Analytic and Unambiguous Phase-Based Algorithm for 3-D Localization of a Single Source with Uniform Circular Array.

Area of Science:

• Signal Processing
• Array Signal Processing
• Electromagnetics

Background:

• Accurate source localization is critical in various applications, including radar and sonar.
• Existing methods often face challenges with computational complexity and ambiguity resolution.
• Uniform Circular Arrays (UCAs) offer unique advantages for directional and positional estimation.

Purpose of the Study:

• To develop an analytic algorithm for 3-D localization of a single source using UCA interferometers.
• To reformulate the localization problem using Fourier transforms for efficient parameter decoupling.
• To address ambiguity resolution and phase range compression analytically.

Main Methods:

• Exploiting Fourier transforms to expand phase distribution and reformulate localization as spectrum manipulation.
• Decoupling 3-D parameters into different Fourier spectrums and establishing algebraic relations.
• Utilizing the high-order difference invariance (HODI) property of UCAs for phase range compression and ambiguity resolution.

Main Results:

• The minimum number of UCA elements required for 3-D localization is five, based on the Fourier sampling theorem.
• Estimation accuracy increases with a larger number of array elements.
• The proposed algorithm achieves simultaneous, analytic ambiguity resolution and 3-D localization, proving computationally efficient.

Conclusions:

• The developed analytic algorithm provides an effective and efficient solution for 3-D source localization with UCAs.
• The method demonstrates superior performance validated by numerical simulations and experimental results.
• The simultaneous analytic processing of localization and ambiguity resolution represents a significant advancement.