Related papers: Stability of Feynman-Kac formulae with path-depend…
We consider numerical solutions for the Allen-Cahn equation with standard double well potential and periodic boundary conditions. Surprisingly it is found that using standard numerical discretizations with high precision computational…
Since the innovation of the ubiquitous Kalman filter more than five decades back it is well known that to obtain the best possible estimates the tuning of its statistics $X_0$, $P_0$, $\Theta$, $R$ and $Q$ namely initial state and…
Kalman Filter (KF) is an optimal linear state prediction algorithm, with applications in fields as diverse as engineering, economics, robotics, and space exploration. Here, we develop an extension of the KF, called a Pathspace Kalman Filter…
We study the stability of general weakly coupled systems subject to a reduced number of local or boundary controls. We show that, under Kalman's rank condition, the exponential stability of the underlying scalar equation implies polynomial…
This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter,…
We consider Kalman filtering problems when the observations are intermittently erased or lost. It was known that the estimates are mean-square unstable when the erasure probability is larger than a certain critical value, and stable…
Predictive safety filters enable the integration of potentially unsafe learning-based control approaches and humans into safety-critical systems. In addition to simple constraint satisfaction, many control problems involve additional…
We analyze the Ensemble and Polynomial Chaos Kalman filters applied to nonlinear stationary Bayesian inverse problems. In a sequential data assimilation setting such stationary problems arise in each step of either filter. We give a new…
In this paper we analyze the convergence of a family of robust Kalman filters. For each filter of this family the model uncertainty is tuned according to the so called tolerance parameter. Assuming that the corresponding state-space model…
State-space models can be used to incorporate subject knowledge on the underlying dynamics of a time series by the introduction of a latent Markov state-process. A user can specify the dynamics of this process together with how the state…
It has been the standard teaching of today that backward stability analysis is taught as absolute, just as in Newtonian physics time is taught absolute time. We will prove it is not true in general. It depends on algorithms. We will prove…
The particle filter is a powerful framework for estimating hidden states in dynamic systems where uncertainty, noise, and nonlinearity dominate. This mini-book offers a clear and structured introduction to the core ideas behind particle…
We prove that for linear, discrete, time-varying, deterministic system (perfect model) with noisy outputs, the Riccati transformation in the Kalman filter asymptotically bounds the rank of the forecast and the analysis error covariance…
In this paper, we present a novel sufficient condition for the stability of discrete-time linear systems that can be represented as a set of piecewise linear constraints, which make them suitable for quadratic programming optimization…
We investigate Kac's many-particle stochastic model of gas dynamics in the case of hard potentials with a moderate angular singularity, and show that the noncutoff particle system can be obtained as the limit of cutoff systems, with a rate…
This paper presents a novel adaptive fading cubature Kalman filter (AFCKF) based on double transitive factors. The developed adaptive algorithm is explained in two stages; stage (i) a single transitive factor is used to update the predicted…
This paper is devoted to an interacting particle system that provides probabilistic interpretation of the wave equation on graphs. A Feynman-Kac-type formula is established, connecting the expectation of the process with the wave equation…
This paper is concerned with the problem of tracking single or multiple targets with multiple non-target specific observations (measurements). For such filtering problems with data association uncertainty, a novel feedback control-based…
The motivation of this work is to get an additional insight into the irreversible energy dissipation on the quantum level. The presented examination procedure is based on the Feynman path integral method that is applied and widened towards…
Sequential and quantum Monte Carlo methods, as well as genetic type search algorithms can be interpreted as a mean field and interacting particle approximations of Feynman-Kac models in distribution spaces. The performance of these…