Unknown input filtering for nonlinear systems and its application to traffic state estimation

This paper considers the estimation problem of traffic state in freeway networks in light of the unknown input filtering (UIF) framework. The freeway traffic flow is modeled as a dynamic stochastic nonlinear system and is based on a recently developed speed-extended cell-transmission model of freeway traffic. Since the environmental conditions on a freeway may change over time, model parameters estimation is also considered. It is shown that the dual state and parameter estimation problem can be solved by applying the UIF to a nonlinear system with unknown inputs. Recently, a nonlinear version of the extended recursive three-step filter, named as the NERTSF, was employed to solve the problem. However, a numerical approximation method is used to calculate the model partial derivatives. To relax that restriction, in this paper a derivative-free versions of the NERTSF is further proposed to solve the addressed estimation problem of the freeway traffic flow.