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.