相关论文: The Kalman-Levy filter

Kalman filtering is a cornerstone of estimation theory, yet learning the optimal filter under unknown and potentially singular noise covariances remains a fundamental challenge. In this paper, we revisit this problem through the lens of…

Data assimilation combines dynamical models with observations to improve state estimates. Ensemble filters sequentially assimilate observations by updating a set of samples over time, alternating between a forecast and an analysis step.…

The paper proposes a new recursive filter for non-linear systems that inherently computes a valid bound on the mean square estimation error. The proposed filter, bound based extended Kalman, (BEKF) is in the form of an extended Kalman…

Reliable state estimation depends on accurately modeled noise covariances, which are difficult to determine in practice. This paper formulates the noise covariance estimation as a bilevel optimization problem that factorizes the joint…

Popular Bayes filters often apply linearization techniques, such as Taylor expansion or stochastic linear regression, to enable the use of the Kalman filter structure, but this can lead to large errors in strongly nonlinear systems. The…

This paper presents an LMI-based design framework for multirate steady-state Kalman filters in systems with sensors operating at different sampling rates. The multirate system is formulated as a periodic time-varying system, where the…

There is a growing interest in using Kalman-filter models in brain modelling. In turn, it is of considerable importance to make Kalman-filters amenable for reinforcement learning. In the usual formulation of optimal control it is computed…

In this paper, we propose a robust Kalman filtering framework for systems with probabilistic uncertainty in system parameters. We consider two cases, namely discrete time systems, and continuous time systems with discrete measurements. The…

The nonlinear and stochastic relationship between noise covariance parameter values and state estimator performance makes optimal filter tuning a very challenging problem. Popular optimization-based tuning approaches can easily get trapped…

We look at a stochastic time-varying optimization problem and we formulate online algorithms to find and track its optimizers in expectation. The algorithms are derived from the intuition that standard prediction and correction steps can be…

Bayesian linear inverse problems aim to recover an unknown signal from noisy observations, incorporating prior knowledge. This paper analyses a data-dependent method to choose the scale parameter of a Gaussian prior. The method we study…

We present a new strategy for filtering high-dimensional multiscale systems characterized by high-order non-Gaussian statistics using observations from leading-order moments. A closed stochastic-statistical modeling framework suitable for…

We consider the nonlinear Kalman filtering problem using Kullback-Leibler (KL) and $\alpha$-divergence measures as optimization criteria. Unlike linear Kalman filters, nonlinear Kalman filters do not have closed form Gaussian posteriors…

This paper derives a \emph{distributed} Kalman filter to estimate a sparsely connected, large-scale, $n-$dimensional, dynamical system monitored by a network of $N$ sensors. Local Kalman filters are implemented on the ($n_l-$dimensional,…

An important part of system modeling is determining parameter values, particularly for biomolecular systems, where direct measurements of individual parameters are typically hard. While Extended Kalman Filters have been used for this…

Accurate estimation of the dynamic states of a synchronous machine (e.g., rotor s angle and speed) is essential in monitoring and controlling transient stability of a power system. It is well known that the covariance matrixes of process…

This work extends a previous study that introduced an algorithm for state estimation on manifolds within the framework of the Kalman filter. Its objective is to address the limitations of the earlier approach. The reversible Kalman filter…

In this work, we address the problem of sensor selection for state estimation via Kalman filtering. We consider a linear time-invariant (LTI) dynamical system subject to process and measurement noise, where the sensors we use to perform…

Many multichannel systems use a linear filter to retrieve a signal of interest corrupted by noise whose statistics are partly unknown. The optimal filter in Gaussian noise requires knowledge of the noise covariance matrix $\Sigma$ and in…

It has been proposed that classical filtering methods, like the Kalman filter and 3DVAR, can be used to solve linear statistical inverse problems. In the work of Iglesias, Lin, Lu, & Stuart (2017), error estimates were obtained for this…