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Wireless Signal Travel Distance Estimation Using Non-Coprime Wavelengths

The Chinese remainder theorem (CRT) is often used to find unwrap signal phase over multiple wavelengths as a means of estimating total travel time of a signal. Existing approaches, implemented efficiently in closed form using either standard CRT or methods derived from lattice theory, require the wavelengths involved to be coprime. This can be a limiting factor in real applications, especially where the available signal bandwidth is limited. In this letter, we derive a new algorithm to extend the closed-form lattice algorithm to accommodate non-coprime wavelengths. The benefit of this development is demonstrated with a Wi-Fi wireless device localization example.