High-gain observer for nonlinear density estimation of traffic networks

A single origin and single destination traffic network with multiple routes and sections is considered. The state variables are assumed to be traffic densities in these sections. For dynamic routing of traffic, accurate measurement of these variables is needed. This requires the placement of numerous sensors, one at each section, which is a costly solution. In this work, a simpler solution is presented based on a single sensor placed at the destination node and the use of a high-gain observer for estimation of traffic densities in individual route sections. It is known that arbitrarily fast high-gain observers can be designed in a deterministic setting. In this case, a high gain observer is used where there is a small noise component and its performance is compared to that of the extended Kalman filter. Two sets of simulations involving estimation of traffic densities in a network with multiple routes and sections provide proof of feasibility of the concepts introduced in this work.