An algorithm for estimating the generalized fundamental traffic variables from point measurements using initial conditions

Fundamental macroscopic traffic variables (flow, density, and average speed) have been defined in two ways: classical (defined as either temporal or spatial averages) and generalized (defined as temporal-spatial averages). In the available literature, 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 not detected during these sampling cycles. The algorithm is introduced for single-lane roads first, and is extended to multi-lane roads. For evaluation of the proposed approach, Next Generation SIMulation (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 compared with other approaches.