We address the problem of estimating the time-of-flight (ToF) of a waveform that is disturbed heavily by additional reflections from nearby objects. These additional reflections cause interference patterns that are difficult to predict. The introduction of a model for the reflection in terms of a non-stationary auto-covariance function leads to a new estimator for the ToF of an acoustic tone burst. This estimator is a generalization of the well known matched filter. In many practical circumstances, for instance beacon-based position estimation in indoor situations, lack of knowledge of the additional reflections can lead to large estimation errors. Experiments show that the application of the new estimator can reduce these errors by a factor of about four. The cost of this improvement is an increase in computational complexity by a factor of about seven.