🤖 AI Summary
Real-time, sparse identification of dynamic models in partially observable systems remains challenging due to limited observability and computational constraints.
Method: This paper proposes an online sparse Kalman identification method that integrates a Bayesian sparsification mechanism—based on Automatic Relevance Determination (ARD)—into the Augmented Kalman Filter (AKF) framework. It establishes an adaptive posterior update scheme enabling the basis function set to evolve dynamically with incoming observations, and derives explicit gradient-descent update rules to accelerate sparse learning.
Contribution/Results: Unlike conventional batch-mode sparse identification methods, the proposed approach enables incremental modeling over sequential data, significantly improving real-time capability and interpretability. Experimental results demonstrate an 84.21% improvement in model accuracy over standard AKF under millisecond-level computational latency, validating its effectiveness and robustness in both simulated and physical systems.
📝 Abstract
Sparse dynamics identification is an essential tool for discovering interpretable physical models and enabling efficient control in engineering systems. However, existing methods rely on batch learning with full historical data, limiting their applicability to real-time scenarios involving sequential and partially observable data. To overcome this limitation, this paper proposes an online Sparse Kalman Identification (SKI) method by integrating the Augmented Kalman Filter (AKF) and Automatic Relevance Determination (ARD). The main contributions are: (1) a theoretically grounded Bayesian sparsification scheme that is seamlessly integrated into the AKF framework and adapted to sequentially collected data in online scenarios; (2) an update mechanism that adapts the Kalman posterior to reflect the updated selection of the basis functions that define the model structure; (3) an explicit gradient-descent formulation that enhances computational efficiency. Consequently, the SKI method achieves accurate model structure selection with millisecond-level efficiency and higher identification accuracy, as demonstrated by extensive simulations and real-world experiments (showing an 84.21% improvement in accuracy over the baseline AKF).