A Novel Method for Asynchronous Time-of-Arrival-Based Source Localization: Algorithms, Performance and Complexity.

Area of Science:

• Signal Processing
• Wireless Communications
• Geospatial Analysis

Background:

• Accurate source localization using time-of-arrival (TOA) relies on precise signal propagation times.
• Practical sensor networks often suffer from clock synchronization errors, leading to asynchronous states.
• Existing asynchronous localization methods often employ convex relaxation (e.g., SDP), causing performance degradation.

Purpose of the Study:

• To develop a novel method for asynchronous source localization that avoids performance-limiting relaxations.
• To address the nonconvex and nonsmooth objective function inherent in asynchronous TOA-based localization.
• To improve localization accuracy and computational efficiency compared to current state-of-the-art algorithms.

Main Methods:

• Proposed a Proximal Alternating Minimization Positioning (PAMP) method to directly minimize the original nonconvex objective function.
• Leveraged the biconvex property of the asynchronous problem to decompose it into clock offset and synchronous localization subproblems.
• Derived a global solution for the clock offset subproblem and employed an efficient subgradient algorithm for the synchronous localization subproblem.

Main Results:

• The PAMP method achieves preferable localization performance without relying on convex relaxation.
• Demonstrated lower computational complexity compared to existing state-of-the-art approaches.
• Established the convergence of the PAMP method within a Lyapunov framework.
• Simulation results show PAMP performance approaching the Cramér-Rao Lower Bound (CRLB).

Conclusions:

• The proposed PAMP method offers an effective solution for asynchronous source localization problems.
• PAMP provides a balance between high accuracy and computational efficiency.
• The method's performance is robust and approaches theoretical optimality limits.