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Localization/Kalmanfilter_basics.ipynb

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"\n",
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"This is for a multivariate distribution. For example, a robot in 2-D space can take values in both x and y. To describe them, a normal distribution with mean in both x and y is needed.\n",
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"\n",
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"For a multivariate distribution, mean $\\mu can be represented as a matrix, \n",
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"For a multivariate distribution, mean $\\mu$ can be represented as a matrix, \n",
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"\n",
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"$$\n",
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"\\mu = \\begin{bmatrix}\\mu_1\\\\\\mu_2\\\\ \\vdots \\\\\\mu_n\\end{bmatrix}\n",

Localization/Kalmanfilter_basics_2.ipynb

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"\n",
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"The filter works in two parts:\n",
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"\n",
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"$\\bullet$ $p(x_{t} | x_{t-1},u_{t})\\rightarrow $**State Transition Probability**\n",
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"$p(x_{t} | x_{t-1},u_{t})$ -> **State Transition Probability**\n",
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"\n",
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"$\\bullet$ $p(z_{t} | x_{t}) \\rightarrow $**Measurement Probability**\n",
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"$p(z_{t} | x_{t})$ -> **Measurement Probability**\n",
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"\n",
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"\n",
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"### Conditional dependence and independence example:\n",

docs/_static/.gitkeep

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docs/modules/Kalmanfilter_basics.rst

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space can take values in both x and y. To describe them, a normal
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distribution with mean in both x and y is needed.
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For a multivariate distribution, mean $:raw-latex:`\mu `can be
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represented as a matrix,
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For a multivariate distribution, mean :math:`\mu` can be represented as
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a matrix,
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.. math::
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docs/modules/Kalmanfilter_basics_2.rst

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The filter works in two parts:
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:math:`\bullet` $p(x_{t} \|
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x_{t-1},u_{t}):raw-latex:`\rightarrow `$\ **State Transition
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Probability**
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:math:`p(x_{t} | x_{t-1},u_{t})` -> **State Transition Probability**
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:math:`\bullet` $p(z_{t} \| x_{t})
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:raw-latex:`\rightarrow `$\ **Measurement Probability**
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:math:`p(z_{t} | x_{t})` -> **Measurement Probability**
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Conditional dependence and independence example:
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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