# A Comparative Study of Spline-Based Trajectory Reconstruction Methods Across Varying Automatic Vehicle Location Data Densities

## TL;DR

This study evaluates 13 trajectory reconstruction methods for AVL data, highlighting the superiority of velocity-aware approaches like VCHIP-ME, especially with dense data, and discusses the trade-offs between accuracy and computational resources.

## Contribution

It provides a comprehensive evaluation of various trajectory reconstruction methods across different data densities, introducing practical metrics and highlighting the effectiveness of velocity-constrained, monotonicity-enforced techniques.

## Key findings

- Velocity-aware methods outperform position-only approaches.
- Smoothing can degrade performance in congested environments.
- VCHIP-ME offers a good balance of accuracy and efficiency.

## Abstract

Automatic vehicle location (AVL) data offers insights into transit dynamics, but its effectiveness is often hampered by inconsistent update frequencies, necessitating trajectory reconstruction. This research evaluates 13 trajectory reconstruction methods, including several novel approaches, using high-resolution AVL data from Austin, Texas. We examine the interplay of four critical factors -- velocity, position, smoothing, and data density -- on reconstruction performance. A key contribution of this study is evaluation of these methods across sparse and dense datasets, providing insights into the trade-off between accuracy and resource allocation. Our evaluation framework combines traditional mathematical error metrics for positional and velocity with practical considerations, such as physical realism (e.g., aligning velocity and acceleration with stopped states, deceleration rates, and speed variability). In addition, we provide insight into the relative value of each method in calculating realistic metrics for infrastructure evaluations. Our findings indicate that velocity-aware methods consistently outperform position-only approaches. Interestingly, we discovered that smoothing-based methods can degrade overall performance in complex, congested urban environments, although enforcing monotonicity remains critical. The velocity constrained Hermite interpolation with monotonicity enforcement (VCHIP-ME) yields optimal results, offering a balance between high accuracy and computational efficiency. Its minimal overhead makes it suitable for both historical analysis and real-time applications, providing significant predictive power when combined with dense datasets. These findings offer practical guidance for researchers and practitioners implementing trajectory reconstruction systems and emphasize the importance of investing in higher-frequency AVL data collection for improved analysis.