Travel time estimation based on piecewise truncated quadratic speed trajectory

A piecewise truncated quadratic speed trajectory is proposed to mimic the unknown speed trajectory between point detectors. The basis functions of the new method consist of quadratic and constant functions of time. The constant functions, corresponding to upper and lower speed bounds, are determined using the maximum likelihood estimates of highest and lowest speeds that have been historically observed within a time interval. The purpose of setting a lower (upper) speed bound for simulating vehicle speed trajectory is to mimic a low (high) average speed during transition flow and congestion, and to restrict a quadratic speed trajectory to be within a realistic speed range, respectively. It was found that travel time estimation using different approaches is similar during free-flow conditions but significantly different during transition flow and congestion conditions. Using the actual travel time obtained from field experiment, the new method yields more accurate travel time estimation than other trajectory-based methods. Compared to travel time estimation using speed and density information, the new method only needs speed measurements, and therefore, it is more robust and easier to implement in practice than density-based methods. Computational implementation of the new trajectory method is tractable and can be done very efficiently, making it suitable for on-line real time travel time estimation.