Related papers: The Kalman-Bucy Filter for Integrable L\'{e}vy Pro…

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…

The objective is to investigate the advantages and performance of Extended Kalman Filter for the estimation of non-linear system where linearization takes place about a trajectory that was continually updated with the state estimates…

We propose a method for inference on moderately high-dimensional, nonlinear, non-Gaussian, partially observed Markov process models for which the transition density is not analytically tractable. Markov processes with intractable transition…

We demonstrate that the extended Kalman filter converges locally for a broad class of nonlinear systems. If the initial estimation error of the filter is not too large then the error goes to zero exponentially as time goes to infinity. To…

The purpose of this review is to present a comprehensive overview of the theory of ensemble Kalman-Bucy filtering for continuous-time, linear-Gaussian signal and observation models. We present a system of equations that describe the flow of…

We consider a combined state and drift estimation problem for the linear stochastic heat equation. The infinite-dimensional Bayesian inference problem is formulated in terms of the Kalman-Bucy filter over an extended state space, and its…

Duality between estimation and optimal control is a problem of rich historical significance. The first duality principle appears in the seminal paper of Kalman-Bucy, where the problem of minimum variance estimation is shown to be dual to a…

This paper revisits the question of duality between minimum variance estimation and optimal control first described for the linear Gaussian case in the celebrated paper of Kalman and Bucy. A duality result is established for nonlinear…

We present recent results on the existence of a continuous time limit for Ensemble Kalman Filter algorithms. In the setting of continuous signal and observation processes, we apply the original Ensemble Kalman Filter algorithm proposed by…

In this paper, we exploit the gradient flow structure of continuous-time formulations of Bayesian inference in terms of their numerical time-stepping. We focus on two particular examples, namely, the continuous-time ensemble Kalman-Bucy…

The classical state-space approach to optimal estimation of stochastic processes is efficient when the driving noises are generated by martingales. In particular, the weight function of the optimal linear filter, which solves a complicated…

We consider finite and infinite systems of particles on the real line and half-line evolving in continuous time. Hereby, the particles are driven by i.i.d. L\'{e}vy processes endowed with rank-dependent drift and diffusion coefficients. In…

The well-known Kalman filters model dynamical systems by relying on state-space representations with the next state updated, and its uncertainty controlled, by fresh information associated with newly observed system outputs. This paper…

The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors…

We study robust nonlinear filtering for stochastic models driven by L\'evy processes, where the signal and observation processes are coupled through common Brownian and jump noise. Robustness, defined as the continuous dependence of the…

The Kalman filter is an established tool for the analysis of dynamic systems with normally distributed noise, and it has been successfully applied in numerous application areas. It provides sequentially calculated estimates of the system…

This paper presents an adaptive Kalman filter for a linear dynamic system perturbed by an additive disturbance. The objective is to estimate both of the state and the unknown disturbance concurrently, while learning the disturbance as a…

We introduce the inverse Kalman filter, which enables exact matrix-vector multiplication between a covariance matrix from a dynamic linear model and any real-valued vector with linear computational cost. We integrate the inverse Kalman…

In the present paper we consider controllability and observability of second order linear time invariant systems in matrix form. Without reducing into first order systems we show how the classical conditions for first order linear systems…

Bayesian filtering approximates the true underlying behavior of a time-varying system by inverting an explicit generative model to convert noisy measurements into state estimates. This process typically requires either storage, inversion,…