From d467021f6cc4b7c775cbe308faf559633c5d6fec Mon Sep 17 00:00:00 2001 From: Flinner Yuu Date: Sat, 24 Feb 2024 23:08:50 +0300 Subject: [PATCH] init --- ...alization Using Carrier-Phase Measurements | 352 ++++++++++++++++++ 1 file changed, 352 insertions(+) create mode 100644 Acoustic Localization Using Carrier-Phase Measurements diff --git a/Acoustic Localization Using Carrier-Phase Measurements b/Acoustic Localization Using Carrier-Phase Measurements new file mode 100644 index 0000000..2f2f5f8 --- /dev/null +++ b/Acoustic Localization Using Carrier-Phase Measurements @@ -0,0 +1,352 @@ +### A Pluto.jl notebook ### +# v0.19.39 + +using Markdown +using InteractiveUtils + +# ╔═╡ d3b7f59a-712b-4520-a413-c5f5eb71a12f +begin + using PlutoUI + TableOfContents() + md"- Pakcages" +end + +# ╔═╡ 29893d76-8153-4b84-89ac-289e41327205 +md""" +# Acoustic Localization Using Carrier-Phase Measurements + +## Introduction + +TODO! + +## Problem Statment + +!!! info "This text is copied from the provided document." + We assume an acoustic localization system with $M$ beacons transmitting signals of a certain carrier frequency. The signals are received by a mobile device (MD) located at ``x = [x, y, z]^T``, while the beacons are located at ``b_i = v = [x_i, y_i, z_i]^T``, ``i = 1, 2, \ldots, M``. The beacons and the MD are all synchronized. + + By processing the received signal from each beacon, the MD estimates its range from each beacon. In addition, the MD can also obtain the phase of the carrier signal received from each beacon. The range measurements for beacon ``i`` can be modelled as + ```math + r_i =\|x − b_i\|_2 + w_i, + ``` + + where wi is additive noise and ``\|\cdot\|_2`` is the Euclidean norm. On the other hand, the phase data can be described as + ```math + \varphi_i = \|x − b_i\|_2 + n_i + v_i, + ``` + + where ``v_i`` is additive noise and ``n_i \in \mathbb{Z}`` is an integer phase ambiguity. In (1) and (2), we assume that the range and phase are + measured in units of cycles or wavelengths. Hence, ``\varphi_i \in [−0.5, 0.5)``. + The objective of this work is to use both sets of measurements in (1) and (2) to estimate the MD position ``x``. To motivate the + use of the carrier phase data, we assume generally that ``\|v_i\|_2 \ll \|w_i\|_2,\, \forall i \in {1, 2, · · · , M}``. However, this is not a necessary condition for the carrier-phase use to be beneficial. To proceed further, we assume that ``w_i`` and ``v_i`` are independent for all ``i`` + values, and that these noise processes are of zero mean and variances ``\alpha_i^2`` and ``\sigma_i^2``, respectively. + +""" + +# ╔═╡ 835ef9c7-727a-4672-bba4-58aa6766b9e6 +md""" +# Outline of the solution + +!!! info "This text is copied from the provided document." + + To formulate the estimation problem, we can define the objective function: + ```math + f(\mathbf{x}, \mathbf{n}) = \sum_{i=1}^M + \alpha_i^{-2} (r_i - \|x-b_i\|_2)^2 + + \sigma_i^{-2} (\varphi_i - \|x-b_i\|_2 - n_i)^2 + ``` +where n ≜ [n1, n2, · · · , nM]T. Hence, we can obtain a MD position estimate by solving the following mixed integer optimization +problem: +ˆx, ˆn = +arg min +x∈R3,n∈ZMf(x, n) +""" + +# ╔═╡ 6040b344-d338-11ee-256a-67ae4cb673c6 +md""" +# Appendex +""" + +# ╔═╡ 00000000-0000-0000-0000-000000000001 +PLUTO_PROJECT_TOML_CONTENTS = """ +[deps] +PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" + +[compat] +PlutoUI = "~0.7.58" +""" + +# ╔═╡ 00000000-0000-0000-0000-000000000002 +PLUTO_MANIFEST_TOML_CONTENTS = """ +# This file is machine-generated - editing it directly is not advised + +julia_version = "1.10.1" +manifest_format = "2.0" +project_hash = "acf8a7d70217bc877a8d448fd5475fd91c6dd480" + +[[deps.AbstractPlutoDingetjes]] +deps = ["Pkg"] +git-tree-sha1 = "c278dfab760520b8bb7e9511b968bf4ba38b7acc" +uuid = "6e696c72-6542-2067-7265-42206c756150" +version = "1.2.3" + +[[deps.ArgTools]] +uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" +version = "1.1.1" + +[[deps.Artifacts]] +uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" + 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