Sparse Kalman Identification for Partially Observable Systems via Adaptive Bayesian Learning

TL;DR

This paper introduces an online Bayesian method combining Kalman filtering and relevance determination to identify sparse, interpretable models from sequential, partially observable data with high efficiency and accuracy.

Contribution

It presents a novel online Sparse Kalman Identification approach that integrates Bayesian sparsification with Kalman filtering for real-time system identification.

Findings

Achieves millisecond-level computational efficiency.

Demonstrates 84.21% accuracy improvement over baseline methods.

Validated through extensive simulations and real-world experiments.

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).