Majorization-Minimization Method for Elliptic Localization in the Absence of Transmitter Position

Area of Science:

• Signal Processing
• Electromagnetics
• Estimation Theory

Background:

• Elliptic localization is crucial for various applications but challenging without known transmitter positions.
• Existing methods struggle with non-convex optimization problems inherent in localization.
• Accurate localization requires robust estimation techniques, especially with indirect signal paths.

Purpose of the Study:

• To develop an efficient iterative method for joint target and transmitter localization.
• To address the non-convex maximum likelihood estimation problem in elliptic localization.
• To extend the method for scenarios with multiple unknown transmitters and receiver errors.

Main Methods:

• Formulation of a non-convex maximum likelihood estimation (MLE) problem using direct and reflected signal paths.
• Application of the majorization-minimization (MM) principle to iteratively solve the non-convex MLE problem.
• Extension of the MM method to handle multiple unknown transmitters and receiver position errors.

Main Results:

• The proposed MM method effectively estimates both target and transmitter positions.
• The method demonstrates superior performance compared to state-of-the-art techniques in numerical simulations.
• The MM approach provides a robust solution for complex localization scenarios.

Conclusions:

• The developed iterative MM method offers an efficient solution for elliptic localization without prior transmitter position knowledge.
• The method is robust and outperforms existing approaches, particularly in challenging environments.
• This work advances localization techniques by effectively handling non-convex optimization and generalized scenarios.