翻訳と辞書 Words near each other ・ Zak Zodiac ・ Zak's Lunch ・ Zak, Iran ・ ZAKA ・ Zaka ・ Zaka (Senatorial constituency) ・ Zaka Alao ・ Zaka Ashraf ・ Zaka District ・ Zaka Siddiqi ・ Zaka Ullah Bhangoo ・ Zaka Valley ・ Zaka, Burkina Faso ・ Zakabar ・ Zakai ・ Zakai equation ・ Zakal ・ Zakale ・ Zakalew ・ Zakaleń ・ Zakalia Koté ・ Zakalinki ・ Zakalinki-Kolonia ・ Zakaliyili ・ Zakalje ・ Zakamensk ・ Zakamensk (disambiguation) ・ Zakamensky District ・ Zakan ・ Zakan Jugelia 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 Zakai equation ： ウィキペディア英語版 Zakai equation In filtering theory the Zakai equation is a linear stochastic partial differential equation for the un-normalized density of a hidden state. In contrast, the Kushner equation gives a non-linear stochastic partial differential equation for the normalized density of the hidden state. In principle either approach allows one to estimate a quantity function (the state of a Dynamical system) from noisy measurements, even when the system is non-linear (thus generalizing the earlier results of Wiener and Kalman for linear systems and solving a central problem in estimation theory). The application of this approach to a specific engineering situation may be problematic however, as these equations are quite complex. The Zakai equation is a bilinear stochastic partial differential equation. It was named after Moshe Zakai. == Overview == Assume the state of the system evolves according to :$dx\; =\; f(x,t)\; dt\; +\; dw$ and a noisy measurement of the system state is available: :$dz\; =\; h(x,t)\; dt\; +\; dv$ where $dw,\; dv$ are independent Wiener processes. Then the unnormalized conditional probability density $p(x,t)$ of the state at time t is given by the Zakai equation: :$dp\; =\; L(p)\; dt\; +\; p\; h^T\; dz$ where the operator $L\; =\; -\backslash sum\; \backslash frac\; +\; \backslash frac12\; \backslash sum\; \backslash frac$ As previously mentioned p is an unnormalized density, i.e. it does not necessarily integrate to 1. After solving for p integration and normalization can be done if desired (an extra step not required in the Kushner approach). Note that if the last two terms on the right hand side are omitted (by choosing h identically zero), the result is a nonstochastic PDE : the familiar Kolmogorov Forward Equation, which describes the evolution of the state when no measurement information is available. 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「Zakai 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.