Blessing Nwonu: Mass-Preserving Reconstruction of Macroscopic Fields for Hyperbolic Conservation Laws from Incomplete Trajectory Data

Modern vehicle trajectory datasets, such as the I-24 MOTION, provide high-resolution microscopic information on traffic flow, but are often affected by missing data, measurement noise, and incomplete structural information. These limitations make it challenging to reconstruct reliable macroscopic fields, which are required to assess how well macroscopic traffic models reproduce observed traffic dynamics.   

In this talk, we present a modeling framework for reconstructing consistent macroscopic fields from imperfect microscopic trajectory observations. The approach combines (i) an acceleration-based minimum cost maximum bipartite matching procedure to identify physically feasible connections between trajectory fragments, and (ii) a probabilistic phantom-density model that distributes missing vehicle mass in regions with incomplete observations. This leads to a reliable reconstruction that preserves mass (i.e., avoids spurious gains or losses of mass), while accounting for the uncertainty induced by incomplete microscopic information. We present visualizations of naively reconstructed density fields and show how incomplete data can introduce spurious variation in mass and artificial discontinuities in the density fields. We then demonstrate that our proposed method reduces these spurious artifacts and produces smoother, physically consistent fields, enabling reliable validation of macroscopic traffic models.