Carsten Fritsche

Michael Roth, Gustaf Hendeby, Carsten Fritsche et al.

The ensemble Kalman filter (EnKF) is a Monte Carlo based implementation of the Kalman filter (KF) for extremely high-dimensional, possibly nonlinear and non-Gaussian state estimation problems. Its ability to handle state dimensions in the order of millions has made the EnKF a popular algorithm in different geoscientific disciplines. Despite a similarly vital need for scalable algorithms in signal processing, e.g., to make sense of the ever increasing amount of sensor data, the EnKF is hardly discussed in our field. This self-contained review paper is aimed at signal processing researchers and provides all the knowledge to get started with the EnKF. The algorithm is derived in a KF framework, without the often encountered geoscientific terminology. Algorithmic challenges and required extensions of the EnKF are provided, as well as relations to sigma-point KF and particle filters. The relevant EnKF literature is summarized in an extensive survey and unique simulation examples, including popular benchmark problems, complement the theory with practical insights. The signal processing perspective highlights new directions of research and facilitates the exchange of potentially beneficial ideas, both for the EnKF and high-dimensional nonlinear and non-Gaussian filtering in general.

Yuanhang Zhang, Zhidi Lin, Yiyong Sun et al.

Deep state-space models (DSSMs) have gained popularity in recent years due to their potent modeling capacity for dynamic systems. However, existing DSSM works are limited to single-task modeling, which requires retraining with historical task data upon revisiting a forepassed task. To address this limitation, we propose continual learning DSSMs (CLDSSMs), which are capable of adapting to evolving tasks without catastrophic forgetting. Our proposed CLDSSMs integrate mainstream regularization-based continual learning (CL) methods, ensuring efficient updates with constant computational and memory costs for modeling multiple dynamic systems. We also conduct a comprehensive cost analysis of each CL method applied to the respective CLDSSMs, and demonstrate the efficacy of CLDSSMs through experiments on real-world datasets. The results corroborate that while various competing CL methods exhibit different merits, the proposed CLDSSMs consistently outperform traditional DSSMs in terms of effectively addressing catastrophic forgetting, enabling swift and accurate parameter transfer to new tasks.