In this paper, the problem of pollutant source localisation and flow is addressed. It is tackled in a one dimensional context such as river or tunnel with the aid of one remote sensor. N possible sources are considered, one of whom is operating. A specific effort is made upon the impulse responses family which are approximated as a bank of FIR filters with specific delays and orders. In order to reduce the set of solutions, a source flow model is considered which introduces time bounds. Using these features, a joint estimation decision is derived in a bayesian framework and it is compared to the case when source assumptions are dropped. The benefit for this kind of solution is shown practically in terms of localisation quality.