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Simplified Statistical Method-Example: Sum of uniform distributions converge to Gaussian distribution
Source publication
In 2011 ESA published the ESA Pointing Error Engineering Handbook as applicable document. The Handbook complements the ECSS control performance standard. It provides guidelines for a step-by-step engineering process from pointing error requirement specification, to systematic pointing error analysis, and the compilation of pointing error budgets. A...
Contexts in source publication
Context 1
... central limit theorem states that the sum of a large number of independent distributed random variables converges to a Gaussian distribution. This is illustrated in Figure 2, which shows an example of the summation of uniform distributions (for n={1;2;3;4} from the left to the right). If the central limit theorem applies, all PES can be entirely described only via their basic statistical moments (mean and variance) neglecting their real underlying probability density function (PDF). ...
Citations
... This assessment confirmed a comparable accuracy but with a significant reduction of computation time and an easier setup and adaptability of the pointing scenarios. Further details on the application of the tool to a case study is presented in a specific paper [10]. ...
Future space missions tend to rely on increasingly demanding pointing performance and/or are driven by the need for a cost-efficient design process. To avoid potential mission-or cost-critical changes late in the design, having at hand a clear pointing error engineering methodology to systematically assess achievable performances for various requirement categories already in early project phases is crucial. The Pointing Error Engineering Tool (PEET) is a software tool which is intended to support systems and AOCS engineers in the setup and calculation of such performance error budgets with a special focus on spacecraft pointing and relative-positioning. Its computational core is based on standardized rules established in the ECSS Control Performance Standard and on the methodology described in the ESA Pointing Error Engineering Handbook. This paper wraps up the translation of this methodology into a software tool and provides an overview of the realized features. Finally, the paper comments on the benefits of PEET and the developed concepts from an ESA and industrial user point of view.
The ATHENA—Advanced Telescope for High-ENergy Astrophysics—mission is currently assessed in a phase A feasibility study as L-class mission in ESA’s Cosmic Vision 2015–2025 plan, with launch foreseen in 2028. Primary mission goal is the mapping of hot gas structures and the determination of their physical properties to search for supermassive black holes. ATHENA is an X-ray telescope with a focal length of 12 m. It has a mass of ~ 7000 kg and it is ~ 15 m high with a diameter of ~ 3 m. The main mass is distributed to the mirror on the one side of the spacecraft and to the science instrument module on the other side of the spacecraft. To achieve its science goals, ATHENA performs a sky survey with precision line-of-sight pointing requirements in the order of arc seconds for absolute pointing and sub-arc seconds for relative pointing in time windows > 1 ks, all at 95% confidence level. That is very demanding for large X-ray telescopes. In addition to the precision pointing requirements, ATHENA cannot violate a certain sun exclusion zone. This is a hard constraint to prevent any stray-light falling onto the instruments, as it would immediately destroy them. The sky survey is defined by an observation plan that is demanding in terms of availability and thus spacecraft agility. The pointing and agility requirements and the fact that ATHENA is a spacecraft with high mass and volume introduce several design challenges for the attitude and orbit control system. This paper presents those challenges, corresponding solutions, and preliminary results, which have been achieved during the phase A study led by Airbus in Friedrichshafen, Germany. The main focus and contribution of this paper are the identification of research and development needs for attitude and orbit control systems to enable the ATHENA mission. In this respect, the ATHENA design challenges are discussed and addressed with the state-of-the-art design methods. This paper concludes with the main identified technology development needs and formulates specific research questions related to practical design problems. In particular, the following attitude and orbit control system design challenges are addressed: autonomous and agile large angle slew manoeuvres with exclusion zones, availability for science observations, precision line-of-sight determination as well as analysis during the design process using the ESA Pointing Error Engineering Tool and pointing control with a hexapod as line-of-sight actuator in the control loop. The last challenge, namely, the hexapod in the control loop, is without precedence in Europe and to the best knowledge of the authors in the world.
