Generalized Least Squares for Vehicle Traffic Estimation

Estimating Origin-Destination (OD) matrices is a fundamental problem in transportation planning, as they provide critical insights into travel demand and traffic flow distribution. Traditional methods rely on traffic surveys, vehicle tracking, and network tomography techniques, but these approaches often suffer from high costs, limited data availability, and significant estimation uncertainties. In this paper, we present a novel approach to OD estimation that leverages joint cumulants and bootstrapping techniques to improve the robustness of OD demand predictions. Unlike previous methodologies that rely on extensive prior information or require full statistical knowledge of network flows, our method operates under realistic constraints where only a subset of flow measurements is available. By estimating the covariance matrix of joint cumulants and applying a generalized least squares (GLS) approach, we systematically reduce estimation errors while ensuring computational efficiency. Simulation results on both synthetic and real-world datasets indicate that our method performs well in terms of accuracy, suggesting its potential usefulness for traffic management applications.