Two fast implementations of the Adaptive Smoothing Method used in highway traffic state estimation

Freeway traffic state estimation is crucial for dynamic traffic management (DTM), Advanced Traveler Information Systems (ATIS) and highway performance analyses. Raw data collected by dual-loop detectors or GPS devices provide information about flow and speed at points in space and time. However, these observations are noisy and incomplete. The Adaptive Smoothing Method (ASM) estimates the traffic state between the observation points and reduces the noise inherent to observations. Current implementations of the ASM apply its model in a straight-forward manner, which leads to high computation times. In this paper, two new implementations are developed that drastically reduce the computation time while preserving the estimation quality. In the first implementation, the ASM is discretized to apply the cross-correlation. This is based on matrix operations, which are efficiently implemented and fast in execution. In the second implementation, the ASM is reformulated to apply the Fast Fourier Transform (FFT). The FFT, too, is based on fast matrix operations. These two new implementations are sequential programs, containing no loops. Experiments with a setup used in practical applications and real data show computation times of just a few seconds. These are computation time improvements of two orders of magnitude. The rapid computation of the traffic state makes the ASM with the proposed implementations applicable for real-time applications.