Trajectory reconstruction using locally weighted regression: a new methodology to identify the optimum window size and polynomial order

Vehicle trajectory data obtained from the semi-automated trackers are prone to white Gaussian noise along with the outliers originated from the occlusion and the other possible human errors. Locally weighted polynomial regression (LWPR) is one of the methods used to smooth the observed vehicle trajectories. The window size, polynomial order, and the weight function are the parameters required for performing the LWPR. Window size and polynomial order primarily control the bias-variance trade-off between the actual and the estimated trajectory. In this study, a method is proposed to identify the optimal window size and polynomial order, considering the dynamics of individual vehicles. The proposed method assumes that the actual trajectory is smooth and continuous and all the observed data points may not be falling on the actual trajectory. Optimum window size was estimated by converging the estimated mean squared error (MSE) to the actual MSE. This procedure minimizes the effect of polynomial order on the bias-variance trade-off. The optimum polynomial order was found through quartile analysis of the MSE corresponding to the optimum window size. We have considered third quartile error value for estimating the optimal polynomial order. The trajectory reconstructed through this approach produces better results in the consistency analysis.