Time-delay Estimation in Time-warping Environments

Time-delay estimation (TDE) is a common requirement of the ranging and localization systems often found in unattended ground sensors. In this paper we consider novel approaches to the TDE problem in a time-warping acoustic environment, such as that encountered when the propagation velocity is not constant—due to wind gusts, for example. An increasing propagation velocity induces a compression of the received signal, while a diminishing velocity dilates the signal. These effects warp the shape of the received signal and can significantly reduce the effectiveness of traditional TDE algorithms This paper presents algorithms and performance bounds for TDE in random velocity environments. We model unknown signal warping as a low-pass random process, which serves as a form of non-additive noise in the time-delay estimation problem. For warping environments, we propose computationally efficient non-parametric algorithms for TDE that significantly outperform traditional time-delay estimators, such as the location of the sample cross-correlation peak. The Cramér-Rao bound for TDE in a time-warping environment is also presented and used to evaluate the proposed estimators. Simulations demonstrate the bounds and estimator performance for acoustic signals.