Transportation Origin-Destination Demand Estimation with Quasi-Sparsity.

This article focuses on the development and analysis of a quasi-sparsity–based origin-destination (OD) demand estimation framework (QSOD) for transportation networks, addressing the characteristic that most OD pairs have small but nonzero demands—a property termed quasi-sparsity. The QSOD framework includes two models: a fixed-mapping QSOD model and a bilevel QSOD model incorporating user equilibrium traffic assignment, both leveraging compressed sensing techniques applied to the deviation between estimated and prior OD demands. Theoretical results establish conditions under which the estimated OD matrix preserves the quasi-sparsity property of the prior OD matrix, and show that for large networks, most estimated OD demands equal either their prior values or zero (or a small positive value in the bilevel case). Numerical experiments on a small network and a downtown Seattle network demonstrate that QSOD models maintain quasi-sparsity consistency with comparable or improved estimation accuracy and computational efficiency relative to existing methods such as generalized least squares (GLS), while also exhibiting robustness to outliers and not requiring hyperparameter tuning or weighting matrices. The study highlights practical implications for preparing representative prior OD matrices and suggests directions for future research including dynamic extensions, integration of diverse data sources, and large-scale applications.