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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.