This paper develops a new methodology for deriving an empirical fundamental relationship from vehicle detector data. The new methodology seeks to address several sources of noise present in conventional measures of the traffic state that arise from the data aggregation process, e.g., averaging across all vehicles over a fixed time period. In the new methodology vehicles are no longer taken successively in the order in which they arrived and there is no requirement to seek out stationary traffic conditions; rather, the traffic state is measured over the headway for each individual vehicle passage and the vehicles are grouped by similar lengths and speeds before aggregation. Care is also taken to exclude measurements that might be corrupted by detector errors. The result is a homogeneous set of vehicles and speeds in each bin. While conventional fixed time averages may have fewer than 10 vehicles in a sample, the new binning process ensures a large number of vehicles in each bin before aggregation. We calculate the median flow and median occupancy for each combined length and speed bin. Then we connect these median points across all of the speed bins for a given vehicle length to derive the empirical fundamental relationship for that length. This use of the median is also important; unlike conventional aggregation techniques that find the average, the median is far less sensitive to outliers arising from uncommon driver behavior or occasional detector errors.
