Related papers: A filtering problem with uncertainty in observatio…

Recently, it has been demonstrated experimentally that adaptive estimation of a continuously varying optical phase provides superior accuracy in the phase estimate compared to static estimation. Here, we show that the mean-square error in…

Measurements of a scalar linear Gauss-Markov process are sent over a fading channel. The fading channel is modeled as independent and identically distributed random variables with known realization at the receiver. The optimal estimator at…

In this paper, we present a novel optimization algorithm designed specifically for estimating state-space models to deal with heavy-tailed measurement noise and constraints. Our algorithm addresses two significant limitations found in…

We derive a novel, provably robust, and closed-form Bayesian update rule for online filtering in state-space models in the presence of outliers and misspecified measurement models. Our method combines generalised Bayesian inference with…

The aim of this article is to overview the problem of mean square optimal estimation of linear functionals which depend on unknown values of periodically correlated stochastic process. Estimates are based on observations of this process and…

We demonstrate optimal state estimation for a cavity optomechanical system through Kalman filtering. By taking into account nontrivial experimental noise sources, such as colored laser noise and spurious mechanical modes, we implement a…

One of the most common misconceptions made about the Kalman filter when applied to linear systems is that it requires an assumption that all error and noise processes are Gaussian. This misconception has frequently led to the Kalman filter…

This paper presents a new approach to distributed linear filtering and prediction. The problem under consideration consists of a random dynamical system observed by a multi-agent network of sensors where the network is sparse. Inspired by…

This paper studies the distributed state estimation in sensor network, where $m$ sensors are deployed to infer the $n$-dimensional state of a linear time-invariant (LTI) Gaussian system. By a lossless decomposition of optimal steady-state…

This paper studies a nonlinear filtering problem over an infinite time interval. The signal to be estimated is driven by a stochastic partial differential equation involves unknown parameters. Based on discrete observation, strongly…

Nonlinear filtering problems are encountered in many applications, and one solution approach is the extended Kalman filter, which is not always convergent. Therefore, it is crucial to identify conditions under which the extended Kalman…

We consider the problem of distributed Kalman filtering for sensor networks in the case there is a limit in data transmission and there is model uncertainty. More precisely, we propose a distributed filtering strategy with event-triggered…

An observer is an estimator of the state of a dynamical system from noisy sensor measurements. The need for observers is ubiquitous, with applications in fields ranging from engineering to biology to economics. The most widely used observer…

Transformer models have shown great success in natural language processing; however, their potential remains mostly unexplored for dynamical systems. In this work, we investigate the optimal output estimation problem using transformers,…

We provide a rigorous derivation of the Ensemble Kalman-Bucy Filter as well as the Ensemble Transform Kalman-Bucy Filter in case of nonlinear, unbounded model and observation operators. We identify them as the continuous time limit of the…

We study the fundamental problems of Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination. Our main contribution is the design of the first sample near-optimal and almost linear-time…

This paper deals with the parametric inference for integrated signals embedded in an additive Gaussian noise and observed at deterministic discrete instants which are not necessarily equidistant. The unknown parameter is multidimensional…

The paper studies a geometrically robust least-squares problem that extends classical and norm-based robust formulations. Rather than minimizing residual error for fixed or perturbed data, we interpret least-squares as enforcing approximate…

This paper derives recursion equations for a robust smoothing problem for a class of nonlinear systems with uncertainties in modeling and exogenous noise sources. The systems considered operate in discrete-time and the uncertainties are…

Adversarially robust training has been shown to reduce the susceptibility of learned models to targeted input data perturbations. However, it has also been observed that such adversarially robust models suffer a degradation in accuracy when…