Stochastic Analysis of Time-Difference and Doppler Estimates for Audio Signals
Pairwise comparison of sound and radio signals can be used to estimate the distance between two units that send and receive signals. In a similar way it is possible to estimate differences of distances by correlating two received signals. There are essentially two groups of such methods, namely methods that are robust to noise and reverberation, but give limited precision and sub-sample refinements that are more sensitive to noise, but also give higher precision when they are initialized close to the real translation. In this paper, we present stochastic models that can explain the precision limits of such sub-sample time-difference estimates. Using these models new methods are provided for precise estimates of time-differences as well as Doppler effects. The developed methods are evaluated and verified on both synthetic and real data.
KeywordsTime-difference of arrival Sub-sample methods Doppler effect Uncertainty measure
This work is supported by the strategic research projects ELLIIT and eSSENCE, Swedish Foundation for Strategic Research project “Semantic Mapping and Visual Navigation for Smart Robots” (grant no. RIT15-0038) and Wallenberg Autonomous Systems and Software Program (WASP).
- 4.Batstone, K., Oskarsson, M., Åström, K.: Robust time-of-arrival self calibration and indoor localization using wi-fi round-trip time measurements. In: Proceedings of International Conference on Communication (2016)Google Scholar
- 6.Cirillo, A., Parisi, R., Uncini, A.: Sound mapping in reverberant rooms by a robust direct method. In: IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 285–288, April 2008Google Scholar
- 8.Crocco, M., Del Bue, A., Bustreo, M., Murino, V.: A closed form solution to the microphone position self-calibration problem. In: ICASSP, March 2012Google Scholar
- 9.Do, H., Silverman, H., Yu, Y.: A real-time SRP-PHAT source location implementation using stochastic region contraction (SRC) on a large-aperture microphone array. In: ICASSP 2007, vol. 1, pp. 121–124, April 2007Google Scholar
- 10.Flood, G., Heyden, A., Åström, K.: Estimating uncertainty in time-difference and doppler estimates. In: 7th International Conference on Pattern Recognition Applications and Methods (2018)Google Scholar
- 12.Kuang, Y., Åström, K.: Stratified sensor network self-calibration from tdoa measurements. In: EUSIPCO (2013)Google Scholar
- 13.Kuang, Y., Burgess, S., Torstensson, A., Åström, K.: A complete characterization and solution to the microphone position self-calibration problem. In: ICASSP (2013)Google Scholar
- 14.Kuang, Y., Åström, K.: Stratified sensor network self-calibration from tdoa measurements. In: 21st European Signal Processing Conference 2013 (2013)Google Scholar
- 17.Petersen, K.B., Pedersen, M.S., et al.: The matrix cookbook. Tech. Univ. Den. 7(15), 510 (2008)Google Scholar
- 19.Pollefeys, M., Nister, D.: Direct computation of sound and microphone locations from time-difference-of-arrival data. In: Proceedings of ICASSP (2008)Google Scholar
- 21.Zhayida, S., Segerblom Rex, S., Kuang, Y., Andersson, F., Åström, K.: An Automatic System for Acoustic Microphone Geometry Calibration based on Minimal Solvers. ArXiv e-prints, October 2016Google Scholar
- 22.Zhayida, S., Andersson, F., Kuang, Y., Åström, K.: An automatic system for microphone self-localization using ambient sound. In: 22st European Signal Processing Conference (2014)Google Scholar