From 2e41e46fb1ca0533dfedc3c1eb59424873dd4548 Mon Sep 17 00:00:00 2001
From: eneller <erikneller@gmx.de>
Date: Fri, 7 Nov 2025 13:11:59 +0100
Subject: [PATCH] lec01

---
 .gitignore |  2 ++
 lec01.md   | 29 +++++++++++++++++++++++++++++
 2 files changed, 31 insertions(+)
 create mode 100644 lec01.md

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 # End of https://www.toptal.com/developers/gitignore/api/R
 
 *.pdf
+*.html
+bib
diff --git a/lec01.md b/lec01.md
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+# Code-Based Positioning
+Code Based Positioning is based on solving the geometric problem of using at least 4 pseudorange measurements from satellites,
+resulting in
+
+$$
+R^j - D^j \simeq \sqrt{(x^j-x)^2 + (y^j-y)^2 + (z^j-z)^2} + c\delta t
+$$
+$$
+j = 1,2,...,n (n\geq 4)
+$$
+It uses the continuosly broadcast signals by satellites to calculate time-of-flight to the receiver's position,
+and then estimating the distance to each of them.
+It is implemented as the standard positioning service.
+
+# Phase-Based Positioning
+If higher accuracy is needed, phase-based positioning is used, which is implemented in Precise Point Positioning (PPP).
+It provides a significantly higher accuracy with centimetre-level positioning but incurs higher computational costs 
+as more corrections have to be applied
+and requires tracking continuity.
+As the name suggests, both code and phase observations are used.
+
+Code and carrier measuremens are modeled as:
+$$
+R^j_C = \rho^j + c(\delta t - \delta t^j) + Tr^j + M^j_C + \epsilon^j_C
+$$
+$$
+\Phi^j_C = \rho^j + c(\delta t - \delta t^j) + Tr^j + \lambda^j_C + B^j_C + m^j_C +\epsilon^j_C
+$$
+Where $R^j$ is the unsmoothed pseudorange measurment for the $j$th satellite and $\Phi^j$ is the corresponding carrier measurement.