In this paper we address the problem of estimating the Time-of-Flight of a transmitted signal when the shape of the received waveform is stochastic. Specifically, we examine the case when the transmission system model is stochastic, linear and time discrete, with additive Gaussian noise, and where the transmitted waveform is known to the receiver. The joint estimation is couched in terms of Maximum a Posteriori (MAP) and Maximum Likelihood estimation. When deriving the MAP estimator we assume a priori knowledge of the probability density of the transmission system impulse response. The MAP estimator is then compared to estimators derived using less a priori information and lower order system models. The ordinary correlation based Time-of-Flight estimator assumes knowledge of the received waveform, that is has a one-dimensional transmission system model. This investigation indicates that a more complex model structure is worthwhile when distortion in excess of low additive noise is present.