A State-Space Kalman Filtering Framework for 2D Motorsport Telemetry Reconstruction

Version 1.1 (March 2026): Added explicit Kalman prediction/update equations, formal Joseph-form covariance definition, and clarified the Velocity Behavior section.A linear Gaussian state-space framework is presented for reconstructing physically consistent two-dimensional motorsport telemetry from noisy positional measurements. The proposed system employs a constant-acceleration motion model within a recursive Kalman filtering structure using Joseph-form covariance stabilization to ensure numerical robustness. Raw telemetry from multiple 2025 Formula 1 circuits was resampled onto a uniform temporal grid and processed using the proposed estimator. Validation across five distinct circuit geometries demonstrates bounded root-mean-square error (RMSE) behavior and systematic suppression of high-frequency velocity artifacts caused by positional noise amplification. The framework achieves computational efficiency suitable for real-time replay applications. Through algorithmic optimization and Numba Just-In-Time compilation, an overall 1500× performance improvement was observed. The presented formulation provides a physically consistent alternative to heuristic interpolation methods for trajectory reconstruction.