update docs

Localization/Kalmanfilter_basics.ipynb

@@ -32,7 +32,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [
     {
@@ -288,7 +288,7 @@
     "$$ \n",
     "f(x, \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} \\exp\\big [{-\\frac{(x-\\mu)^2}{2\\sigma^2} }\\big ]\n",
     "$$\n",
-    "Range is [$-\\inf,\\inf $]\n",
+    "Range is $$[-\\inf,\\inf] $$\n",
     "\n",
     "\n",
     "This is just a function of mean($\\mu$) and standard deviation ($\\sigma$) and what gives the normal distribution the charecteristic **bell curve**. "

Localization/Kalmanfilter_basics_2.ipynb

@@ -13,7 +13,7 @@
    "source": [
     " ### Probabilistic Generative Laws\n",
     " \n",
-    "**1st Law**:\n",
+    "#### 1st Law:\n",
     "The belief representing the state $x_{t}$, is conditioned on all past states, measurements and controls. This can be shown mathematically by the conditional probability shown below:\n",
     "\n",
     "$$p(x_{t} | x_{0:t-1},z_{1:t-1},u_{1:t})$$\n",
@@ -31,7 +31,7 @@
     "\n",
     "$$p(x_{t} | x_{0:t-1},z_{1:t-1},u_{1:t})=p(x_{t} | x_{t-1},u_{t})$$\n",
     "\n",
-    "**2nd Law**:\n",
+    "#### 2nd Law:\n",
     "\n",
     "If $x_{t}$ is complete, then:\n",
     "\n",
@@ -84,7 +84,7 @@
     "### Bayes Rule:\n",
     "\n",
     "\n",
-    "Posterior = $\\frac{Likelihood*Prior}{Marginal} $\n",
+    "Posterior = $$\\frac{Likelihood*Prior}{Marginal} $$\n",
     "\n",
     "Here,\n",
     "\n",
@@ -274,7 +274,7 @@
     "\\end{aligned}$$\n",
     "\n",
     "\n",
-    "**$K$ is the *Kalman gain*. It's the crux of the Kalman filter. It is a scaling term that chooses a value partway between $\\mu_z$ and $\\bar\\mu$.**"
+    "$K$ is the *Kalman gain*. It's the crux of the Kalman filter. It is a scaling term that chooses a value partway between $\\mu_z$ and $\\bar\\mu$."
    ]
   },
   {