Polynomial-Based Trajectory Reconstruction versus Kalman Filtering for Vehicle Localization

This paper presents a simulation study that compares a batch polynomial trajectory reconstruction approach with a standard Kalman filter (KF) baseline for localization of a moving vehicle. A parametric ground-truth path with time-varying speed is used to generate GPS (۱ Hz) and odometry (۱۰ Hz) measurements subject to bias, Gaussian noise, occasional dropouts and rare large outliers. Polynomial fits of degrees ۳, ۵, ۷ and ۹ are estimated in the path parameter u by (weighted) least squares, and time-indexed predictions are produced via the known mapping tu(t). Experiments evaluate two scenarios using all GPS samples (including simulated outliers) and using cleaned GPS samples with outliers removed - and report MSE/ RMSE and running-RMSE statistics. Results show that outliers substantially degrade KF performance (RMSE ۹.۱۸ m with outliers, ۵.۴۴ m after cleaning), while a high-degree polynomial fit on cleaned data attains the best overall accuracy (deg-۹, RMSE ۲.۶۸ m). The findings highlight that, for offline/global trajectory reconstruction and with effective outlier handling, polynomial fitting can outperform a basic KF; conversely, KF remains necessary for online estimation but benefits critically from robust outlier rejection.

کلیدواژه ها:

Localization ، Polynomial trajectory reconstruction ، Kalman filter ، Outlier detection ، RMSE-based evaluation