daviddoji/Kalman-and-Bayesian-Filters-in-Python
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

in equations that update a variable using its previous value use different symbols (written as pseudocode it would be ok, but not written as an equation)

Browse Source
This commit is contained in:
Kloppenburg Ernst (CR/PJ-AI-R4) 2018-01-25 08:09:16 +01:00
parent e6eadee933
commit 628acab04e
1 changed files with 8 additions and 8 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

16
10-Unscented-Kalman-Filter.ipynb
View File

@ -381,8 +381,8 @@
"\n",
"through the nonlinear system:\n",
"\n",
"$$\\begin{cases}\\begin{aligned}x&=x+y\\\\\n",
"y &= 0.1x^2 + y^2\\end{aligned} \\end{cases}$$ "
"$$\\begin{cases}\\begin{aligned}\\bar x&=x+y\\\\\n",
"\\bar y&= 0.1x^2 + y^2\\end{aligned} \\end{cases}$$ "
]
},
{
@ -2787,17 +2787,17 @@
"\n",
"After the move forward for time $\\Delta t$ the new position and orientation of the robot is\n",
"\n",
"$$\\begin{aligned} x &= C_x + R\\sin(\\theta + \\beta) \\\\\n",
"y &= C_y - R\\cos(\\theta + \\beta) \\\\\n",
"\\theta &= \\theta + \\beta\n",
"$$\\begin{aligned} \\bar x &= C_x + R\\sin(\\theta + \\beta) \\\\\n",
"\\bar y &= C_y - R\\cos(\\theta + \\beta) \\\\\n",
"\\bar \\theta &= \\theta + \\beta\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"Once we substitute in for $C$ we get\n",
"\n",
"$$\\begin{aligned} x &= x - R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n",
"y &= y + R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n",
"\\theta &= \\theta + \\beta\n",
"$$\\begin{aligned} \\bar x &= x - R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n",
"\\bar y &= y + R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n",
"\\bar \\theta &= \\theta + \\beta\n",
"\\end{aligned}\n",
"$$\n",
"\n",