From c6c0a61d495f234c1cff77f1f79a0676f6aa9f8a Mon Sep 17 00:00:00 2001 From: "Kenta Yonekura(a.k.a. yoneken)" Date: Sat, 1 Feb 2020 22:59:52 +0900 Subject: [PATCH] [Kalman Basics] Align some subscripts on the text --- Localization/Kalmanfilter_basics.ipynb | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/Localization/Kalmanfilter_basics.ipynb b/Localization/Kalmanfilter_basics.ipynb index 37428791..bbc10ce5 100644 --- a/Localization/Kalmanfilter_basics.ipynb +++ b/Localization/Kalmanfilter_basics.ipynb @@ -354,14 +354,14 @@ "\n", "Here for the numerator, $P(Z \\mid X),P(X)$ both are gaussian.\n", "\n", - "$N(\\bar\\mu, \\bar\\sigma^1)$ and $N(\\bar\\mu, \\bar\\sigma^2)$ are their mean and variances.\n", + "$N(\\mu_1, \\sigma_1^2)$ and $N(\\mu_2, \\sigma_2^2)$ are their mean and variances.\n", "\n", "New mean is \n", "\n", - "$$\\mu_\\mathtt{new} = \\frac{\\sigma_z^2\\bar\\mu + \\bar\\sigma^2z}{\\bar\\sigma^2+\\sigma_z^2}$$\n", + "$$\\mu_\\mathtt{new} = \\frac{\\mu_1 \\sigma_2^2 + \\mu_2 \\sigma_1^2}{\\sigma_1^2+\\sigma_2^2}$$\n", "New variance is\n", "$$\n", - "\\sigma_\\mathtt{new} = \\frac{\\sigma_z^2\\bar\\sigma^2}{\\bar\\sigma^2+\\sigma_z^2}\n", + "\\sigma_\\mathtt{new} = \\frac{\\sigma_1^2\\sigma_2^2}{\\sigma_1^2+\\sigma_2^2}\n", "$$" ] }, @@ -759,4 +759,4 @@ }, "nbformat": 4, "nbformat_minor": 2 -} +} \ No newline at end of file