A GRU-Augmented Kalman Filter for State Estimation in Systems with Colored Noise

Although the Kalman filter is optimal for linear Gaussian systems, its performance degrades in practical scenarios when noise is colored rather than white. Additionally, the Kalman filter requires substantial domain knowledge to derive parametric forms. To overcome these limitations, this paper proposes a data-driven filtering method that operates in the presence of colored noise and with partial information without requiring exact prior knowledge. We propose CKFNet, a novel real-time filtering framework that integrates a linear state-space model under colored noise with a gated recurrent unit. The network replaces the traditional Kalman gain computation, enabling the model to implicitly learn noise statistics from data and adapt to colored noise dynamics. Experiments across various colored noise conditions and model mismatch scenarios show that CKFNet outperforms baseline methods in most tested scenarios, and remains robust where model-based filters degrade. The results indicate that CKFNet effectively combines the interpretability and efficiency of state-space models with the adaptive learning capability of neural networks, offering a reliable filtering solution under realistic noise assumptions.