Related papers: The Kalman Filter: a didactical overview
The extended Kalman filter (EKF) is a common state estimation method for discrete nonlinear systems. It recursively executes the propagation step as time goes by and the update step when a set of measurements arrives. In the update step,…
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…
This report provides a brief historical evolution of the concepts in the Kalman filtering theory since ancient times to the present. A brief description of the filter equations its aesthetics, beauty, truth, fascinating perspectives and…
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…
A stochastic filter uses a series of measurements over time to produce estimates of unknown variables based on a dynamic model. For a quantum system, such an algorithm is provided by a quantum filter, which is also known as a stochastic…
This paper presents a novel filter with low computational demand to address the problem of orientation estimation of a robotic platform. This is conventionally addressed by extended Kalman filtering of measurements from a sensor suit which…
The ensemble Kalman filter is widely used in applications because, for high dimensional filtering problems, it has a robustness that is not shared for example by the particle filter; in particular it does not suffer from weight collapse.…
The spatial dependent unknown acoustic source is reconstructed according noisy multiple frequency data on a remote closed surface. Assume that the unknown function is supported on a bounded domain. To determine the support, we present a…
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…
State estimation of dynamical systems from noisy observations is a fundamental task in many applications. It is commonly addressed using the linear Kalman filter (KF), whose performance can significantly degrade in the presence of outliers…
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.…
In this article, we propose a new filtering algorithm based in the Koopman operator, showing that a nonlinear filtering problem can be seen as an equivalent problem where the dynamics is infinite dimensional, but linear. Using Extended…
This paper proposes new methodology for sequential state and parameter estimation within the ensemble Kalman filter. The method is fully Bayesian and propagates the joint posterior density of states and parameters over time. In order to…
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 considers the simultaneous state and unknown input estimation for continuous-discrete stochastic systems. Two types of approaches (with and without modeling of unknown inputs) which can address this issue are investigated. A…
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 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…
The Kalman filter is a fundamental tool for state estimation in dynamical systems. While originally developed for linear Gaussian settings, it has been extended to nonlinear problems through approaches such as the extended and unscented…
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…
Data assimilation provides algorithms for widespread applications in various fields. It is of practical use to deal with a large amount of information in the complex system that is hard to estimate. Weather forecasting is one of the…