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.