Macroscopic traffic state estimation using relative flows from stationary and moving observers

•Point-observations of the cumulative vehicle number are obtained from relative flow data collected by stationary and moving observers.•Methodology to estimate flow and density in a pre-defined space-time mesh based on point-observations of the cumulative vehicle number.•Conservation of vehicles is the basis for the proposed estimation methodology.•The methodology does not rely on information in the form of a traffic flow model or historical data.•Estimation performance depends on the homogeneity and stationarity of traffic in combination with the sampling of the observations in space and time. This article presents a procedure to estimate the macroscopic traffic state in a pre-defined space-time mesh using relative flow data collected by stationary and moving observers. The procedure consist of two consecutive and independent processes: (1) estimate point observations of the cumulative vehicle number in space-time, i.e., N(x, t), based on relative flow data from the observers and (2) estimate flow and density in a pre-define space-time mesh based on the point observations of N. In this paper, the principles behind the first process are explained and a methodology (the Point-Observations N (PON) estimation methodology) is introduced for the second process. This methodology does not incorporate information in the form of a traffic flow model or historical data. To evaluate this performance and improve our understanding of the methodology, a microscopic simulation study is conducted. The estimation performance is effected by the homogeneity and stationarity of traffic in estimation area and in the sample area. In case of large changes in traffic conditions, e.g., from free-flow to congestion or stop-and-go waves, a better sampling resolution will improve localizing these changes in space and time and hence improve the estimation performance. In the simulation study, the proposed methodology is also compared with estimates based on loop-detector data. This indicates that the combination of the proposed methodology and data yields an alternative for existing combinations of methodology and data. Especially, in terms of density estimation the introduced methodology shows promising results.