Related papers: A geometric perspective of state estimation using …
The extended Kalman filter (EKF) has been the industry standard for state estimation problems over the past sixty years. The classical formulation of the EKF is posed for nonlinear systems defined on global Euclidean spaces. The design…
While many works exploiting an existing Lie group structure have been proposed for state estimation, in particular the Invariant Extended Kalman Filter (IEKF), few papers address the construction of a group structure that allows casting a…
The well-known Kalman filters model dynamical systems by relying on state-space representations with the next state updated, and its uncertainty controlled, by fresh information associated with newly observed system outputs. This paper…
This report derives a generalized, converted measurement Kalman filter for the class of filtering problems with a linear state equation and nonlinear measurement equation, for which a bijective mapping exists between the state and…
In this article, we consider the implications of unobservable subspaces in the construction of a Kalman filter. In particular, we consider dynamical systems which are invariant with respect to a group action, and which are therefore…
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…
This paper proposes a simple, accurate and computationally efficient method to apply the ordinary unscented Kalman filter developed in Euclidean space to systems whose dynamics evolve on manifolds.We use the mathematical theory called…
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…
Unscented Kalman Filters (UKFs) have become popular in the research community. Most UKFs work only with Euclidean systems, but in many scenarios it is advantageous to consider systems with state-variables taking values on Riemannian…
This paper analyzes directional tracking in 2D with the extended Kalman filter on Lie groups (LG-EKF). The study stems from the problem of tracking objects moving in 2D Euclidean space, with the observer measuring direction only, thus…
Kalman filtering has been traditionally applied in three application areas of estimation, state estimation, parameter estimation (a.k.a. model updating), and dual estimation. However, Kalman filter is often not sufficient when experimenting…
The Kalman filter is an established tool for the analysis of dynamic systems with normally distributed noise, and it has been successfully applied in numerous application areas. It provides sequentially calculated estimates of the system…
Estimating the state of a dynamical system from partial and noisy observations is a ubiquitous problem in a large number of applications, such as probabilistic weather forecasting and prediction of epidemics. Particle filters are a widely…
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…
The kinematics of many control systems, especially in the robotics field, naturally live on smooth manifolds. Most classical state-estimation algorithms, including the extended Kalman filter, are posed on Euclidean space. Although any…
In this paper, a new filter model called set-membership Kalman filter for nonlinear state estimation problems was designed, where both random and unknown but bounded uncertainties were considered simultaneously in the discrete-time system.…
Kalman filtering is a classic state estimation technique used in application areas such as signal processing and autonomous control of vehicles. It is now being used to solve problems in computer systems such as controlling the voltage and…
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…
This paper presents a new filter for state-space models based on Bellman's dynamic-programming principle, allowing for nonlinearity, non-Gaussianity and degeneracy in the observation and/or state-transition equations. The resulting Bellman…
The real-world applications in signal processing generally involve estimating the system state or parameters in nonlinear, non-Gaussian dynamic systems. The estimation problem may get even more challenging when there are physical…