Estimating Erratic Measurement Errors in Network-Wide Traffic Flow via Virtual Balance Sensors

Large-scale traffic flow data are collected by numerous sensors for managing and operating transport systems. However, various measurement errors exist in the sensor data and their distributions or structures are usually not known in the real world, which diminishes the reliability of the collected data and impairs the performance of smart mobility applications. Such irregular error is referred to as the erratic measurement error and has not been well investigated in existing studies. In this research, we propose to estimate the erratic measurement errors in networked traffic flow data. Different from existing studies that mainly focus on measurement errors with known distributions or structures, we allow the distributions and structures of measurement errors to be unknown except that measurement errors occur based on a Poisson process. By exploiting the flow balance law, we first introduce the concept of virtual balance sensors and develop a mixed integer nonlinear programming model to simultaneously estimate sensor error probabilities and recover traffic flow. Under suitable assumptions, the complex integrated problem can be equivalently viewed as an estimate-then-optimize problem: first, estimation using machine learning (ML) methods, and then optimization with mathematical programming. When the assumptions fail in more realistic scenarios, we further develop a smart estimate-then-optimize (SEO) framework that embeds the optimization model into ML training loops to solve the problem. Compared with the two-stage method, the SEO framework ensures that the optimization process can recognize and compensate for inaccurate estimations caused by ML methods, which can produce more reliable results. Finally, we conduct numerical experiments using both synthetic and real-world examples under various scenarios. Results demonstrate the effectiveness of our decomposition approach and the superiority of the SEO framework.