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The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partial, noisily observed dynamical systems, and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences,…
Achieving highly accurate dynamic or simulator models that are close to the real robot can facilitate model-based controls (e.g., model predictive control or linear-quadradic regulators), model-based trajectory planning (e.g., trajectory…
We review optimization-based approaches to smoothing nonlinear dynamical systems. These approaches leverage the fact that the Extended Kalman Filter and corresponding smoother can be framed as the Gauss-Newton method for a nonlinear least…
The ensemble Kalman filter (EnKF) has become a standard methodology for state estimation in high-dimensional systems, yet its various stochastic and deterministic formulations often appear conceptually disconnected. In this paper, a unified…
Non-Gaussian noise and the uncertainty of noise distribution are the common factors that reduce accuracy in dynamic state estimation of power systems (PS). In addition, the optimal value of the free coefficients in the unscented Kalman…
Natural disasters, such as hurricanes and typhoons, pose significant challenges to public safety and infrastructure. While government agencies rely on multi million dollar UAV systems for storm data collection and disaster response, smaller…
In recent years, machine learning has witnessed extensive adoption across various sectors, yet its application in medical image-based disease detection and diagnosis remains challenging due to distribution shifts in real-world data. In…
We study the problem of distributed Kalman filtering for sensor networks in the presence of model uncertainty. More precisely, we assume that the actual state-space model belongs to a ball, in the Kullback-Leibler topology, about the…
In this paper we address the problem of estimating the posterior distribution of the static parameters of a continuous time state space model with discrete time observations by an algorithm that combines the Kalman filter and a particle…
In this work, we present an aided inertial navigation system for an autonomous underwater vehicle (AUV) using an unscented Kalman filter on manifolds (UKF-M). The inertial navigation estimate is aided by a Doppler velocity log (DVL), depth…
Sequential Bayesian filters in non-linear dynamic systems require the recursive estimation of the predictive and posterior distributions. This paper introduces a Bayesian filter called the adaptive kernel Kalman filter (AKKF). With this…
In inverse problems, the goal is to estimate unknown model parameters from noisy observational data. Traditionally, inverse problems are solved under the assumption of a fixed forward operator describing the observation model. In this…
This paper introduces a Gaussian Bayesian Network-based Extended Kalman Filter (GBN-EKF) for non-linear state estimators on stiff and ill-conditioned continuous-discrete stochastic systems, with a further analysis on systems with…
In this work, we explore the recent advances in equivariant filtering for inertial navigation systems to improve state estimation for uncrewed aerial vehicles (UAVs). Traditional state-of-the-art estimation methods, e.g., the multiplicative…
Many nonlinear extensions of the Kalman filter, e.g., the extended and the unscented Kalman filter, reduce the state densities to Gaussian densities. This approximation gives sufficient results in many cases. However, this filters only…
A novel method for distributed estimation of the frequency of power systems is introduced based on the cooperation between multiple measurement nodes. The proposed distributed widely linear complex Kalman filter (D-ACKF) and the distributed…
The models of partially observed linear stochastic differential equations with unknown initial values of the non-observed component are considered in two situations. In the first problem, the initial value is deterministic, and in the…
This paper investigates the distributed Kalman filter (DKF) for linear systems, with specific attention on measurement fusion, which is a typical way of information sharing and is vital for enhancing stability and improving estimation…
Heavy tails is a common feature of filtering distributions that results from the nonlinear dynamical and observation processes as well as the uncertainty from physical sensors. In these settings, the Kalman filter and its ensemble version -…
We introduce a method for the estimation of uncertainties in density-functional-theory (DFT) calculations for atomistic systems. The method is based on the construction of an uncertainty-aware functional distribution (UAFD) in a space…