A. Jamshidnejad and B. De Schutter, "An algorithm for estimating the generalized fundamental traffic variables from point measurements using initial conditions," Transportmetrica B: Transport Dynamics, vol. 6, no. 4, pp. 251-285, 2018.
Fundamental macroscopic traffic variables (flow, density, and average speed) have been defined and formulated in two different ways: the classical definitions (defined as either temporal or spatial averages) and the generalized definitions (defined as temporal-spatial averages). The available literature has considered estimation of the classical variables, while estimation of the generalized variables is still missing. This paper proposes a new efficient sequential algorithm for estimating the generalized traffic variables using point measurements. The algorithm takes into account those vehicles that stay between two consecutive measurement points for more than one sampling cycle and that are thus not detected during these sampling cycles. The algorithm is introduced for single-lane roads first, and then is extended to multi-lane roads. For evaluation of the proposed approach, NGSIM data, which provides detailed information on trajectories of the vehicles on a segment of the interstate freeway I-80 in San Francisco, California is used. The simulation results illustrate the excellent performance of the sequential procedure for estimating the generalized traffic variables compared with other approaches.