Estimating Uncertainty in Time-difference and Doppler Estimates

Sound and radio can be used to estimate the distance between a transmitter and a sender by correlating the emitted and received signal. Alternatively by correlating two received signals it is possible to estimate distance difference. Such methods can be divided into methods that are robust to noise and reverberation, but give limited precision and sub-sample refinements that are sensitive to noise, but give higher precision when initialized close to the real translation. In this paper we develop stochastic models that can explain the limits in the precision of such sub-sample time-difference estimates. Using such models we provide new methods for precise estimates of time-differences as well as Doppler effects. The method is verified on both synthetic and real data.