From 63d9b4a78bfcc7bc12f9e8b13b5a3397bc6b4063 Mon Sep 17 00:00:00 2001 From: Edward L Ionides Date: Wed, 17 Feb 2016 23:47:52 -0500 Subject: [PATCH] notes9 more typos --- notes9/notes9.Rmd | 6 +++--- notes9/notes9.html | 6 +++--- 2 files changed, 6 insertions(+), 6 deletions(-) diff --git a/notes9/notes9.Rmd b/notes9/notes9.Rmd index b6efd33..21c87d2 100644 --- a/notes9/notes9.Rmd +++ b/notes9/notes9.Rmd @@ -981,20 +981,20 @@ $\Sigma_n^S(\data{y_{1:N}})=\var\big(X_n\given Y_{1:N}\equals \data{y_{1:N}}\big
[KF3] $\myeq{ - \mu_{n+1}^P(y_{1:n}) = \matA_n \mu_{n}^F(y_{1:n}) + \mu_{n+1}^P(y_{1:n}) = \matA_{n+1} \mu_{n}^F(y_{1:n}) }$,
[KF4] $\myeq{ - \Sigma_{n+1}^P = \matA_n \Sigma_{n}^F \matA_n^\transpose + \covmatX + \Sigma_{n+1}^P = \matA_{n+1} \Sigma_{n}^F \matA_{n+1}^\transpose + \covmatX_{n+1} }$.
[KF5] $\myeq{ - \Sigma_{n}^F = \big([\Sigma_n^P]^{-1} + \matB_n^\transpose\covmatY_n^{-1}\covmatY\big)^{-1} + \Sigma_{n}^F = \big([\Sigma_n^P]^{-1} + \matB_n^\transpose\covmatY_n^{-1}\matB_n\big)^{-1} }$.
diff --git a/notes9/notes9.html b/notes9/notes9.html index 5b043f0..87ec454 100644 --- a/notes9/notes9.html +++ b/notes9/notes9.html @@ -638,11 +638,11 @@

9.7.1 Review of the multivariate

  • From the results for linear combinations of Normal random variables, we get the Kalman filter and prediction recursions:


    • -

    [KF3] \({{\quad\quad}\displaystyle \mu_{n+1}^P(y_{1:n}) = {\mathbb{A}}_n \mu_{n}^F(y_{1:n}) }\),

    +

    [KF3] \({{\quad\quad}\displaystyle \mu_{n+1}^P(y_{1:n}) = {\mathbb{A}}_{n+1} \mu_{n}^F(y_{1:n}) }\),


    -

    [KF4] \({{\quad\quad}\displaystyle \Sigma_{n+1}^P = {\mathbb{A}}_n \Sigma_{n}^F {\mathbb{A}}_n^{\scriptsize{T}}+ {\mathbb{U}}}\).

    +

    [KF4] \({{\quad\quad}\displaystyle \Sigma_{n+1}^P = {\mathbb{A}}_{n+1} \Sigma_{n}^F {\mathbb{A}}_{n+1}^{\scriptsize{T}}+ {\mathbb{U}}_{n+1} }\).


    -

    [KF5] \({{\quad\quad}\displaystyle \Sigma_{n}^F = \big([\Sigma_n^P]^{-1} + {\mathbb{B}}_n^{\scriptsize{T}}{\mathbb{V}}_n^{-1}{\mathbb{V}}\big)^{-1} }\).

    +

    [KF5] \({{\quad\quad}\displaystyle \Sigma_{n}^F = \big([\Sigma_n^P]^{-1} + {\mathbb{B}}_n^{\scriptsize{T}}{\mathbb{V}}_n^{-1}{\mathbb{B}}_n\big)^{-1} }\).


    [KF6] \({{\quad\quad}\displaystyle \mu_{n}^F(y_{1:n}) = \mu_{n}^P(y_{1:n-1}) + \Sigma_n^F {\mathbb{B}}^{\scriptsize{T}}_n{\mathbb{V}}_n^{-1}\big\{y_n - {\mathbb{B}}\mu_n^P(y_{1:n-1})\big\} }\).