Adapting Covariance Propagation to Account for the Presence of Modeled and Unmodeled Maneuvers

This paper explores techniques that can be used to adapt the standard linearized propagation of an orbital covariance matrix to the case where there is a maneuver and an associated execution uncertainty. A Monte Carlo technique is used to construct a final orbital covariance matrix for a 'prop-burn-prop' process that takes into account initial state uncertainty and execution uncertainties in the maneuver magnitude. This final orbital covariance matrix is regarded as 'truth' and comparisons are made with three methods using modified linearized covariance propagation. The first method accounts for the maneuver by modeling its nominal effect within the state transition matrix but excludes the execution uncertainty by omitting a process noise matrix from the computation. The second method does not model the maneuver but includes a process noise matrix to account for the uncertainty in its magnitude. The third method, which is essentially a hybrid of the first two, includes the nominal portion of the maneuver via the state transition matrix and uses a process noise matrix to account for the magnitude uncertainty. The first method is unable to produce the final orbit covariance except in the case of zero maneuver uncertainty. The second method yields good accuracy for the final covariance matrix but fails to model the final orbital state accurately. Agreement between the simulated covariance data produced by this method and the Monte Carlo truth data fell within 0.5-2.5 percent over a range of maneuver sizes that span two orders of magnitude (0.1-20 m/s). The third method, which yields a combination of good accuracy in the computation of the final covariance matrix and correct accounting for the presence of the maneuver in the nominal orbit, is the best method for applications involving the computation of times of closest approach and the corresponding probability of collision, PC. However, applications for the two other methods exist and are briefly discussed. Although the process model ("prop-burn-prop") that was studied is very simple - point-mass gravitational effects due to the Earth combined with an impulsive delta-V in the velocity direction for the maneuver - generalizations to more complex scenarios, including high fidelity force models, finite duration maneuvers, and maneuver pointing errors, are straightforward and are discussed in the conclusion

GPS Based Autonomous Navigation Study for the Lunar Gateway

This paper describes and predicts the performance of a conceptual autonomous GPS-based navigation system for NASA's planned lunar Gateway. This system is based on the flight-proven Magnetospheric Multiscale (MMS) GPS navigation system, augmented with an earth-pointed high-gain antenna and with an option for an atomic clock. High-fidelity simulations, calibrated against MMS flight data and making use of GPS transmitter patterns from the GPS Antenna Characterization Experiment (ACE) project are developed for operation of the system in the Gateway Near-Rectilinear Halo Orbit (NRHO). The results indicate that GPS can provide an autonomous, realtime navigation capability with comparable, or superior, performance to traditional Deep Space Network approach with eight hours of tracking per day

Relative navigation for spacecraft formation flying

The Goddard Space Flight Center Guidance, Navigation, and Control Center (GNCC) is currently developing and implementing advanced satellite systems to provide autonomous control of formation flyers. The initial formation maintenance capability will be flight-demonstrated on the Earth-Orbiter-1 (EO-1) satellite, which is planned under the National Aeronautics and Space Administration New Millennium Program to be a coflight with the Landsat-7 (L-7) satellite. Formation flying imposes relative navigation accuracy requirements in addition to the orbit accuracy requirements for the individual satellites. In the case of EO-1 and L-7, the two satellites are in nearly coplanar orbits, with a small difference in the longitude of the ascending node to compensate for the Earth's rotation. The GNCC has performed trajectory error analysis for the relative navigation of the EO-1/L-7 formation, as well as for a more advanced tracking configuration using cross-link satellite communications. This paper discusses the orbit determination and prediction accuracy achievable for EO-1 and L-7 under various tracking and orbit determination scenarios and discusses the expected relative separation errors in their formation flying configuration

Lattice Dynamics in the FeSb₃ Skutterudite

Thin films of FeSb3 were characterized by electronic transport, magnetometry, x-ray diffraction, 57Fe and 121Sb nuclear inelastic scattering, and 57Fe Mössbauer spectroscopy. Resistivity and magnetometry measurements reveal semiconducting behavior with a 16.3(4) meV band gap and an effective paramagnetic moment of 0.57(6) B, respectively. A systematic comparison of the lattice dynamics with CoSb3 and EuFe 4Sb12 reveals that the Fe4Sb12 framework is softer than the Co4Sb12 framework, and that the observed softening and the associated lowering of the lattice thermal conductivity in the RFe4Sb12 filled skutterudites are not only related to the filler but also to the Fe4Sb12 framework

Virtual Constraints and Hybrid Zero Dynamics for Realizing Underactuated Bipedal Locomotion

Underactuation is ubiquitous in human locomotion and should be ubiquitous in bipedal robotic locomotion as well. This chapter presents a coherent theory for the design of feedback controllers that achieve stable walking gaits in underactuated bipedal robots. Two fundamental tools are introduced, virtual constraints and hybrid zero dynamics. Virtual constraints are relations on the state variables of a mechanical model that are imposed through a time-invariant feedback controller. One of their roles is to synchronize the robot's joints to an internal gait phasing variable. A second role is to induce a low dimensional system, the zero dynamics, that captures the underactuated aspects of a robot's model, without any approximations. To enhance intuition, the relation between physical constraints and virtual constraints is first established. From here, the hybrid zero dynamics of an underactuated bipedal model is developed, and its fundamental role in the design of asymptotically stable walking motions is established. The chapter includes numerous references to robots on which the highlighted techniques have been implemented.Comment: 17 pages, 4 figures, bookchapte

Multi-donor × elite-based populations reveal QTL for low-lodging wheat

Low-lodging high-yielding wheat germplasm and SNP-tagged novel alleles for lodging were identified in a process that involved selecting donors through functional phenotyping for underlying traits with a designed phenotypic screen, and a crossing strategy involving multiple-donor × elite populations

Pain assessment for people with dementia: a systematic review of systematic reviews of pain assessment tools.

BACKGROUND: There is evidence of under-detection and poor management of pain in patients with dementia, in both long-term and acute care. Accurate assessment of pain in people with dementia is challenging and pain assessment tools have received considerable attention over the years, with an increasing number of tools made available. Systematic reviews on the evidence of their validity and utility mostly compare different sets of tools. This review of systematic reviews analyses and summarises evidence concerning the psychometric properties and clinical utility of pain assessment tools in adults with dementia or cognitive impairment. METHODS: We searched for systematic reviews of pain assessment tools providing evidence of reliability, validity and clinical utility. Two reviewers independently assessed each review and extracted data from them, with a third reviewer mediating when consensus was not reached. Analysis of the data was carried out collaboratively. The reviews were synthesised using a narrative synthesis approach. RESULTS: We retrieved 441 potentially eligible reviews, 23 met the criteria for inclusion and 8 provided data for extraction. Each review evaluated between 8 and 13 tools, in aggregate providing evidence on a total of 28 tools. The quality of the reviews varied and the reporting often lacked sufficient methodological detail for quality assessment. The 28 tools appear to have been studied in a variety of settings and with varied types of patients. The reviews identified several methodological limitations across the original studies. The lack of a 'gold standard' significantly hinders the evaluation of tools' validity. Most importantly, the samples were small providing limited evidence for use of any of the tools across settings or populations. CONCLUSIONS: There are a considerable number of pain assessment tools available for use with the elderly cognitive impaired population. However there is limited evidence about their reliability, validity and clinical utility. On the basis of this review no one tool can be recommended given the existing evidence

'Just open your eyes a bit more': The methodological challenges of researching black and minority ethnic students' experiences of physical education teacher education

In this paper we discuss some of the challenges of centralising 'race' and ethnicity in Physical Education (PE) research, through reflecting on the design and implementation of a study exploring Black and minority ethnic students' experiences of their teacher education. Our aim in the paper is to contribute to ongoing theoretical and methodological debates about intersectionality, and specifically about difference and power in the research process. As McCorkel and Myers notes, the 'researchers' backstage'-the assumptions, motivations, narratives and relations-that underpin any research are not always made visible and yet are highly significant in judging the quality and substance of the resulting project. As feminists, we argue that the invisibility of 'race' and ethnicity within Physical Education Teacher Education (PETE), and PE research more widely, is untenable; however, we also show how centralising 'race' and ethnicity raised significant methodological and epistemological questions, particularly given our position as White researchers and lecturers. In this paper, we reflect on a number of aspects of our research 'journey': the theoretical and methodological challenges of operationalising concepts of 'race' and ethnicity, the practical issues and dilemmas involved in recruiting participants for the study, the difficulties of 'talking race' personally and professionally and challenges of representing the experiences of 'others'. © 2012 Copyright Taylor and Francis Group, LLC