPS signals long enough to down load the broadcast ephemeris and then generate position and velocity solutions. AP3 is currently in its eclipse season, and thus most of the spacecraft subsystems have been powered off. In Spring 2002, they will again be powered up and AP3 will be placed into a three-axis stabilization mode. This will significantly enhance the likelihood that point solutions can be generated, and perhaps more important, that the receiver clock can be synchronized to GPS time. This is extremely important for real-time and post-processed orbit determination, where removal of receiver clock bias from the data time tags is needed, for time-tagging of science observations. Current analysis suggests that the inability to generate point solutions has allowed the TANS Vector clock bias to drift freely, being perhaps as large as 5-7 seconds by October, 2001, thus causing up to 50 km of along-track orbit error. The data collected in May, 2002 while in three-axis stabilized mode should provide a significant improvement in the orbit determination results.

Description: A global grid search is performed to find axi= and doubly=symmetric periodic orbits in the Restricted Three Body Problem using the dimensioned parameters associated with the Jupiter-Europa system.

Description: 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.

Description: The filter/smoother combination provides the most accurate means of trajectory reconstruction. Not all parameters of interest can be determined from a given flight test data set: need to check observability. A variety of ground & onboard sensors may be used; trend appears to be toward increasing reliance on onboard GPS.