Penalized denoising of vehicle trajectories collected by a swarm of drones

Vehicle trajectory datasets collected in urban traffic environments with drones pose unique chal- lenges in terms of denoising due to extensive visual restrictions, perspective distortions and human- induced errors. This article taps into the unexplored potential of penalties in the context of vehicle trajectory reconstruction with the example of the massive pNEUMA dataset. We contribute to the literature by shifting the focus of denoising from smoothing to anomaly detection. Specifically, we distinguish between stationary and non-stationary errors and argue that the latter accounts for the largest part of the noise. We propose a re-purposing of the Butterworth filter for the detection of anomalous events and enforce spatial autocorrelation constraints on the errors with functional data analysis. The calibration of our reconstruction makes further use of penalties and is inspired by the theory of human-machine interaction. Our method can be used for quantifying autocorrelated errors or for identifying network segments that are devoid of errors.