Created using Colaboratory

tutorial-mot.ipynb

@@ -97,6 +97,13 @@
  "id": "_ifMn-urtPG-"
  }
  },
+ {
+ "cell_type": "markdown",
+ "source": [],
+ "metadata": {
+ "id": "AwdKdcan_1kZ"
+ }
+ },
  {
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  "source": [
@@ -127,13 +134,6 @@
  "id": "ZBQmsqU0EXYh"
  }
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- {
- "cell_type": "markdown",
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@@ -201,11 +201,12 @@
  "g_{k}\\left(o_{k} \\mid x_{k}\\right)=N\\left(o_{k} ; h_{k}\\left(x_{k}\\right), R_{k}\\right)\n",
  "$$\n",
  "\n",
- "$o_k$ - measurement at time $k$\n",
  "\n",
- "$h_k(x_k)$ - expected measurement given state $x$ at time $k$\n",
+ "where\n",
  "\n",
- "$g_{k}\\left(o_{k} \\mid x_{k}\\right)$ - likelihood of $o_k$ given state $x_k$"
+ "* $o_k$ - measurement at time $k$\n",
+ "* $h_k(x_k)$ - expected measurement given state $x$ at time $k$\n",
+ "* $g_{k}\\left(o_{k} \\mid x_{k}\\right)$ - likelihood of $o_k$ given state $x_k$"
  ],
  "metadata": {
  "id": "C9gZxFvM7BYD"
@@ -282,6 +283,45 @@
  "id": "rtLPQ4LF7Mo5"
  }
  },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "\n",
+ " Clutter observations are uniformly distributed in the field of view.\n",
+ " \\item At each timestep, there's a random number of clutter detections.\n",
+ " \\item The appropriate distribution to model this randomness is Poisson.\n",
+ "\n",
+ "* Clutter observations are uniformly distributed in the field of view.\n",
+ "* At each timestep, there's a random number of clutter detections.\n",
+ "* The appropriate distribution to model this randomness is Poisson.\n",
+ "\n",
+ "\\subsection*{Poisson Distribution}\n",
+ "The probability mass function of the Poisson distribution is given by:\n",
+ "\\[\n",
+ "f(k, \\lambda) = \\frac{e^{-\\lambda}\\lambda^k}{k!}\n",
+ "\\]\n",
+ "where:\n",
+ "\\begin{itemize}\n",
+ " \\item \\(k\\) - the number of events,\n",
+ " \\item \\(\\lambda\\) - the average number of events occurring in the interval [a, b].\n",
+ "\\end{itemize}\n",
+ "\n",
+ "\\subsection*{Properties}\n",
+ "\\begin{itemize}\n",
+ " \\item Numbers of arrivals in disjoint time intervals are independent.\n",
+ " \\item The Poisson distribution can be used as an approximation to the Binomial distribution when the sample size \\(n\\) is large and the probability product \\(np\\) is small. Specifically:\n",
+ "\\[\n",
+ "Y \\sim \\text{Binom}(n, p) \\implies Y \\approx \\text{Poisson}(np) \\text{ for large } n \\text{ and small } np.\n",
+ "\\]\n",
+ "\\end{itemize}\n",
+ "\n",
+ "\\end{document}\n",
+ "$$"
+ ],
+ "metadata": {
+ "id": "eoSg7e1ABvg0"
+ }
+ },
  {
  "cell_type": "markdown",
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