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Various alignment problems arising in cryo-electron microscopy, community detection, time synchronization, computer vision, and other fields fall into a common framework of synchronization problems over compact groups such as Z/L, U(1), or…

The main contribution of this paper is an invariant extended Kalman filter (EKF) for visual inertial navigation systems (VINS). It is demonstrated that the conventional EKF based VINS is not invariant under the stochastic unobservable…

In urban areas, the quality of global navigation satellite system (GNSS) signals deteriorates, leading to reduced positioning accuracy. To address this issue, 3D-mapping-aided (3DMA) techniques, such as shadow matching and zonotope shadow…

Objective Kalman filtering has previously been applied to track neural model states and parameters, particularly at the scale relevant to EEG. However, this approach lacks a reliable method to determine the initial filter conditions and…

Particle Marginal Metropolis-Hastings (PMMH) is a general approach to Bayesian inference when the likelihood is intractable, but can be estimated unbiasedly. Our article develops an efficient PMMH method that scales up better to higher…

This paper proposes an event-triggered variational Bayesian filter for remote state estimation with unknown and time-varying noise covariances. After presetting multiple nominal process noise covariances and an initial measurement noise…

In this work, we consider nonnegative matrix factorization (NMF) with a regularization that promotes small volume of the convex hull spanned by the basis matrix. We present highly efficient algorithms for three different volume…

State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and…

An adaptive state observer is proposed for a class of overparametrized uncertain linear time-invariant systems without restrictive requirement of their representation in the observer canonical form. It evolves the method of generalized…

Deep generative models have been successfully applied to Zero-Shot Learning (ZSL) recently. However, the underlying drawbacks of GANs and VAEs (e.g., the hardness of training with ZSL-oriented regularizers and the limited generation…

The Linear Multistep Method Particle Filter (LMM PF) is a method for predicting the evolution in time of a evolutionary system governed by a system of differential equations. If some of the parameters of the governing equations are…

In this paper, we propose an approach for computing invariant sets of discrete-time nonlinear systems by lifting the nonlinear dynamics into a higher dimensional linear model. In particular, we focus on the \emph{maximal admissible…

State estimation and sensor selection problems for nonlinear networks and systems are ubiquitous problems that are important for the control, monitoring, analysis, and prediction of a large number of engineered and physical systems. Sensor…

The ensemble Kalman filter (EnKF) is a data assimilation technique that uses an ensemble of models, updated with data, to track the time evolution of a usually non-linear system. It does so by using an empirical approximation to the…

Scalable safety verification of continuous state dynamic systems has been demonstrated through both reachability and viability analyses using parametric set representations; however, these two analyses are not interchangable in practice for…

Some system identification problems impose nonnegativity constraints on the parameters to estimate due to inherent physical characteristics of the unknown system. The nonnegative least-mean-square (NNLMS) algorithm and its variants allow to…

In this paper, we propose and develop a methodology for nonlinear systems health monitoring by modeling the damage and degradation mechanism dynamics as "slow" states that are augmented with the system "fast" dynamical states. This…

This paper addresses the challenging problem of parameter estimation in bilinear systems under colored noise. A novel approach, termed B-PF-RLS, is proposed, combining a particle filter (PF) with a recursive least squares (RLS) estimator.…

This paper introduces a novel Kalman filter framework designed to achieve robust state estimation under both process and measurement noise. Inspired by the Weighted Observation Likelihood Filter (WoLF), which provides robustness against…

The majority of data assimilation (DA) methods in the geosciences are based on Gaussian assumptions. While these assumptions facilitate efficient algorithms, they cause analysis biases and subsequent forecast degradations. Non-parametric,…