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Data assimilation is concerned with sequentially estimating a temporally-evolving state. This task, which arises in a wide range of scientific and engineering applications, is particularly challenging when the state is high-dimensional and…
Kernel Adaptive Filtering (KAF) are mathematically principled methods which search for a function in a Reproducing Kernel Hilbert Space. While they work well for tasks such as time series prediction and system identification they are…
The robustness of the Kalman filter to double talk and its rapid convergence make it a popular approach for addressing acoustic echo cancellation (AEC) challenges. However, the inability to model nonlinearity and the need to tune control…
Many data-science problems can be formulated as an inverse problem, where the parameters are estimated by minimizing a proper loss function. When complicated black-box models are involved, derivative-free optimization tools are often…
Ensemble Kalman inversion (EKI) is a derivative-free optimizer aimed at solving inverse problems, taking motivation from the celebrated ensemble Kalman filter. The purpose of this article is to consider the introduction of adaptive Tikhonov…
Real-time control and estimation are pivotal for applications such as industrial automation and future healthcare. The realization of this vision relies heavily on efficient interactions with nonlinear systems. Therefore, Koopman learning,…
The Kalman filter is the most powerful tool for estimation of the states of a linear Gaussian system. In addition, using this method, an expectation maximization algorithm can be used to estimate the parameters of the model. However, this…
We consider the problem of online prediction for an unknown, non-explosive linear stochastic system. With a known system model, the optimal predictor is the celebrated Kalman filter. In the case of unknown systems, existing approaches based…
We describe an application of the Invariant Extended Kalman Filter (IEKF) design methodology to the scan matching SLAM problem. We review the theoretical foundations of the IEKF and its practical interest of guaranteeing robustness to poor…
The Ensemble Kalman Filter (EnKF) has achieved great successes in data assimilation in atmospheric and oceanic sciences, but its failure in convergence to the right filtering distribution precludes its use for uncertainty quantification. We…
The ensemble Kalman filter is a well-known and celebrated data assimilation algorithm. It is of particular relevance as it used for high-dimensional problems, by updating an ensemble of particles through a sample mean and covariance…
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…
Due to the state trajectory-independent features of invariant Kalman filtering (InEKF), it has attracted widespread attention in the research community for its significantly improved state estimation accuracy and convergence under…
Large language model pretraining is compute-intensive, yet many tokens contribute marginally to learning, resulting in inefficiency. We introduce Efficient Selective Language Modeling (ESLM), a risk-aware algorithm that improves training…
Accurate estimation of the dynamic states of a synchronous machine (e.g., rotor s angle and speed) is essential in monitoring and controlling transient stability of a power system. It is well known that the covariance matrixes of process…
As neural networks are increasingly being applied to real-world applications, mechanisms to address distributional shift and sequential task learning without forgetting are critical. Methods incorporating network expansion have shown…
Backpropagation dominates modern machine learning, yet it is not the only principled method for optimizing dynamical systems. We propose Kalman World Models (KWM), a class of learned state-space models trained via recursive Bayesian…
The Extended Kalman Filter (EKF) is a well established technique for position and velocity estimation. However, the performance of the EKF degrades considerably in highly non-linear system applications as it requires local linearisation in…
This thesis presents a novel approach to neural network training that addresses the challenge of determining the optimal number of learning factors. The proposed Adaptive Multiple Optimal Learning Factors (AMOLF) algorithm dynamically…
The Kalman filter (KF) provides optimal recursive state estimates for linear-Gaussian systems and underpins applications in control, signal processing, and others. However, it is vulnerable to outliers in the measurements and process noise.…