Related papers: Unified Linearization-based Nonlinear Filtering
We study a distributed Kalman filtering problem in which a number of nodes cooperate without central coordination to estimate a common state based on local measurements and data received from neighbors. This is typically done by running a…
The Kalman filter is a fundamental filtering algorithm that fuses noisy sensory data, a previous state estimate, and a dynamics model to produce a principled estimate of the current state. It assumes, and is optimal for, linear models and…
Complex systems are often described with competing models. Such divergence of interpretation on the system may stem from model fidelity, mathematical simplicity, and more generally, our limited knowledge of the underlying processes.…
The unscented Kalman filter is a nonlinear estimation algorithm commonly used in navigation applications. The prediction of the mean and covariance matrix is crucial to the stable behavior of the filter. This prediction is done by…
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…
The Derivative-free nonlinear Kalman Filter is proposed for state estimation and fault diagnosis in distributed parameter systems and particularly in dynamical systems described by partial differential equations of the nonlinear wave type.…
The Kalman filter (KF) provides optimal recursive state estimates for linear-Gaussian systems and underpins applications in control, signal processing, and others. However, it is vulnerable to outliers in the measurements and process noise.…
We derive a novel, provably robust, and closed-form Bayesian update rule for online filtering in state-space models in the presence of outliers and misspecified measurement models. Our method combines generalised Bayesian inference with…
We cast Amari's natural gradient in statistical learning as a specific case of Kalman filtering. Namely, applying an extended Kalman filter to estimate a fixed unknown parameter of a probabilistic model from a series of observations, is…
Motivated by the maneuvering target tracking with sensors such as radar and sonar, this paper considers the joint and recursive estimation of the dynamic state and the time-varying process noise covariance in nonlinear state space models.…
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…
This work introduces an algorithm for state estimation on manifolds within the framework of the Kalman filter. Its primary objective is to provide a methodology enabling the evaluation of the precision of existing Kalman filter variants…
Several numerical tools designed to overcome the challenges of smoothing in a nonlinear and non-Gaussian setting are investigated for a class of particle smoothers. The considered family of smoothers is induced by the class of linear…
This paper is concerned with the problem of distributed Kalman filtering in a network of interconnected subsystems with distributed control protocols. We consider networks, which can be either homogeneous or heterogeneous, of linear…
Estimation of a dynamical system's latent state subject to sensor noise and model inaccuracies remains a critical yet difficult problem in robotics. While Kalman filters provide the optimal solution in the least squared sense for linear and…
This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades of research effort. To…
The application of neural networks in modeling dynamic systems has become prominent due to their ability to estimate complex nonlinear functions. Despite their effectiveness, neural networks face challenges in long-term predictions, where…
Simultaneous state and parameter estimation arises from various applicational areas but presents a major computational challenge. Most available Markov chain or sequential Monte Carlo techniques are applicable to relatively low dimensional…
In this work, we present methods for state estimation in continuous-discrete nonlinear systems involving stochastic differential equations. We present the extended Kalman filter, the unscented Kalman filter, the ensemble Kalman filter, and…
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…