Non-linear approximation filtering in estimating the origin of contaminant particles in a fluid flow using fixed sensors

The problem of accurately locating the origin of contaminant particles from noisy measurements obtained from a finite number of fixed sensors is treated here. The main methodology used here is particle filtering techniques in conjunction with model reduction. The physical system considered here consists of contaminant particles originating from an unknown location in a confined space, which are being carried away by the airflow inside a room. The path of the particles is influenced by both air flow inside the room as well as the inherent random movement of the particles. Concentration of the particles at each sensor is measured at discrete time instances. These measurements are inaccurate due to additive random noise and would be processed under a particle filter algorithm to estimate the origin of contaminant particles. Particle filters in nature involve heavy computational cost and it is shown that it can be greatly reduced by executing the algorithm in multi stages, modifying the importance weights formula, generating initial points using observations and reducing the dimensionality of the mathematical model. Extensive simulation experiments are carried out to show the effectiveness of particle filters in calculating the origin of contaminant.