Merge pull request rlabbe#403 from AchmadFathoni/AchmadFathoni

Elaborate how c_0=x_0

Author: rlabbe

07-Kalman-Filter-Math.ipynb

@@ -294,6 +294,13 @@
     "x = e^ce^{kt} \\\\\n",
     "x = c_0e^{kt}\\end{gathered}$$\n",
     "\n",
+    "When $t=0$, $x=x_0$. Substitute these to equation above.\n",
+    "\n",
+    "$$\\begin{gathered}x_0 = c_0e^{k(0)} \\\\\n",
+    "x_0 = c_01 \\\\\n",
+    "x_0 = c_0 \\\\\n",
+    "x = x_0e^{kt}\\end{gathered}$$\n",
+    "\n",
     "Using similar math, the solution to the first-order equation \n",
     "\n",
     "$$\\dot{\\mathbf x} = \\mathbf{Ax} ,\\, \\, \\, \\mathbf x(0) = \\mathbf x_0$$\n",