TY - JOUR
T1 - The Number of Global Solutions for GPS Source Localization in Two-Dimension
AU - Kwon, Kiwoon
N1 - Publisher Copyright:
© 2024 Kiwoon Kwon.
PY - 2024
Y1 - 2024
N2 - Source localization is widely used in many areas including GPS, but the influence of possible noises cannot be overlooked. Many optimization methods have been attempted to mitigate different kinds of noises. However, the stability of the solution, even the number of global solutions, is not fully known. Only local convergence or stability for the optimization problem is known in simple L1 or L2 settings. In this paper, we prove that the number of possible two-dimensional source locations with three measurements in L2 setting is at most 5. We also showed the sufficient and necessary condition for the number of the solutions being 1, 2, 3, 4, and 5, where the measurement triangle is isosceles and the measurement distance for the two isosceles triangles is the same.
AB - Source localization is widely used in many areas including GPS, but the influence of possible noises cannot be overlooked. Many optimization methods have been attempted to mitigate different kinds of noises. However, the stability of the solution, even the number of global solutions, is not fully known. Only local convergence or stability for the optimization problem is known in simple L1 or L2 settings. In this paper, we prove that the number of possible two-dimensional source locations with three measurements in L2 setting is at most 5. We also showed the sufficient and necessary condition for the number of the solutions being 1, 2, 3, 4, and 5, where the measurement triangle is isosceles and the measurement distance for the two isosceles triangles is the same.
UR - http://www.scopus.com/inward/record.url?scp=85207370956&partnerID=8YFLogxK
U2 - 10.1155/2024/7980810
DO - 10.1155/2024/7980810
M3 - Article
AN - SCOPUS:85207370956
SN - 2314-4629
VL - 2024
JO - Journal of Mathematics
JF - Journal of Mathematics
M1 - 7980810
ER -