Diff-Kalman: Difference-Driven Learning for Structure-Preserving Kalman Filtering

State estimation is a critical challenge in modeling dynamic systems. Traditional Kalman filters and data-driven methods have shown good results in complex, nonlinear systems. However, most existing methods optimize the posterior without considering prior modeling, which leaves room for improvement in state estimation accuracy, and predict high-dimensional Kalman parameters end-to-end, which lead to unstable training and poor convergence. To address this, we propose Diff-Kalman, which leverages state differences to predict state increments and scaling matrices for correcting both the prediction and update phases of the Kalman filter. Diff-Kalman combines traditional dynamic models with neural networks to adaptively correct system behavior. In the prediction phase, Diff-Kalman utilizes a Transformer-based architecture with self-attention to extract localized patterns from historical states, followed by cross-attention to predict future state increments. These increments are then fused with model-based priors from the dynamic model. In the update phase, a GRU-based Scaling Predictor (GSP) dynamically adjusts the Kalman covariance and gain matrices based on differential residuals, which improves the accuracy and robustness of the estimation. Experimental results on linear MOT trajectories and nonlinear Lorenz dynamics show that Diff-Kalman improves estimation accuracy over representative baselines.