Coprime Baseline Requirement in Chinese Remainder Theorem for Multi-Baseline Phase Interferometer Ambiguity Resolution

In phase interferometer systems, multi-baseline configurations are commonly employed to enhance direction-finding accuracy and resolve phase ambiguity issues. The application of the Chinese Remainder Theorem serves as a crucial mathematical tool, enabling the reconstruction of true phase differences from multiple measurement results through modular arithmetic operations.

The core of the ambiguity resolution process lies in utilizing phase difference residues measured by different baselines. Baseline lengths determine the periodicity of phase differences - when baseline lengths are coprime (having a greatest common divisor of 1), their periodic characteristics avoid overlapping repetition, thereby ensuring the Chinese Remainder Theorem can uniquely determine the true phase value. In code implementation, this involves calculating residue values using modulo operations with baseline-specific periods and applying CRT algorithms to combine these residues.

If baseline relationships are not coprime, measurements from multiple baselines will produce periodic coincidences, leading to ambiguity resolution failure or multiple possible solutions. Therefore, when designing multi-baseline phase interferometers, engineers must ensure baseline lengths satisfy the coprime condition to improve computational reliability and accuracy. This typically involves implementing GCD verification algorithms during the baseline design phase and optimizing baseline length selection.

This methodology finds widespread application in radar systems, radio astronomy, and other fields requiring high-precision angle measurement, providing the theoretical foundation for advanced direction-finding systems with practical implementation through specialized signal processing algorithms.