Extended spectral envelope method for detecting and analyzing traffic oscillations

We propose using a spectral envelope method to analyze traffic oscillations using data collected from multiple sensors. Spectral envelops can reveal not only the salient frequencies of periodic oscillations of traffic flow, but also the relative strength of these oscillations at different locations. This paper first introduces time dimension into the existing spectral envelope method so that it can be applied to study the evolution of vehicular traffic oscillations. The extended spectral envelope method proposed in this paper, or ESPE, discards the normalization procedure in the standard method. A new Contributing Index (CI) is proposed to measure the relative strength of oscillations at different locations. The extended spectral envelops can be constructed on long-term or short-term time scales. While the long-term analysis helps extract salient frequencies of traffic oscillations, the short-term analysis promises to reveal their detailed spatial-temporal profiles. ESPE offers two distinctive advantages. First, it is more robust against the impacts of noises. Second, it is able to uncover complicated oscillatory behaviors which are otherwise difficult to notice. These advantages are demonstrated in case studies constructed on both simulated and real data.