Resampling - Artificial Intelligence for RoboticsYouTube↗  IA↗(long shot)
Education  7.2K views 11 likes 0 dislikes   29 May 2012
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皆さんが考えているほど簡単ではありませんが そのやり方をお見せします
and it turns out it's actually harder than you think but I'm going to show you
それが一度できれば どんな粒子フィルタにも
how to do it and once you've done it you can use the exact same code for ever for
そのプログラムがずっと使えます
any particle fighter but let me be
しかし再サンプリングの意味を強調させてください
precise for what resampling actually
それぞれ3つの値を持つ粒子Nが 与えられていて
means we are given n particles each of which has three values and there's n of
さらにそれぞれが重みを持っているとします
them and they also not have weights
それは浮動小数点か連続した値です
these are simple floats or continuous
大文字Wはこれら全部の重みの合計とします
values let's call Big W the sum of all these
ではどうするか検討するために 正規化してみましょう
weights and let's normalize them just for the consideration of what to do and
αは正規化された重みです
it's called the normalized weights alpha
α1は重み1を正規化群Wで割ったものです これをNの数だけ続けます 正規化したため言うまでもなく
so alpha 1 would be the weight 1 divided by the normalizer W and so on all the way to alpha N and obviously goes without saying that the sum of all
αの合計は1です
alphas is no 1 since we normalize them
再サンプリングはこれらすべての粒子と
what resampling no does it puts all these particles in the normalized
正規化した重みを大きな袋に入れます
weights into a big bag and then it draws
そして確率αで各粒子を選び
with replacement and new particles by
再配置することにより新粒子Nを選び出します 例えばα2が大きければP2が選び出されます
picking each particle with probability alpha so example alpha 2 might be large so we're going to pick this one p 2
α3も大きかったらP3が選び出されます
alpha theme and also be large we pick
α4はとても小さいですが たまたま選び出されることもあります
that one alpha 4 might be really small just by just by chance you might
P4が残りさらに再びα2が選び出されます
actually pick it so we have P 4 over here and then we might pick out 4 to
これにより2つのP2を得ますが確率によっては 3つ得ることもあり得ます
again so you get two versions of P 2 perhaps even three versions of P do depending on the probabilities we have n
上が元の粒子Nです
particles over here we do this thing n
この再配置をN回行うことで
times which is so I said with
同じ粒子の複数のコピーを 選び出すことができます
replacement you can draw multiple copies of the same particle and in the end
最後には高度に正規化された 重みαを持つ粒子が
those particles they have a high normalized weight alpha over here will
新しい集合の中に頻繁に発生します
occur likely more frequently in the new
これが再サンプリングです
set over here that's called resampling
皆さんの理解度を見るために いくつか小テストを出しましょう
so to make sure you understand this let me ask you a couple of quizzes suppose
次の重要度重みを持つ 5つの粒子があるとします
we have 5 particles with the following
0．6、 1．2、 2．4、 0．6、 1．2です
importance weights 0.6 1.2 to 2.4 one six and one point two if I in the
再サンプリングの過程で
process of resampling randomly draw a
正規化した重要度重みに従って 粒子をランダムに選び出すとします
particle in accordance to the normalized importance weights what is the
P1からP5までの確率を計算して下さい
probability of drawing p1 p2 p4 and p5
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