Combining the classical Kalman filter (KF) with a deep neural network (DNN) enables tracking in partially known state space (SS) models. A major limitation of current DNN-aided designs stems from the need to train them to filter data originating from a specific distribution and underlying SS model. Consequently, changes in the model parameters may require lengthy retraining. While the KF adapts through parameter tuning, the black-box nature of DNNs makes identifying tunable components difficult. Hence, we propose Adaptive KalmanNet (AKNet), a DNN-aided KF that can adapt to changes in the SS model without retraining. Inspired by recent advances in large language model fine-tuning paradigms, AKNet uses a compact hypernetwork to generate context-dependent modulation weights. Numerical evaluation shows that AKNet provides consistent state estimation performance across a continuous range of noise distributions, even when trained using data from limited noise settings.

People with brain or spinal cord-related paralysis often need to rely on others for basic tasks, limiting their independence. A potential solution is brain-machine interfaces (BMIs), which could allow them to voluntarily control external devices (e.g., robotic arm) by decoding brain activity to movement commands. In the past decade, deep-learning decoders have achieved state-of-the-art results in most BMI applications, ranging from speech production to finger control. However, the 'black-box' nature of deep-learning decoders could lead to unexpected behaviors, resulting in major safety concerns in real-world physical control scenarios. In these applications, explainable but lower-performing decoders, such as the Kalman filter (KF), remain the norm. In this study, we designed a BMI decoder based on KalmanNet, an extension of the KF that augments its operation with recurrent neural networks to compute the Kalman gain. This results in a varying “trust” that shifts between inputs and dynamics. We used this algorithm to predict finger movements from the brain activity of two monkeys. We compared KalmanNet results offline (pre-recorded data, $n=13$ days) and online (real-time predictions, $n=5$ days) with a simple KF and two recent deep-learning algorithms: tcFNN (non-ReFIT version) and LSTM. KalmanNet achieved comparable or better results than other deep learning models in offline and online modes, relying on the dynamical model for stopping while depending more on neural inputs for initiating movements. We further validated this mechanism by implementing a heteroscedastic KF that used the same strategy, and it also approached state-of-the-art performance while remaining in the explainable domain of standard KFs. However, we also see two downsides to KalmanNet. KalmanNet shares the limited generalization ability of existing deep-learning decoders, and its usage of the KF as an inductive bias limits its performance in the presence of unseen noise distributions. Despite this trade-off, our analysis successfully integrates traditional controls and modern deep-learning approaches to motivate high-performing yet still explainable BMI designs.

The smoothing task is the core of many signal processing applications. It deals with the recovery of a sequence of hidden state variables from a sequence of noisy observations in a one-shot manner. In this work we propose RTSNet, a highly efficient model-based and data-driven smoothing algorithm. RTSNet integrates dedicated trainable models into the flow of the classical Rauch-Tung-Striebel (RTS) smoother, and is able to outperform it when operating under model mismatch and non-linearities while retaining its efficiency and interpretability. Our numerical study demonstrates that although RTSNet is based on more compact neural networks, which leads to faster training and inference times, it outperforms the state-of-the-art, data-driven smoother in a non-linear use case.

Age of information (AoI) is recently introduced to serve as a performance metric that quantifies the freshness of information for wireless applications with time-sensitive data. This paper studies AoI of wireless energy harvesting nodes in a multiuser cognitive radio network. In the envisioned network, primary users (PUs) and secondary users (SUs) coexist in such way that SUs harvest wireless energy from active PUs and access the primary spectrum opportunistically to transmit status updates. We model the distributions of PUs and SUs by a homogeneous Poisson point process and a binomial point process, respectively. We consider a greedy policy where each SU transmits an update whenever it harvests sufficient energy. A nonlinear energy harvesting model is used for SUs. Under the greedy policy, the average AoI of the secondary network is analyzed. An upper bound and a lower bound of the average AoI are derived. Simulation results demonstrate that the bounds closely approximate the average AoI.