Cooperative Localization Using Distance Measurements for Mobile Nodes
Abstract
:1. Introduction
2. Multidimensional Scaling Algorithm
The Ambiguity Problem
3. Resolving Rotation and Flip Ambiguities
3.1. Analysis of Rotation Ambiguity
3.2. Analysis of Rotation and Flip Ambiguities
4. Proposed Algorithm Robust to Ambiguity and Noise
Algorithm 1: Algorithm to estimate locations of mobile nodes. |
|
5. Simulations
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
The distance between nodes i and j | |
Euclidean distance matrix given the collection of locations | |
Rotation matrix for given angle | |
True coordinates of the ith node | |
Collection of the true locations of all of the nodes | |
Output of multidimensional scaling given the distance matrix | |
Rotation of the output of multidimensional scaling, , using rotation matrix with the angle, , obtained from the function | |
Function to solve the possible rotation angle between the true positions and using the associated parameters | |
The diagonal elements of |
The parameter after the first movement | |
The parameter after the second movement | |
The change in the parameter after the first movement | |
The change in the parameter, relative to the original, after the second movement |
Appendix A
Appendix B
Appendix C
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Li, W.; Jelfs, B.; Kealy, A.; Wang, X.; Moran, B. Cooperative Localization Using Distance Measurements for Mobile Nodes. Sensors 2021, 21, 1507. https://doi.org/10.3390/s21041507
Li W, Jelfs B, Kealy A, Wang X, Moran B. Cooperative Localization Using Distance Measurements for Mobile Nodes. Sensors. 2021; 21(4):1507. https://doi.org/10.3390/s21041507
Chicago/Turabian StyleLi, Wenchao, Beth Jelfs, Allison Kealy, Xuezhi Wang, and Bill Moran. 2021. "Cooperative Localization Using Distance Measurements for Mobile Nodes" Sensors 21, no. 4: 1507. https://doi.org/10.3390/s21041507
APA StyleLi, W., Jelfs, B., Kealy, A., Wang, X., & Moran, B. (2021). Cooperative Localization Using Distance Measurements for Mobile Nodes. Sensors, 21(4), 1507. https://doi.org/10.3390/s21041507