From 628acab04e9927febcdaaba97783cf80a1a0e975 Mon Sep 17 00:00:00 2001 From: "Kloppenburg Ernst (CR/PJ-AI-R4)" Date: Thu, 25 Jan 2018 08:09:16 +0100 Subject: [PATCH] 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) --- 10-Unscented-Kalman-Filter.ipynb | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/10-Unscented-Kalman-Filter.ipynb b/10-Unscented-Kalman-Filter.ipynb index b2fe9be..dad808a 100644 --- a/10-Unscented-Kalman-Filter.ipynb +++ b/10-Unscented-Kalman-Filter.ipynb @@ -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",