update docs

SLAM/FastSLAM1/FastSLAM1.ipynb

@@ -37,6 +37,19 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "### Simulation\n",
+    "\n",
+    "This is a feature based SLAM example using FastSLAM 1.0.\n",
+    "\n",
+    "The blue line is ground truth, the black line is dead reckoning, the red\n",
+    "line is the estimated trajectory with FastSLAM.\n",
+    "\n",
+    "The red points are particles of FastSLAM.\n",
+    "\n",
+    "Black points are landmarks, blue crosses are estimated landmark\n",
+    "positions by FastSLAM.\n",
+    "\n",
+    "\n",
     "![gif](https://github.com/AtsushiSakai/PythonRobotics/raw/master/SLAM/FastSLAM1/animation.gif)"
    ]
   },
@@ -487,7 +500,9 @@
     "\n",
     "The figure shows 100 particles distributed uniformly between [-0.5, 0.5] with the weights of each particle distributed according to a Gaussian funciton. \n",
     "\n",
-    "The resampling picks $i \\in 1,...,N$ particles with probability to pick particle with index $i \\propto \\omega_i $, where $\\omega_i$ is the weight of that particle\n",
+    "The resampling picks \n",
+    "\n",
+    "$i \\in 1,...,N$ particles with probability to pick particle with index $i ∝ \\omega_i$, where $\\omega_i$ is the weight of that particle\n",
     "\n",
     "\n",
     "To get the intuition of the resampling step we will look at a set of particles which are initialized with a given x location and weight. After the resampling the particles are more concetrated in the location where they had the highest weights. This is also indicated by the indices \n"
@@ -653,7 +668,7 @@
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    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.5"
+   "version": "3.6.7"
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