Related papers: Optimization viewpoint on Kalman smoothing, with a…
We propose a new robust filtering paradigm considering the situation in which model uncertainty, described through an ambiguity set, is present only in the observations. We derive the corresponding robust estimator, referred to as…
This research enhances linear regression models by integrating a Kalman filter and analysing curve areas to minimize loss. The goal is to develop an optimal linear regression equation using stochastic gradient descent (SGD) for weight…
We consider the robust filtering problem for a state-space model with outliers in correlated measurements. We propose a new robust filtering framework to further improve the robustness of conventional robust filters. Specifically, the…
We introduce a novel nonlinear Kalman filter that utilizes reparametrization gradients. The widely used parametric approximation is based on a jointly Gaussian assumption of the state-space model, which is in turn equivalent to minimizing…
Ensemble Kalman inversion is a parallelizable methodology for solving inverse or parameter estimation problems. Although it is based on ideas from Kalman filtering, it may be viewed as a derivative-free optimization method. In its most…
In this paper, we propose a new asymptotic expansion approach for nonlinear filtering based on a small parameter in the system noise. This method expresses the filtering distribution as a power series in the noise level, where the…
The universality of the celebrated Kalman filtering can be found in control theory. The Kalman filter has found its striking applications in sophisticated autonomous systems and smart products, which are attributed to its realization in a…
Nonlinear filtering problems are encountered in many applications, and one solution approach is the extended Kalman filter, which is not always convergent. Therefore, it is crucial to identify conditions under which the extended Kalman…
The Kalman filter combines forecasts and new observations to obtain an estimation which is optimal in the sense of a minimum average quadratic error. The Kalman filter has two main restrictions: (i) the dynamical system is assumed linear…
We introduce the inverse Kalman filter, which enables exact matrix-vector multiplication between a covariance matrix from a dynamic linear model and any real-valued vector with linear computational cost. We integrate the inverse Kalman…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
We study the problem of optimal estimation and control of linear systems using quantized measurements, with a focus on applications over sensor networks. We show that the state conditioned on a causal quantization of the measurements can be…
We present a step by step mathematical derivation of the Kalman filter using two different approaches. First, we consider the orthogonal projection method by means of vector-space optimization. Second, we derive the Kalman filter using…
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.…
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…
We present recent results on the existence of a continuous time limit for Ensemble Kalman Filter algorithms. In the setting of continuous signal and observation processes, we apply the original Ensemble Kalman Filter algorithm proposed by…
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 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…
Estimating the state of a dynamical system from a series of noise-corrupted observations is fundamental in many areas of science and engineering. The most well-known method, the Kalman smoother (and the related Kalman filter), relies on…
The problem of Bayesian filtering and smoothing in nonlinear models with additive noise is an active area of research. Classical Taylor series as well as more recent sigma-point based methods are two well-known strategies to deal with these…