From 04190ae27825c601d97b14c7667d9c6951a00814 Mon Sep 17 00:00:00 2001 From: Andreas Stefl Date: Thu, 5 Dec 2024 13:12:08 +0100 Subject: [PATCH] docs: Change to 6x6 track parameter covariance to include time (#3941) I think we rarely work with a 5x5 covariance matrix and the time parameter is already introduced above. ## Summary by CodeRabbit - **Documentation** - Updated the `tracking.md` document with enhanced explanations on track parametrization and covariance matrices. - Expanded the covariance matrix to a $6 \times 6$ format to include time as a parameter. - Improved clarity and coherence of the content, including restructured sections and maintained visual aids. - Refined descriptions of numerical integration techniques and uncertainty handling in particle propagation. --- docs/tracking.md | 13 +++++++------ 1 file changed, 7 insertions(+), 6 deletions(-) diff --git a/docs/tracking.md b/docs/tracking.md index 54e582d1e0f..442a3793adc 100644 --- a/docs/tracking.md +++ b/docs/tracking.md @@ -97,16 +97,17 @@ position $l$ and the momentum vector $\vec p$ are shown. Aside from the nominal quantities captured in $\vec x$, the related uncertainties and correlations need to be taken into account as well. They -can be expressed as a $5\times 5$ covariance matrix like +can be expressed as a $6\times 6$ covariance matrix like \begin{equation*} C = \begin{bmatrix} - \sigma^2(l_0)& \text{cov}(l_0,l_1) & \text{cov}(l_0, \phi) & \text{cov}(l_0, \theta) & \text{cov}(l_0, q/p) \\ - . & \sigma^2(l_1) & \text{cov}(l_1, \phi) & \text{cov}(l_1, \theta) & \text{cov}(l_1, q/p) \\ - . & . & \sigma^2(\phi) & \text{cov}(\phi,\theta) & \text{cov}(\phi, q/p) \\ - . & . & . & \sigma^2(\theta) & \text{cov}(\theta, q/p) \\ - . & . & . & . & \sigma^2(q/p) + \sigma^2(l_0)& \text{cov}(l_0,l_1) & \text{cov}(l_0, \phi) & \text{cov}(l_0, \theta) & \text{cov}(l_0, q/p) & \text{cov}(l_0, t) \\ + . & \sigma^2(l_1) & \text{cov}(l_1, \phi) & \text{cov}(l_1, \theta) & \text{cov}(l_1, q/p) & \text{cov}(l_1, t) \\ + . & . & \sigma^2(\phi) & \text{cov}(\phi,\theta) & \text{cov}(\phi, q/p) & \text{cov}(\phi, t) \\ + . & . & . & \sigma^2(\theta) & \text{cov}(\theta, q/p) & \text{cov}(\theta, t) \\ + . & . & . & . & \sigma^2(q/p) & \text{cov}(q/p, t) \\ + . & . & . & . & . & \sigma^2(t) \end{bmatrix} \end{equation*}