A ST-Copula method for highway traffic data interpolation in monitoring blind areas

Abstract

A comprehensive understanding of the traffic situation in the Monitoring Blind Areas (MBA) of highway is very important for traffic management. However, the complete absence of historical data renders conventional traffic data imputation methods, including tensor decomposition and deep learning algorithms, ineffective. In this paper, a Spatio-temporal Copula (ST-Copula) method is proposed based on the theory of spatial statistics to interpolate traffic data in MBA. Firstly, based on the data series of observation points, the corresponding marginal distribution functions are obtained by data fitting. These marginal functions then be aggregated into a joint function using Copula theory. Secondly, a spatiotemporal correlation matrix is constructed with the spatial variation function to describe the dependent structure of the traffic data, and the maximum likelihood method is adopted to estimate the parameters. Finally, conditional probability density function is constructed according to the spatial location, and Monte-Carlo sampling is applied to deduce the traffic data of the MBA. Based on the above methodology, speed data from a freeway in Zhejiang Province are collected to evaluate the effectiveness of the ST-Copula model. The results showed that compared to Kriging and Copula-based methods, the ST-Copula achieves reductions of 36.4 % and 34.8 % in MAPE and RMSE values, respectively, across various conditions. ST-Copula reduces the limitations of inherent Gaussian assumptions in traditional spatial statistical methods, demonstrating robustness in handling high spatiotemporal variability. The proposed method demonstrates the feasibility of inferring global traffic conditions from limited observations, effectively allowing the monitoring of entire road networks using fewer detectors, thereby reducing road construction costs and rapid response to emergencies.