Related papers: On the anticipative nonlinear filtering problem an…

This article is devoted to the stochastic anticipating equations with the extended stochastic integral with respect to the Gaussian processes of a special type and its application to the smoothing problem in the case when noise is…

State estimation of dynamical systems from noisy observations is a fundamental task in many applications. It is commonly addressed using the linear Kalman filter (KF), whose performance can significantly degrade in the presence of outliers…

This paper is concerned with nonlinear filtering of the coefficients in asset price models with stochastic volatility. More specifically, we assume that the asset price process $ S=(S_{t})_{t\geq0} $ is given by \[…

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update…

The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based…

The linearization of nonlinear systems is an important digital enhancement technique. In this paper, a real-time capable post- and pre-linearization method for the widely applicable time-varying discrete-time Volterra series is presented.…

Observers are well known in control theory. Originally designed to estimate the hidden states of dynamical systems given some measurements, the observers scope has been recently extended to the estimation of some unknowns, for systems…

This paper analyzes the correlation matrix between the a priori error and measurement noise vectors for affine projection algorithms (APA). This correlation stems from the dependence between the filter tap estimates and the noise samples,…

This paper proposes a novel particle filter for tracking time-varying states of multiple targets jointly from superpositional data, which depend on the sum of contributions of all targets. Many conventional tracking methods rely on…

In this paper we propose a (non-linear) smoothing algorithm for group-affine observation systems, a recently introduced class of estimation problems on Lie groups that bear a particular structure. As most non-linear smoothing methods, the…

In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly…

A novel approximate Bayesian filter based on backward stochastic differential equations is introduced. It uses a nonlinear Feynman--Kac representation of the filtering problem and the approximation of an unnormalized filtering density using…

Vendor interoperability is one of the desired future characteristics of optical networks. This means that the transmission system needs to support a variety of hardware with different components, leading to system uncertainties throughout…

At the beginning of this century, a real time solution of the nonlinear filtering problem without memory was proposed in [1, 2] by the third author and his collaborator, and it is later on referred to as Yau-Yau algorithm. During the last…

Signal extraction out of background noise is a common challenge in high precision physics experiments, where the measurement output is often a continuous data stream. To improve the signal to noise ratio of the detection, witness sensors…

This paper considers the approximation of the continuous time filtering equation for the case of a multiple timescale (slow-intermediate, and fast scales) that may have correlation between the slow-intermediate process and the observation…

We consider the problem of performing inverse reinforcement learning when the trajectory of the expert is not perfectly observed by the learner. Instead, a noisy continuous-time observation of the trajectory is provided to the learner. This…

Integral equations are widely used in fields such as applied modeling, medical imaging, and system identification, providing a powerful framework for solving deterministic problems. While parameter identification for differential equations…

In this paper, we consider a secure distributed filtering problem for linear time-invariant systems with bounded noises and unstable dynamics under compromised observations. A malicious attacker is able to compromise a subset of the agents…

This paper proposes a nonlinear estimator for the robust reconstruction of process and sensor faults for a class of uncertain nonlinear systems. The proposed fault estimation method augments the system dynamics with an ultra-local (in time)…