Probabilistic Speed-Estimation Measurement Errors through Video Images

Many data-collection methods are available from simple manual methods to advanced automatic image processing techniques. For many practical purposes video recording has become a widely used tool. Though this method is simple and is extensively used, accuracy in estimating actual speed and associated measurement errors have not been quantitatively examined. This paper investigates the mathematical properties of measurement error in vehicular speed data reduced from video images. Primary focus was on the measurement-error probability function, which incorporates the effects of the embedded video camera time-base resolution, fiducial mark interval, and actual vehicle speed. Mathematical derivations of the probability density function (PDF) are presented, and a Monte Carlo simulation technique was applied verifying the mathematically derived probability function. Both graphical comparisons and goodness-of-fit tests demonstrated very good agreement. The probability function presented in this paper provides a very useful tool because it allows traffic engineers to quantify in advance the probability of occurrence of certain measurement-error magnitudes and to adjust the data-collection plan accordingly.