相关论文: The Convergence of the Extended Kalman Filter

We consider the problem of performing Bayesian inference for logistic regression using appropriate extensions of the ensemble Kalman filter. Two interacting particle systems are proposed that sample from an approximate posterior and prove…

The widely-used Extended Kalman Filter (EKF) provides a straightforward recipe to estimate the mean and covariance of the state given all past measurements in a causal and recursive fashion. For a wide variety of applications, the EKF is…

We discuss two separate techniques for Kalman Filtering in the presence of state space equality constraints. We then prove that despite the lack of similarity in their formulations, under certain conditions, the two methods result in…

The linear delta expansion is applied to the 3-dimensional O(N) scalar field theory at its critical point in a way that is compatible with the large-N limit. For a range of the arbitrary mass parameter, the linear delta expansion for…

The Kalman filter (KF) is used in a variety of applications for computing the posterior distribution of latent states in a state space model. The model requires a linear relationship between states and observations. Extensions to the Kalman…

This paper is concerned with the filtering problem in continuous-time. Three algorithmic solution approaches for this problem are reviewed: (i) the classical Kalman-Bucy filter which provides an exact solution for the linear Gaussian…

The ensemble Kalman filter has become a popular data assimilation technique in the geosciences. However, little is known theoretically about its long term stability and accuracy. In this paper, we investigate the behavior of an ensemble…

Data assimilation schemes are confronted with the presence of model errors arising from the imperfect description of atmospheric dynamics. These errors are usually modeled on the basis of simple assumptions such as bias, white noise, first…

We study an approximation method for the one-dimensional nonlinear filtering problem, with discrete time and continuous time observation. We first present the method applied to the Fokker-Planck equation. The convergence of the…

We consider the problem of randomly choosing the sensors of a linear time-invariant dynamical system subject to process and measurement noise. We sample the sensors independently and from the same distribution. We measure the performance of…

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…

The ensemble Kalman inversion is widely used in practice to estimate unknown parameters from noisy measurement data. Its low computational costs, straightforward implementation, and non-intrusive nature makes the method appealing in various…

The Kalman filter is indispensable for state estimation across diverse fields but faces computational challenges with higher dimensions. Approaches such as Riccati equation approximations aim to alleviate this complexity, yet ensuring…

This paper is concerned with the linear/nonlinear Kalman-like filtering problem under binary sensors. Since innovation represents new information in the sensor measurement and serves to correct the prediction for the Kalman-like filter…

Most Kalman filters for non-linear systems, such as the unscented Kalman filter, are based on Gaussian approximations. We use Poincar\'e inequalities to bound the Wasserstein distance between the true joint distribution of the prediction…

We derive symmetry preserving invariant extended Kalman filters (IEKF) on matrix Lie groups. These Kalman filters have an advantage over conventional extended Kalman filters as the error dynamics for such filters are independent of the…

This paper aims to introduce an application to Kalman Filtering Theory, which is rather unconventional. Recent experiments have shown that many natural phenomena, especially from ecology or meteorology, could be monitored and predicted more…

State estimation that combines observational data with mathematical models is central to many applications and is commonly addressed through filtering methods, such as ensemble Kalman filters. In this article, we examine the signal-tracking…

We develop a generalization of unobserved components models that allows for a wide range of long-run dynamics by modelling the permanent component as a fractionally integrated process. The model does not require stationarity and can be cast…

In this paper, we present a unified optimal and exponentially stable filter for linear discrete-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense, without making any…