Solving Vehicle Speed and Acceleration from Video Evidence Using Optimization

<div class="section abstract"><div class="htmlview paragraph"/><div class="htmlview paragraph">This paper introduces a method to solve the instantaneous speed and acceleration of a vehicle from one or more sources of video evidence by using optimization to determine the best fit speed profile that tracks the measured path of a vehicle through a scene.</div><div class="htmlview paragraph">Mathematical optimization is the process of seeking the variables that drive an objective function to some optimal value, usually a minimum, subject to constraints on the variables. In the video analysis problem, the analyst is seeking a speed profile that tracks measured vehicle positions over time. Measured positions and observations in the video constrain the vehicle’s motion and can be used to determine the vehicle’s instantaneous speed and acceleration. The variables are the vehicle’s initial speed and an unknown number of periods of approximately constant acceleration. Optimization can be used to determine the speed profile that minimizes the total error between the vehicle’s calculated distance traveled at each measured position, subject to various constraints.</div><div class="htmlview paragraph">A test was designed to demonstrate the proposed method, using two synchronized video cameras and an instrumented test vehicle coming to a hard stop on a controlled roadway. The cameras were positioned to capture the vehicle approach in the initial field of view, and the final point of rest in the secondary field of view, with an area of indeterminate vehicle motion occurring in the region between the two camera setups. The test vehicle was driven at an unknown speed and initiated a hard brake in the uncovered region between camera systems. Using camera match photogrammetry, the position of the vehicle was measured at discrete times as it traversed the scene. Using the proposed method, optimization was shown to accurately determine the hard braking point and the speed of the vehicle as it traveled between camera systems.</div></div>