Cooperative Maximum Likelihood estimation for fluid flow dynamics in biosensor arrays

This paper deals with estimation of the concentration of target molecules in a fluid when it flows past multiple biosensors. The fluid flow is modelled as an advection diffusion partial differential equation. Estimating the concentration from multiple biosensors then is equivalent to solving an inverse problem. We use averaging theory methods to model the asymptotic behaviour of PDE model by a system of ordinary differential equations. The resulting nonlinear least squares problem is then solved numerically. We also use the new model to derive the mean squared estimation error of concentration analytically. As a case study, we illustrate our results on a biosensor built out of protein molecules to verify the accuracy of proposed method.