Achievable accuracy in Gaussian plume parameter estimation using a network of binary sensors

• Theoretical Cramér–Rao bounds derived for parameter estimation of an atmospheric dispersion model.
• The work important for hazard modelling in the context of toxic source localisation.
• Bounds derived for the binary sensor network, as well as for the non-quantised (analogue measurement) sensor network.
• Theoretical bounds examined as a function of the binary threshold, sensor placement, and prior uncertainty.
• A comparison of the theoretical bound with empirical RMS errors of an MCMC estimation technique provided as a validation.

The Gaussian plume model is the core of most regulatory atmospheric dispersion models. The parameters of the model include the source characteristics (e.g. location, strength) and environmental parameters (wind speed, direction, atmospheric stability conditions). The paper presents a theoretical analysis of the best achievable accuracy in estimation of Gaussian plume parameters in the context of a continuous point-source release and using a binary sensor network for acquisition of measurements. The problem is relevant for automatic localisation of atmospheric pollutants with applications in public health and defence. The theoretical bounds of achievable accuracy provide a guideline for sensor network deployment and its performance under various environmental conditions. The bounds are compared with empirical errors obtained using a Markov chain Monte Carlo (MCMC) parameter estimation technique.