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Small fixes

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MBulli
2018-09-16 20:16:47 +02:00
parent 05da3a9324
commit 08af2ad411
9 changed files with 33 additions and 29 deletions
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tex/chapters/estimation.tex
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@@ -29,10 +29,10 @@ In the case of particle filters the MMSE estimate equals to the weighted-average
where $W_t=\sum_{i=1}^{N}w^i_t$ is the sum of all weights.
While producing an overall good result in many situations, it fails when the posterior is multimodal.
In these situations the weighted-average estimate will find the estimate somewhere between the modes.
Clearly, such a position between modes is extremely unlikely the real position of the pedestrian.
Clearly, such a position between modes is extremely unlikely the position of the pedestrian.
The real position is more likely to be found at the position of one of the modes, but virtually never somewhere between.
In the case of a multimodal posterior the system should estimate the position based on the most highest mode.
In the case of a multimodal posterior the system should estimate the position based on the highest mode.
Therefore, the maximum a posteriori (MAP) estimate is a suitable choice for such a situation.
A straightforward approach is to select the particle with the highest weight.
However, this is in fact not necessarily a valid MAP estimate, because only the weight of the particle is taken into account.