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 development and validation of traffic micro-simulation models. Recent advancements in digital technology have opened up new horizons in researching this field. In spite of the high precision of these techniques, estimating time series data of speeds and accelerations from positions with the required accuracy is still a demanding task. The core of the problem is to filter noisy trajectory data of each vehicle without altering platoon data consistency, i.e. speeds and accelerations of following vehicles have to be estimated so that resulting inter-vehicle 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 non-stationary Kalman filter that uses measurements and time-varying error information from differential GPS devices. The Kalman filter, not applicable to estimate the speeds of one vehicle from its position measurements alone, was fruitfully applied here to the speed estimation of the whole platoon by including inter-vehicle spacings as additional measurements (assumed as reference measurements). The closed solution of an optimisation problem ensuring strict observation of the “true” inter-vehicle spacings concludes the estimation process. The stationary counterpart of the devised filter is suitable to be applied to position data whichever technique is used, e.g. video cameras.