Lectionary 60 - Revision history

en>Monkbot: Task 5: Fix CS1 deprecated coauthor parameter errors

2014-06-17T20:36:48Z

Task 5: Fix CS1 deprecated coauthor parameter errors

← Older revision		Revision as of 22:36, 17 June 2014
Line 1:		Line 1:
	~~In [[Filtering problem (stochastic processes)\|filtering theory]]~~ the ~~'''Kushner equation'''<ref>~~[~~[Harold J~~. ~~Kushner\|Kushner H~~.J.~~]] (1964) ''On~~ the ~~differential equations satisfied by conditional probability~~		Most people terribly lack cable or perhaps satellite, most people see throughout-some of the-temperature broadcast [http://www.youtube.com/watch?v=wGT0pc4_wbk 12 volt tv walmart] as well as internet based solutions towards our television and additionally film finding. With the help of that, this situation fix collect several more and more programmes as compared to old loaded with an online to be able to parallel ripper tools package performed. Seriously appears to receive few over some other High-definition kits e our home. Photograph understanding is literally i'm all over this, although I did so have got to adjust they colour & tint a bit from OOTB controls - many people seemed a tiny bit red. The mp3 is okay with a Television within the kitchen area, master bedroom, exercising area - some thing like your. Never be expecting all the largemouth bass or perhaps wealth within the audio, it almost cheesy sounding. Definitely not surprising taking into consideration the organize for the automated talker, although truly even worse as compared to the expected it becomes. Only various other issue is made gold watches for various purpose this comes to starting activates, your picture is really earth-friendly - it all of a sudden adjusts alone. Uncertain what can trigger this situation, then again i have never attained different Tv try this. Moreover, just as said located on the product classification site, while it provides the the amazon website finest banner, it will not in fact get the job done as of yet. So long as you make sure to use it the television shows the firmware up grade provides a more recent Amazon.com software later on (equally as some of the Amazon . com website countries). Now the professional / con review: <br><br>
	~~densities~~ of ~~Markov processes~~, with ~~applications~~.''. ~~J. SIAM Control Ser. A~~, ~~2(1)~~, ~~pp. 106~~-~~119~~.~~</ref> (after Harold Kushner) is an equation for~~ the ~~[[conditional probability]] [[probability density function\|density]] of~~ the ~~state of a [[stochastic process\|stochastic]] non-linear [[dynamical system]]~~, ~~given noisy measurements of~~ the ~~state. It therefore provides~~ the ~~solution of~~ the ~~[[nonlinear filter]]ing problem in [[estimation theory]]~~. ~~The equation~~ is ~~sometimes referred~~ to ~~as the '''Stratonovich–Kushner'''<ref>[[Ruslan L. Stratonovich\|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.</ref><ref>[[Ruslan L~~. ~~Stratonovich\|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.</ref><ref>[[Ruslan L. Stratonovich\|Stratonovich, R.L.]] (1960) ''Application of~~ the Markov processes theory to optimal filtering''. Radio Engineering and Electronic Physics, 5:11, pp. 1–19.</ref><ref>[[Ruslan L. Stratonovich\|Stratonovich, R.L.]] (1960). ''Conditional Markov Processes''. Theory of ~~Probability and its Applications, 5, pp~~.~~ 156–178.</ref> (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 Bucy~~.~~<ref>[[Bucy, R. S.]] (1965~~) ~~''Nonlinear filtering theory''~~. ~~IEEE Transactions on Automatic Control,~~
	~~10, pp. 198–198. [http~~:~~//ieeexplore.ieee.org/xploreAssets/images/absImages/01098109.png]~~<~~/ref~~>

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	~~Assume~~ the ~~state of the system evolves according to~~

	:~~<math>dx = f(x,t) \, dt + \sigma dw<~~/~~math>~~

	~~and a noisy measurement of the system state is available:~~

	~~:<math>dz = h(x,t) \, dt + \eta dv<~~/~~math>~~

	~~where ''w'', ''~~v~~'' are independent [[Wiener process~~]~~]es~~. ~~Then~~ the ~~conditional probability density ''p''(''x''~~,~~ ''t'')~~ of the ~~state at time ''t'' is given by the Kushner equation~~:

	~~:<math>dp(x,t)~~ = ~~L[p(x,t)] dt + p(x,t) [h(x,t)-E_t h(x,t)~~ ]~~^T \eta^{-\top}\eta^{~~-1} [~~dz-E_t h(x,t) dt]~~.</~~math>~~

	~~where <math>L p~~ = ~~-\sum \frac{\partial (f_i p)}{\partial x_i} + \frac{1}{2} \sum (\sigma \sigma^\top)_{i,j} \frac{\partial^2 p}{\partial x_i \partial x_j}<~~/~~math> is the Kolmogorov Forward operator and <math>dp(x,t)~~ = ~~p(x,t + dt)~~ - ~~p(x~~,~~t)</math> is the variation of~~ the ~~conditional probability.~~

	~~The term <math>dz-E_t h~~(~~x,t) dt</math> is~~ the ~~[[innovation (signal processing~~)~~\|innovation]] i~~.e~~. the difference between the measurement and its expected value.~~


	~~===Kalman-Bucy filter===~~

	~~One can simply use the Kushner equation~~ to ~~derive~~ the ~~[[Kalman~~-~~Bucy filter]] for a linear diffusion process. Suppose we have <math> f~~(~~x,t~~) ~~= a x</math>~~ and ~~<math> h~~(~~x,t~~) ~~= c x </math>~~. ~~The Kushner equation will be given by~~
	~~:<math>~~
	dp(~~x,t~~) ~~= L[p~~(x,~~t)] dt + p(x~~,~~t) [c x- c \mu(t)]^T \eta^{-\top}\eta^{-1} [dz-c \mu(t~~) ~~dt],~~
	<~~/math~~>
	~~where~~ <~~math> \mu(t) </math~~> is the ~~mean of the conditional probability at time <math> t</math>~~. ~~Multiplying by <math> x</math>~~ and ~~integrating over it~~, ~~we obtain the variation~~ of the ~~mean~~
	~~:<math>~~
	~~d\mu(t) = a \mu(t) dt + \Sigma(t) c^\top \eta^{-\top}\eta^{-1} \left(dz - c\mu(t) dt\right).~~
	~~</math>~~
	~~Likewise~~, the ~~variation of~~ the ~~variance <math>\Sigma(t)</math>~~ is ~~given by~~
	~~:<math>~~
	~~\frac{d\Sigma(t)}{dt} =~~ a~~\Sigma(t) + \Sigma(t)~~ a~~^\top + \sigma^\top \sigma-\Sigma(t) c^\top\eta^{-\top} \eta^{-1} c \Sigma(t)~~.
	~~</math>~~
	~~The conditional probability~~ is ~~then given~~ at ~~every instant by~~ a ~~normal distribution <math>\mathcal{N}(\mu(t)~~,~~\Sigma~~(t)~~)</math>~~.

	~~== References ==~~
	~~<references />~~

	~~== See also ==~~

	*[[Zakai equation]]

	~~[[Category:Signal processing]]~~
	~~[[Category:Estimation theory]]~~
	~~[[Category:Stochastic processes]]~~
	~~[[Category:Nonlinear filters]]~~

en>Leszek Jańczuk: Editio Critica Maior

2013-11-19T14:04:42Z

Editio Critica Maior

← Older revision		Revision as of 16:04, 19 November 2013
Line 1:		Line 1:
	~~But building link acceptance some times really hard if you do not know how to do-it.~~ <br>~~<br>Among the problem for new webmasters is to reunite connect to their just stablish sites~~. ~~Dig up further on~~ the ~~affiliated article directory~~ by ~~visiting [http://www~~.~~eird~~.~~org/country-profiles/profiles/index~~.~~php?title=MaiseyAngle851 http://www~~.k-~~9companions~~.~~com~~/]~~. <br><br>Most~~ of ~~us knew that right back link or link popularity is just~~ a ~~major factor to get good place in any search engines~~. ~~<br><br>But building link acceptance some times really hard if you don"t learn how to do it. <br><br>Among~~ the problem ~~for new webmasters~~ is to ~~get back connect to their newly stablish sites.~~ <br>~~<br>No-one need to change link to new internet sites~~, ~~you may get free link from those new site also~~. ~~But if you <br><br>want~~ a ~~link from~~ a ~~site~~ with ~~large PR you must buy it~~. <br><br>~~Others send their website to directories~~, ~~but it is frustrating~~ and ~~not all directories have become~~ <br><br>~~helpful~~ to ~~raise your link popularity~~. ~~Sometimes it takes~~ 1 ~~to 4 months before SE get your site from a directory~~. <br><br>~~When I am new also nowadays~~ of ~~web~~, ~~I don~~&~~quot~~;~~t discover how I obtain a quality link from other web sites~~. <br><br>~~I tried to send my site to almost all major directories out there~~, ~~their~~, ~~the however the issue isn"t so easy to get listed to them~~. ~~Navigating To~~ [http://~~syskrack~~.org/~~wiki~~/~~index~~.~~php?title=Dog_Training_for_Right_Behavior click here for~~] ~~maybe provides aids you could give to your sister.~~ <br>~~<br>I make serious study how these effective webmasters get a lot~~ of ~~straight back link with their site which give them high link recognition~~ <br><br>and ~~needless to say traffic as~~ the ~~more site linking to you the more chances you got traffic. <br><br>Then I learn that there~~ is ~~no real solution to obtain top quality link from other web sites.~~ <br><br>~~What they do would be to write articles~~. ~~Yes articles similar to this one. by creating an articles~~ of ~~something that~~ is <br>~~<br>Associated with your website is a great solution to get a lot of back~~-~~link~~. ~~Individuals are looking for free articles that~~ <br><br>~~they can use to post in their site~~, ~~to incorporate content. Therefore should they publish your free article within their site for~~ <br><br>~~sure you will get a totally free back link from that site.~~ <br>~~<br>So that you get credit when you write an article make sure to include link back to your website~~. ~~Then after~~ <br><br>~~writing your article send them to these article <br><br>Sites like <br><br>http://www~~.~~article-publishers~~.~~com <br><br>http://www~~.~~articlesarchieve~~.~~com~~ <br><~~br>http:~~/~~/www.articlescabinet.com <br~~><~~br>http://www.articlescopy.com <br~~><~~br>http:/~~/~~www.articlesfolder.net <br~~>~~<br>http://www~~.~~articleslead.com <br><br>http~~:~~//www.articlesnet.net~~ <br><~~br>http:/~~/~~www.articlesnetwork.net <br~~><~~br>http://www.articlesreader.com <br~~><~~br>http:~~/~~/www.articlesroom.com <br~~><br>~~http://www.bizarticles.net~~ <~~br><br>http:~~/~~/www.collectedarticles.com <br><br~~>~~http://www~~.~~copyarticles.com~~ <br><~~br>http:/~~/~~www.copyarticles.com <br~~>~~<br>http~~:~~//www.koolarticles.com~~ <br>~~<br>http://www~~.~~rentarticles.com~~ <~~br><br>http:~~/~~/www.siteforarticles.com <br~~><~~br>http://www.somearticles.com <br~~><~~br>http:~~/~~/www.sourceofarticles.com <br~~>~~<br>http~~:~~//www.ezinearticles.com~~ <br>~~<br>http://www.goarticles~~.~~com <br>~~<~~br>http:/~~/~~www.edraft.net <br~~>~~<br>It~~ is ~~possible to publish your articles to the aforementioned article sites and since people keep visiting those sites for~~ <br><br>~~sure they"ll see your report and they might be interested on it and post on their site~~. <br>~~<br>Best of luck.<br><br>If you beloved this post and you wish to receive more information relating to personal health (~~[~~http~~:~~//www.kiwibox.com/kaputgestu603/blog check this link right here now~~]~~) i implore you to check out the web-site.~~		In [[Filtering problem (stochastic processes)\|filtering theory]] the '''Kushner equation'''<ref>[[Harold J. Kushner\|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.</ref> (after Harold Kushner) is an equation for the [[conditional probability]] [[probability density function\|density]] of the state of a [[stochastic process\|stochastic]] non-linear [[dynamical system]], given noisy measurements of the state. It therefore provides the solution of the [[nonlinear filter]]ing problem in [[estimation theory]]. The equation is sometimes referred to as the '''Stratonovich–Kushner'''<ref>[[Ruslan L. Stratonovich\|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.</ref><ref>[[Ruslan L. Stratonovich\|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.</ref><ref>[[Ruslan L. Stratonovich\|Stratonovich, R.L.]] (1960) ''Application of the Markov processes theory to optimal filtering''. Radio Engineering and Electronic Physics, 5:11, pp. 1–19.</ref><ref>[[Ruslan L. Stratonovich\|Stratonovich, R.L.]] (1960). ''Conditional Markov Processes''. Theory of Probability and its Applications, 5, pp. 156–178.</ref> (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 Bucy.<ref>[[Bucy, R. S.]] (1965) ''Nonlinear filtering theory''. IEEE Transactions on Automatic Control,
			10, pp. 198–198. [http://ieeexplore.ieee.org/xploreAssets/images/absImages/01098109.png]</ref>

			== Overview ==

			Assume the state of the system evolves according to

			:<math>dx = f(x,t) \, dt + \sigma dw</math>

			and a noisy measurement of the system state is available:

			:<math>dz = h(x,t) \, dt + \eta dv</math>

			where ''w'', ''v'' are independent [[Wiener process]]es. Then the conditional probability density ''p''(''x'', ''t'') of the state at time ''t'' is given by the Kushner equation:

			:<math>dp(x,t) = L[p(x,t)] dt + p(x,t) [h(x,t)-E_t h(x,t) ]^T \eta^{-\top}\eta^{-1} [dz-E_t h(x,t) dt].</math>

			where <math>L p = -\sum \frac{\partial (f_i p)}{\partial x_i} + \frac{1}{2} \sum (\sigma \sigma^\top)_{i,j} \frac{\partial^2 p}{\partial x_i \partial x_j}</math> is the Kolmogorov Forward operator and <math>dp(x,t) = p(x,t + dt) - p(x,t)</math> is the variation of the conditional probability.

			The term <math>dz-E_t h(x,t) dt</math> is the [[innovation (signal processing)\|innovation]] i.e. the difference between the measurement and its expected value.


			===Kalman-Bucy filter===

			One can simply use the Kushner equation to derive the [[Kalman-Bucy filter]] for a linear diffusion process. Suppose we have <math> f(x,t) = a x</math> and <math> h(x,t) = c x </math>. The Kushner equation will be given by
			:<math>
			dp(x,t) = L[p(x,t)] dt + p(x,t) [c x- c \mu(t)]^T \eta^{-\top}\eta^{-1} [dz-c \mu(t) dt],
			</math>
			where <math> \mu(t) </math> is the mean of the conditional probability at time <math> t</math>. Multiplying by <math> x</math> and integrating over it, we obtain the variation of the mean
			:<math>
			d\mu(t) = a \mu(t) dt + \Sigma(t) c^\top \eta^{-\top}\eta^{-1} \left(dz - c\mu(t) dt\right).
			</math>
			Likewise, the variation of the variance <math>\Sigma(t)</math> is given by
			:<math>
			\frac{d\Sigma(t)}{dt} = a\Sigma(t) + \Sigma(t) a^\top + \sigma^\top \sigma-\Sigma(t) c^\top\eta^{-\top} \eta^{-1} c \Sigma(t).
			</math>
			The conditional probability is then given at every instant by a normal distribution <math>\mathcal{N}(\mu(t),\Sigma(t))</math>.

			== References ==
			<references />

			== See also ==

			*[[Zakai equation]]

			[[Category:Signal processing]]
			[[Category:Estimation theory]]
			[[Category:Stochastic processes]]
			[[Category:Nonlinear filters]]

en>Leszek Jańczuk: link

2012-09-01T21:29:12Z

link

New page

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