翻訳と辞書 Words near each other ・ Kushkuiyeh, Kerman ・ Kushkuiyeh, Yazd ・ Kushla ・ Kushla Peak ・ Kushla, Alabama ・ Kushlu ・ Kushlukia ・ Kushma Municipality-12, Chuwa, Parbat ・ Kushmanda ・ Kushmandi (community development block) ・ Kushmandi (Vidhan Sabha constituency) ・ Kushnaq ・ Kushnarenkovo ・ Kushnarenkovsky District ・ Kushner ・ Kushner equation ・ Kushner Properties ・ Kushner Real Estate Group ・ Kushner Studios ・ Kushnir ・ Kushok Bakula Rimpochee Airport ・ Kushok Bakula Rinpoche ・ Kushok Chimey Luding ・ Kushovë ・ Kushtagi ・ Kushtaka ・ Kushtanka River ・ Kushtegirmon ・ Kushtepin ・ Kushti Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Kushner equation ： ウィキペディア英語版 Kushner equation In filtering theory the Kushner equation〔Kushner H.J. (1964) ''On the differential equations satisfied by conditional probability densities of Markov processes, with applications.''. J. SIAM Control Ser. A, 2(1), pp. 106-119.〕 (after Harold Kushner) is an equation for the conditional probability density of the state of a stochastic non-linear dynamical system, given noisy measurements of the state. It therefore provides the solution of the nonlinear filtering problem in estimation theory. The equation is sometimes referred to as the Stratonovich–Kushner〔Stratonovich, R.L. (1959). ''Optimum nonlinear systems which bring about a separation of a signal with constant parameters from noise''. Radiofizika, 2:6, pp. 892–901.〕〔Stratonovich, R.L. (1959). ''On the theory of optimal non-linear filtering of random functions''. Theory of Probability and its Applications, 4, pp. 223–225.〕〔Stratonovich, R.L. (1960) ''Application of the Markov processes theory to optimal filtering''. Radio Engineering and Electronic Physics, 5:11, pp. 1–19.〕〔Stratonovich, R.L. (1960). ''Conditional Markov Processes''. Theory of Probability and its Applications, 5, pp. 156–178.〕 (or Kushner–Stratonovich) equation. However, the correct equation in terms of Itō calculus was first derived by Kushner although a more heuristic Stratonovich version of it appeared already in Stratonovich's works in late fifties. However, the derivation in terms of Itō calculus is due to Richard Bucy.〔Bucy, R. S. (1965) (Nonlinear filtering theory ). IEEE Transactions on Automatic Control, 10, pp. 198–198.〕 == Overview == Assume the state of the system evolves according to :$dx\; =\; f(x,t)\; \backslash ,\; dt\; +\; \backslash sigma\; dw$ and a noisy measurement of the system state is available: :$dz\; =\; h(x,t)\; \backslash ,\; dt\; +\; \backslash eta\; dv$ where ''w'', ''v'' are independent Wiener processes. Then the conditional probability density ''p''(''x'', ''t'') of the state at time ''t'' is given by the Kushner equation: :$dp(x,t)\; =\; L()\; dt\; +\; p(x,t)\; (h(x,t))^T\; \backslash eta^\backslash eta^\; (h(x,t)\; dt).$ where $L\; p\; =\; -\backslash sum\; \backslash frac\; +\; \backslash frac\; \backslash sum\; (\backslash sigma\; \backslash sigma^\backslash top)\_\; \backslash frac$ is the Kolmogorov Forward operator and $dp(x,t)\; =\; p(x,t\; +\; dt)\; -\; p(x,t)$ is the variation of the conditional probability. The term $dz-E\_t\; h(x,t)\; dt$ is the innovation i.e. the difference between the measurement and its expected value. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Kushner equation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.