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Nonlinear mapping of Gaussian state uncertainties
https://jaxa.repo.nii.ac.jp/records/7622
https://jaxa.repo.nii.ac.jp/records/762280c87e2d-692e-45f5-bf90-307f4ea2429e
Item type | 会議発表論文 / Conference Paper(1) | |||||
---|---|---|---|---|---|---|
公開日 | 2015-03-26 | |||||
タイトル | ||||||
言語 | en | |||||
タイトル | Nonlinear mapping of Gaussian state uncertainties | |||||
言語 | ||||||
言語 | eng | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | ガウス型状態不確実性 | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | 非線形マッピング | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | 状態遷移テンソル | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | STT | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | フォッカー・プランク方程式 | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | 確率密度関数 | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | 2体問題 | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | 3体問題 | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | ホーマン遷移軌道 | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | 数学的解析 | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | ガウス分布 | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | 確率 | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | モンテカルロ法 | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | Gaussian state uncertainty | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | nonlinear mapping | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | state transition tensor | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | STT | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | Fokker-Planck equation | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | probability density function | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | two body problem | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | three body problem | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | Hohmann transfer orbit | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | mathematical analysis | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | Gaussian distribution | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | probability | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | Monte Carlo method | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_5794 | |||||
資源タイプ | conference paper | |||||
アクセス権 | ||||||
アクセス権 | metadata only access | |||||
アクセス権URI | http://purl.org/coar/access_right/c_14cb | |||||
著者 |
Park, Ryan S.
× Park, Ryan S.× Scheeres, Daniel J. |
|||||
著者所属 | ||||||
University of Michigan Department of Aerospace Engineering | ||||||
著者所属 | ||||||
University of Michigan Department of Aerospace Engineering | ||||||
著者所属(英) | ||||||
en | ||||||
University of Michigan Department of Aerospace Engineering | ||||||
著者所属(英) | ||||||
en | ||||||
University of Michigan Department of Aerospace Engineering | ||||||
出版者 | ||||||
出版者 | 宇宙航空研究開発機構宇宙科学研究本部 | |||||
出版者(英) | ||||||
出版者 | Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency (JAXA/ISAS) | |||||
書誌情報 |
第15回アストロダイナミクスシンポジウム講演後刷り集 2005 en : Proceedings of 15th Workshop on JAXA Astrodynamics and Flight Mechanics p. 364-377, 発行日 2006-03 |
|||||
抄録(英) | ||||||
内容記述タイプ | Other | |||||
内容記述 | This paper presents the nonlinear propagation of orbit uncertainties via solutions of the Fokker-Planck equation. We first derive an analytic expression of a nonlinear trajectory solution by incorporating the higher order Taylor series that describes the localized nonlinear motion, and by solving for the higher order state solution as functions of initial conditions. A systematic way to define the sufficient order of higher order solutions that defines the localized nonlinear motion is also presented. We then solve the Fokker-Planck equation for a deterministic system with a Gaussian boundary condition and discuss how the propagated phase volume and Gaussian statistics characterize the spacecraft orbit uncertainties. The phase volume approach presents the integral invariance of the probability density function, and thus, the probability of the initial confidence region remains the same as it is mapped over time. The statistical method shows that the propagated trajectory uncertainties remain no longer Gaussian in general; however, we can still approximate the first two moments (mean and covariance matrix) to define the true confidence region of the nonlinear system. We utilize the higher order Taylor series solutions to approximate the true nonlinear trajectory statistics and compare with the conventional linear theory and Monte-Carlo simulations to explain its significance. The result shows that the nonlinear solution provides a superior result than the linear solution when the system is under a strong nonlinearity or mapped over a long time span. Moreover, the higher order Taylor series approach becomes essentially the same as the Monte-Carlo result when sufficient order of Taylor series is considered. The two-body and Hill three-body problems are chosen as examples and realistic initial uncertainty models are considered. | |||||
資料番号 | ||||||
内容記述タイプ | Other | |||||
内容記述 | 資料番号: AA0063480057 |