From 6dd31f822c0440b685d7eae7a440ac0335b462d9 Mon Sep 17 00:00:00 2001
From: Peter Schneider <peteryschneider@gmail.com>
Date: Sat, 29 Jul 2017 01:41:14 -0700
Subject: [PATCH] fix Jacobian matrices

---
 11-Extended-Kalman-Filters.ipynb | 24 ++++++++++++------------
 1 file changed, 12 insertions(+), 12 deletions(-)

diff --git a/11-Extended-Kalman-Filters.ipynb b/11-Extended-Kalman-Filters.ipynb
index 6082f0c..5de983f 100644
--- a/11-Extended-Kalman-Filters.ipynb
+++ b/11-Extended-Kalman-Filters.ipynb
@@ -964,15 +964,15 @@
     "We find The $\\mathbf F$ by taking the Jacobian of $f(x,u)$.\n",
     "\n",
     "$$\\mathbf F = \\frac{\\partial f(x, u)}{\\partial x} =\\begin{bmatrix}\n",
-    "\\frac{\\partial \\dot x}{\\partial x} & \n",
-    "\\frac{\\partial \\dot x}{\\partial y} &\n",
-    "\\frac{\\partial \\dot x}{\\partial \\theta}\\\\\n",
-    "\\frac{\\partial \\dot y}{\\partial x} & \n",
-    "\\frac{\\partial \\dot y}{\\partial y} &\n",
-    "\\frac{\\partial \\dot y}{\\partial \\theta} \\\\\n",
-    "\\frac{\\partial \\dot{\\theta}}{\\partial x} & \n",
-    "\\frac{\\partial \\dot{\\theta}}{\\partial y} &\n",
-    "\\frac{\\partial \\dot{\\theta}}{\\partial \\theta}\n",
+    "\\frac{\\partial f_1}{\\partial x} & \n",
+    "\\frac{\\partial f_1}{\\partial y} &\n",
+    "\\frac{\\partial f_1}{\\partial \\theta}\\\\\n",
+    "\\frac{\\partial f_2}{\\partial x} & \n",
+    "\\frac{\\partial f_2}{\\partial y} &\n",
+    "\\frac{\\partial f_2}{\\partial \\theta} \\\\\n",
+    "\\frac{\\partial f_3}{\\partial x} & \n",
+    "\\frac{\\partial f_3}{\\partial y} &\n",
+    "\\frac{\\partial f_3}{\\partial \\theta}\n",
     "\\end{bmatrix}\n",
     "$$\n",
     "\n",
@@ -1087,9 +1087,9 @@
     "If this was a linear problem we would convert from control space to state space using the by now familiar $\\mathbf{FMF}^\\mathsf T$ form. Since our motion model is nonlinear we do not try to find a closed form solution to this, but instead linearize it with a Jacobian which we will name $\\mathbf{V}$. \n",
     "\n",
     "$$\\mathbf{V} = \\frac{\\partial f(x, u)}{\\partial u} \\begin{bmatrix}\n",
-    "\\frac{\\partial \\dot x}{\\partial v} & \\frac{\\partial \\dot x}{\\partial \\alpha} \\\\\n",
-    "\\frac{\\partial \\dot y}{\\partial v} & \\frac{\\partial \\dot y}{\\partial \\alpha} \\\\\n",
-    "\\frac{\\partial \\dot{\\theta}}{\\partial v} & \\frac{\\partial \\dot{\\theta}}{\\partial \\alpha}\n",
+    "\\frac{\\partial f_1}{\\partial v} & \\frac{\\partial f_1}{\\partial \\alpha} \\\\\n",
+    "\\frac{\\partial f_2}{\\partial v} & \\frac{\\partial f_2}{\\partial \\alpha} \\\\\n",
+    "\\frac{\\partial f_3}{\\partial v} & \\frac{\\partial f_3}{\\partial \\alpha}\n",
     "\\end{bmatrix}$$\n",
     "\n",
     "These partial derivatives become very difficult to work with. Let's compute them with SymPy. "