Short pulse multi-frequency phase-based time delay estimation

An approach for time delay estimation, based on phase difference detection, is presented. A multiple-frequency short continuous wave pulse is used to solve the well-known phase ambiguity problem when the maximum distance exceeds a full wavelength. Within an unambiguous range defined with the lowest frequency difference between components, the corresponding phase difference is unique and any distance within this range can be determined. Phase differences between higher frequency components are used to achieve a finer resolution. The concept will be presented and the effectiveness of the approach will be investigated through theoretical and practical examples. The method will be validated using underwater acoustic measurements, simulating noisy environments, demonstrating resolutions better than a 50th of a wavelength, even in the presence of high levels (−5 dB) of additive Gaussian noise. Furthermore, the algorithm is simple to use and can be easily implemented, being based on phase detection using the discrete Fourier transform.