deletions | additions       diff --git a/subsection_Approximation_of_probability_distribution__.tex b/subsection_Approximation_of_probability_distribution__.tex  index 8f53bf2..c92b485 100644  --- a/subsection_Approximation_of_probability_distribution__.tex  +++ b/subsection_Approximation_of_probability_distribution__.tex 
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Given a trajectory $T$, the probability $p(x,y)$ of $(x,y)$ is the sum of the contribution of each $(x',y')$ in $T$. The contributions are functions of a Gaussian kernel.  Hence the following definition of the probability of $(x,y)$ given $T$:  \[P((x,y),T) \[P_{PW}((x,y),T)  = \sum_{(x',y')\in T}K((x,y),(x',y'))\] where $K$ is a gaussian kernel. In practice we take a discrete gaussian kernel filter for $K$, given by the 3x3 matrix:  \[ M_{K} = \left| \begin{array}{ccc}