From c713f26870dd95e61ffabe64064bc3bba6d833fc Mon Sep 17 00:00:00 2001
From: Atsushi Sakai <asakai.amsl+github@gmail.com>
Date: Sat, 17 Nov 2018 21:12:04 +0900
Subject: [PATCH] add some docs

---
 .../extended_kalman_filter_localization.ipynb | 27 ++++++++++++++++++-
 1 file changed, 26 insertions(+), 1 deletion(-)

diff --git a/Localization/extended_kalman_filter/extended_kalman_filter_localization.ipynb b/Localization/extended_kalman_filter/extended_kalman_filter_localization.ipynb
index 068f89ce..e1089eaf 100644
--- a/Localization/extended_kalman_filter/extended_kalman_filter_localization.ipynb
+++ b/Localization/extended_kalman_filter/extended_kalman_filter_localization.ipynb
@@ -25,7 +25,32 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Kalman Filter"
+    "### Filter Design\n",
+    "\n",
+    "In this simulation, the robot has a state vector includes 4 states at time $t$.\n",
+    "\n",
+    "$$\\textbf{x}_t=[x_t, y_t, \\theta_t, v_t]$$\n",
+    "\n",
+    "x, y are a 2D x-y position, $\\theta$ is orientation, and v is velocity.\n",
+    "\n",
+    "\n",
+    "The robot has a speed sensor and a gyro sensor.\n",
+    "\n",
+    "So, the input vecor can be used as each time step\n",
+    "\n",
+    "$$\\textbf{u}_t=[v_t, \\omega_t]$$\n",
+    "\n",
+    "Also, the robot has a GNSS sensor, it means that the robot can observe x-y position at each time.\n",
+    "\n",
+    "$$\\textbf{z}_t=[x_t,y_t]$$\n",
+    "\n",
+    "The input and observation vector includes sensor noise.\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n"
    ]
   },
   {