Sparse Kalman Identification for Partially Observable Systems via Adaptive Bayesian Learning
This addresses the need for real-time, interpretable model identification in engineering systems, though it appears incremental as it builds on existing Kalman filter and sparsity techniques.
The paper tackled the problem of sparse dynamics identification for partially observable systems by proposing an online Sparse Kalman Identification method, which achieved an 84.21% improvement in accuracy over the baseline Augmented Kalman Filter with millisecond-level efficiency.
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).