diff --git a/07-Kalman-Filter-Math.ipynb b/07-Kalman-Filter-Math.ipynb index 8e81d37..bf1f710 100644 --- a/07-Kalman-Filter-Math.ipynb +++ b/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",