# Time-Difference-of-Arrival Estimation Based on Cross Recurrence Plots, with Application to Underwater Acoustic Signals

## Abstract

The estimation of the time difference of arrival (TDOA) consists of the determination of the travel-time of a wavefront between two spatially separated receivers, and it is the first step of processing systems dedicated to the identification, localization and tracking of radiating sources. This article presents a TDOA estimator based on cross recurrence plots and on recurrence quantification analysis. Six recurrence quantification analyses measures are considered for this purpose, including two new ones that we propose in this article. Simulated signals are used to study the influence of the parameters of the cross recurrence plot, such as the embedding dimension, the similarity function, and the recurrence threshold, on the reliability and effectiveness of the estimator. Finally, the proposed method is validated on real underwater acoustic data, for which the cross recurrence plot estimates correctly 77.6 % of the TDOAs, whereas the classical cross-correlation estimates correctly only 70.2 % of the TDOAs.

## Keywords

Correct Estimate Recurrence Pattern Simulated Signal Recurrence Plot Recurrence Quantification Analysis## Notes

### Acknowledgments

The authors would like to thank the DGA for supporting the postdoctoral scholarship of O. Le Bot, the Water Agency of Rhone-Mediterranean-Corsica for supporting the project SEAcoustic during which the acoustic data were recorded, the research team STARESO based in Calvi, and Julie Lossent for technical support during the recording of the data in the Bay of Calvi (France).

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