Nonstationary Kalman Filter for Estimation of Accurate and Consistent Car-Following Data

Difficulty in obtaining accurate car-following data has traditionally been regarded as a considerable drawback in understanding real phenomena and has affected the development and validation of traffic microsimulation models. Recent advancements in digital technology have opened up new horizons in the conduct of research in this field. Despite the high degrees of precision of these techniques, estimation of time series data of speeds and accelerations from positions with the required accuracy is still a demanding task. The core of the problem is filtering the noisy trajectory data for each vehicle without altering platoon data consistency; i.e., the speeds and accelerations of following vehicles must be estimated so that the resulting intervehicle spacings are equal to the real one. Otherwise, negative spacings can also easily occur. The task was achieved in this study by considering vehicles of a platoon as a sole dynamic system and reducing several estimation problems to a single consistent one. This process was accomplished by means of a nonstationary Kalman filter that used measurements and time-varying error information from differential Global Positioning System devices. The Kalman filter was fruitfully applied here to estimation of the speed of the whole platoon by including intervehicle spacings as additional measurements (assumed to be reference measurements). The closed solution of an optimization problem that ensures strict observation of the true intervehicle spacings concludes the estimation process. The stationary counterpart of the devised filter is suitable for application to position data, regardless of the data collection technique used, e.g., video cameras.