Related papers: On the convergence of a Risk Sensitive like Filter

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…

A contraction analysis of risk-sensitive Riccati equations is proposed. When the state-space model is reachable and observable, a block-update implementation of the risk-sensitive filter is used to show that the N-fold composition of the…

Convergence of the Kalman filter is best analyzed by studying the contraction of the Riccati map in the space of positive definite (covariance) matrices. In this paper, we explore how this contraction property relates to a more fundamental…

We consider a robust state space filtering problem in the case that the transition probability density is unknown and possibly degenerate. The resulting robust filter has a Kalman-like structure and solves a minimax game: the nature selects…

We consider a robust filtering problem where the robust filter is designed according to the least favorable model belonging to a ball about the nominal model. In this approach, the ball radius specifies the modeling error tolerance and the…

A multiplicative relative value iteration algorithm for solving the dynamic programming equation for the risk-sensitive control problem is studied for discrete time controlled Markov chains with a compact Polish state space, and controlled…

We consider a family of divergence-based minimax approaches to perform robust filtering. The mismodeling budget, or tolerance, is specified at each time increment of the model. More precisely, all possible model increments belong to a ball…

This paper studies the stability of covariance-intersection (CI)-based distributed Kalman filtering in time-varying systems. For the general time-varying case, a relationship between the error covariance and the observability Gramian is…

This article is concerned with the convergence of the state estimate obtained from the discrete time Kalman filter to the continuous time estimate as the temporal discretization is refined. We derive convergence rate estimates for different…

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…

In robotics, designing robust algorithms in the face of estimation uncertainty is a challenging task. Indeed, controllers often do not consider the estimation uncertainty and only rely on the most likely estimated state. Consequently,…

The stability properties of matrix-valued Riccati diffusions are investigated. The matrix-valued Riccati diffusion processes considered in this work are of interest in their own right, as a rather prototypical model of a matrix-valued…

In this article, we complement recent results on the convergence of the state estimate obtained by applying the discrete-time Kalman filter on a time-sampled continuous-time system. As the temporal discretization is refined, the estimate…

The paper studies the asymptotic behavior of Random Algebraic Riccati Equations (RARE) arising in Kalman filtering when the arrival of the observations is described by a Bernoulli i.i.d. process. We model the RARE as an order-preserving,…

Contraction properties of the Riccati operator are studied within the context of non-stationary linear-quadratic optimal control. A lifting approach is used to obtain a bound on the rate of strict contraction, with respect to the Riemannian…

In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…

The contraction properties of the Extended Kalman Filter, viewed as a deterministic observer for nonlinear systems, are analyzed. This yields new conditions under which exponential convergence of the state error can be guaranteed. As…

This paper considers robust filtering for a nominal Gaussian state-space model, when a relative entropy tolerance is applied to each time increment of a dynamical model. The problem is formulated as a dynamic minimax game where the…

A recursive state estimation procedure is derived for a linear time varying system with both parametric uncertainties and stochastic measurement droppings. This estimator has a similar form as that of the Kalman filter with intermittent…

Reinforcement Learning (RL) has shown exceptional performance across various applications, enabling autonomous agents to learn optimal policies through interaction with their environments. However, traditional RL frameworks often face…