Closed-form estimation of the speed of propagating waves from time measurements

Annibale P, Rabenstein R (2014)

Publication Language: English

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2014


Publisher: Springer Verlag (Germany)

Book Volume: 25

Pages Range: 361-378

Journal Issue: 2

DOI: 10.1007/s11045-013-0231-x


The propagating speed of waves depends on the physical properties of the transmitting material. Since these properties can vary along the propagation path, they cannot be determined from local measurements. However, mean values of the propagation speed can be obtained from time measurements, either between distributed sources and sensors (Time Of Arrival, TOA) if both are synchronized or otherwise from time differences between distributed sensors (Time Difference Of Arrivals, TDOA). This contribution investigates the required assumptions for speed estimation from time measurements and provides closedform solutions for the synchronized and unsynchronized case. Furthermore the achievable accuracy is determined in terms of Cramer-Rao bounds. The analysis is carried out for the propagation of sound waves in air, where the propagation speed varies with the air temperature. Example results from loudspeaker-microphone recordings are provided. However the closed-form relations apply also to the propagation of other types of waves in linear regimes. This manuscript extends previous work by the authors by providing closed-form solutions and by a parallel treatment of the TOA and the TDOA measurements. © Springer Science+Business Media New York 2013.

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How to cite


Annibale, P., & Rabenstein, R. (2014). Closed-form estimation of the speed of propagating waves from time measurements. Multidimensional Systems and Signal Processing, 25(2), 361-378.


Annibale, Paolo, and Rudolf Rabenstein. "Closed-form estimation of the speed of propagating waves from time measurements." Multidimensional Systems and Signal Processing 25.2 (2014): 361-378.

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