Applications of Kalman Filtering in Traffic Management and Control

In many areas of traffic management and control the variables that are of most interest are often the ones that are most difficult to measure and estimate. Take for example vehicular density (vehicles per kilometer) and space-mean speed (kilometers per hour). A reliable real-time estimate of these quantities is critically important for real-time control of traffic networks. However, neither can be straightforwardly deduced from available sensor data. Similarly elusive quantities are origin–destination (OD) flows. These depict the amount of vehicles per hour planning to go from one place to another at a certain moment. Unless we literally know the origin and destination of all vehicles on a traffic network, advanced estimation techniques are required to extract OD patterns from whatever data and prior knowledge we have available. One intuitive and highly effective method to solve these types of problems (i.e., estimating a quantity x when all we have are observations y and prior knowledge about the process) is the Kalman filter, first proposed by Rudolf Kalman in 1960. In this tutorial we explain with many examples how this technique can be applied in the domain of traffic management and control to solve real-world problems. We will see that Kalman filtering is a powerful technique that works surprisingly well in many cases, but there are also clear limitations that relate to the many assumptions underlying its application.