From b0ad96543958472ee919cf965373a2e37c1a79bd Mon Sep 17 00:00:00 2001 From: "Kloppenburg Ernst (CR/PJ-AI-R13)" Date: Thu, 9 Jan 2020 15:11:18 +0100 Subject: [PATCH] fix typos --- 07-Kalman-Filter-Math.ipynb | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/07-Kalman-Filter-Math.ipynb b/07-Kalman-Filter-Math.ipynb index ba448fa..7639362 100644 --- a/07-Kalman-Filter-Math.ipynb +++ b/07-Kalman-Filter-Math.ipynb @@ -1009,7 +1009,7 @@ "$$\\mathbf P = (\\mathbf I-\\mathbf {KH})\\mathbf{\\bar P}(\\mathbf I-\\mathbf{KH})^\\mathsf T + \\mathbf{KRK}^\\mathsf T$$\n", "\n", "\n", - "I frequently get emails and/or GitHub issues raised, claiming the implementation is a bug. It is not a bug, and I use it for several reasons. First, the subtraction $(\\mathbf I - \\mathbf{KH})$ can lead to nonsymmetric matrices results due to floating point errors. Covariances must be symmetric, and so becoming nonsymmetric usually leads to the Kalman filter diverging, or even for the code to raise an exception because of the checks built into `NumPy`.\n", + "I frequently get emails and/or GitHub issues raised, claiming the implementation is a bug. It is not a bug, and I use it for several reasons. First, the subtraction $(\\mathbf I - \\mathbf{KH})$ can lead to nonsymmetric matrix results due to floating point errors. Covariances must be symmetric, and so becoming nonsymmetric usually leads to the Kalman filter diverging, or even for the code to raise an exception because of the checks built into `NumPy`.\n", "\n", "A traditional way to preserve symmetry is the following formula:\n", "\n", @@ -1024,7 +1024,7 @@ "\\mathbf P = (\\mathbf P + \\mathbf P^\\mathsf T) / 2$$\n", "\n", "\n", - "Let's just derive the equation from first principles. It's not too bad, and you need to understand the derivation to understand the purpose of the equation, and, more importantly, diagnose issues if you filter diverges due to numerical instability. This derivation comes from Brown[4].\n", + "Let's just derive the equation from first principles. It's not too bad, and you need to understand the derivation to understand the purpose of the equation, and, more importantly, diagnose issues if your filter diverges due to numerical instability. This derivation comes from Brown[4].\n", "\n", "First, some symbology. $\\mathbf x$ is the true state of our system. $\\mathbf{\\hat x}$ is the estimated state of our system - the posterior. And $\\mathbf{\\bar x}$ is the estimated prior of the system. \n", "\n",