From 10203d3a42e32edf315cc05d39a543a27a60f30e Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Mon, 4 May 2020 17:40:00 -0700 Subject: [PATCH] Fixed math for P = FPF^ #274 --- 06-Multivariate-Kalman-Filters.ipynb | 7 +++---- 1 file changed, 3 insertions(+), 4 deletions(-) diff --git a/06-Multivariate-Kalman-Filters.ipynb b/06-Multivariate-Kalman-Filters.ipynb index 9124990..fb20cb2 100644 --- a/06-Multivariate-Kalman-Filters.ipynb +++ b/06-Multivariate-Kalman-Filters.ipynb @@ -1769,12 +1769,11 @@ "If you have some experience with linear algebra and statistics, this may help. The covariance due to the prediction can be modeled as the expected value of the error in the prediction step, given by this equation. \n", "\n", "$$\\begin{aligned}\n", - "\\bar{\\mathbf P} &= \\mathbb E[(\\mathbf{Fx})(\\mathbf{Fx})^\\mathsf T]\\\\\n", - " &= \\mathbb E[\\mathbf{Fxx}^\\mathsf T\\mathbf F^\\mathsf T] \\\\\n", - " &= \\mathbf F\\, \\mathbb E[\\mathbf{xx}^\\mathsf T]\\, \\mathbf F^\\mathsf T\n", + "\\bar{\\mathbf P} &= \\mathbb E[(\\mathbf{Fx - \\bar \\mu})(\\mathbf{Fx - \\bar\\mu})^\\mathsf T]\\\\\n", + " &= \\mathbf F\\, \\mathbb E[\\mathbf{(x- \\bar\\mu)(x- \\bar\\mu)}^\\mathsf T]\\, \\mathbf F^\\mathsf T\n", "\\end{aligned}$$\n", "\n", - "Of course, $\\mathbb E[\\mathbf{xx}^\\mathsf T]$ is just $\\mathbf P$, giving us\n", + "Of course, $\\mathbb E[\\mathbf{(x- \\bar\\mu)(x- \\bar\\mu)}^\\mathsf T]$ is just $\\mathbf P$, giving us\n", "\n", "$$\\bar{\\mathbf P} = \\mathbf{FPF}^\\mathsf T$$\n", "\n",