Adjoint-enhanced positioning algorithm for sensor network in turbulent environments

Accurate and swift identification of pollution source locations by remote measurements is challenging given the uncertainty in the background turbulent dispersion and the diffusion process. A multi-sensor algorithm based on the forward-adjoint duality relation is built for quick detection of a localized, continuous pollution source with unknown location and intensity in turbulence. According to the duality relation, the ratio of the observations of the scalar concentration at the sensor locations is mathematically related to the ratio of the corresponding adjoint fields at the source location, which provides important information to determine the source location. With a known velocity field, only four sensor measurements are required to locate a three-dimensional source. Having more measurement data will increase the robustness of the algorithm. When the background turbulence is unknown, the adjoint field of a sensor could be represented as a probability distribution, and the source location can be estimated through MCMC. As a result, the algorithm has the potential to quickly identify the probability of source locations according to the remote measurements of a sensor network. Preliminary results are demonstrated in the channel flow as well as isotropic turbulence setups.