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added comments to usage and mvg

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fixed some minor errors
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toni
2018-02-15 09:48:06 +01:00
parent aac248a6c3
commit 7d631c2cc5
3 changed files with 15 additions and 8 deletions
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2
tex/chapters/kde.tex
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@@ -163,7 +163,7 @@ Using the Gaussian kernel from \eqref{eq:gausKern} in conjunction with the BKDE
As already stated the above formula is a convolution operation of the data and the kernel.
More precisely it is a discrete convolution of the finite data grid and the Gaussian function.
In terms of DSP this is analogous to filter the binned data with a Gaussian filter.
\commentByToni{hier vielleicht nochmal explizit erwähnen, also mit Namen, das der Gauss jetzt die BKDE approximiert und das diese erkenntniss toll und wichtig ist, weil wir so ein komplexes problem total einfach und schnell dargestellt haben.}

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tex/chapters/mvg.tex
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@@ -50,7 +50,7 @@ y[i]=\frac{1}{2r+1} \sum_{j=-r}^{r}x[i+j] \text{.}
Such a filter requires clearly $\landau{Nw}$ operations, where $N$ is the signal length.
It is well-known that a moving average filter can approximate a Gaussian filter by repetitive recursive computations.
\eqref{eq:symMovAvg} is equal to convolution of the input signal and the rectangular function.
Given by the central limit theorem of probability repetitive convolution of a rectangular function with itself eventually yields a Gaussian in the limit.
Given by the central limit theorem of probability, repetitive convolution of a rectangular function with itself eventually yields a Gaussian in the limit.
Likewise, filtering a signal with the moving average filter in several passes approximately converges to a Gaussian filter.
In practice three or five iterations are most likely enough to obtain a reasonable close Gaussian approximation \cite{kovesi2010fast}.
@@ -104,11 +104,15 @@ However, the overall shape will not change.
Just like the conventional box filter, the extended version has a uniform value in the range $[-r; r]$, but unlike the conventional the extended box filter has different values at its edges.
This extension introduces only marginal computational overhead over conventional box filtering.
\commentByToni{Warum benutzen wir den extended box filter nicht? oder tun wir das? Liest sich so, als wäre er der heilige Gral.
Ansonsten: Kapitel find ich gut. Vielleicht kann man hier und da noch paar sätze fusionieren um etwas Platz zu sparen.}
\commentByToni{Aber irgendwie fehlt mir hier noch so ein Absatz oder Kapitel "Zusammenstecken" der Mathematik. Die Usage kommt wieder so Hart. Und nochmal eine kleine Diskussion zum Zusammenstecken. Vielleicht kann man das mit dem 2D verbinden? Weil aktuell haben wir die beiden Verfahren besprochen, aber der eigene Anteil ist irgendwie nicht ersichtlich. Was war jetzt deine tolle Leistung hier? Das muss durch eine gute Diskussion klar werden.}
\todo{box filter vs moving average filter vs einfahc eine Abkürzung? :D}
\commentByToni{Kann man eq(12) und eq(9) nicht irgendwie verbinden?}

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tex/chapters/usage.tex
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@@ -11,7 +11,7 @@
\todo{Absatz zum Thema 2D}
The objective of our method is to allow reliable recover the most probable state from a time-sequential Monte Carlo sensor fusion system.
The objective of our method is to allow a reliable recover of the most probable state from a time-sequential Monte Carlo sensor fusion system.
Assuming a sample based representation, our method allows to estimate the density of the unknown distribution of the state space in a narrow time frame.
Such systems are often used to obtain an estimation of the most probable state in near real time.
As the density estimation poses only a single step in the whole process, its computation needs to be as fast as possible.
@@ -48,4 +48,7 @@ Due to its simple indexing scheme, the recursive box filter can easily be comput
Finally, the most likely state can be obtained from the filtered data, i.e. from the estimated discrete density, by searching filtered data for its maximum value.
\commentByToni{An sich ganz cooles Kapitel, aber wir müssen den Bezug nach oben stärker aufbauen. Also die Formeln zitieren. irgendwie halt nach oben referenzieren, damit niemand abgehängt wird.
Würde es Sinn machen das obere irgendwie Algorithmisch darzustellen? Also mit Pseudocode? Weil irgendwie/wo müssen wir ja "DAS IST UNSER APPROACH" stehen haben}.