# Adaptive Smoothing for Trajectory Reconstruction

arXiv: https://arxiv.org/abs/1803.07184 · HTML: https://mlsanity.com/paper/1803.07184/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2018.

## Built on by (most cited first, 2 of 2)

- [Interaction Dataset of Autonomous Vehicles with Traffic Lights and Signs](https://mlsanity.com/paper/2501.12536/) (2025)
- [Inferring Missing Trajectory Data with Temporal Convolutional Networks](https://mlsanity.com/paper/2607.25147/) (2026)

## Abstract (arXiv)

Trajectory reconstruction is the process of inferring the path of a moving object between successive observations. In this paper, we propose a smoothing spline -- which we name the V-spline -- that incorporates position and velocity information and a penalty term that controls acceleration. We introduce a particular adaptive V-spline designed to control the impact of irregularly sampled observations and noisy velocity measurements. A cross-validation scheme for estimating the V-spline parameters is given and we detail the performance of the V-spline on four particularly challenging test datasets. Finally, an application of the V-spline to vehicle trajectory reconstruction in two dimensions is given, in which the penalty term is allowed to further depend on known operational characteristics of the vehicle.