TORKF: A Dual-Driven Kalman Filter for Outlier-Robust State Estimation and Application to Aircraft Tracking

This study addresses the limitations of conventional filtering methods in handling irregular outliers and missing observations, which can compromise filter robustness and accuracy. We propose the Transformer-based Outlier-Robust Kalman Filter (TORKF), a hybrid data and knowledge hybrid-driven framework for stochastic discrete-time systems. Initially, this study derives the filtering formulas applicable when outliers exist in observation vectors and, based on these formulations, proposes a novel method capable of accurately identifying observation vectors containing outliers. In addition, a transformer-based prediction compensation approach is employed to compute the prediction vector compensation value in scenarios involving outliers. This method utilizes a specially designed data structure to ensure the transformer encoder fully extracts the input features. Furthermore, to address outlier-induced inaccuracy in prediction error covariance, a compensation method aggregating all prediction outcomes is proposed, leading to enhanced filtering accuracy. Aircraft tracking presents challenges from complex motion models and outlier-prone observations, making it an ideal testbed for robust filtering algorithms. TORKF demonstrates superior performance, with a 12.7% lower RMSE than state-of-the-art methods across both propeller and jet datasets, while maintaining sub-90 ms single-frame processing to meet real-time requirements. Ablation studies confirm that all three proposed methods enhance accuracy and demonstrate synergistic improvements.