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The ability of ensemble Kalman filter (EnKF) algorithms to extract information from observations is analyzed with the aid of the concept of the degrees of freedom for signal (DFS). A simple mathematical argument shows that DFS for EnKF is…

This paper introduces a Gaussian Bayesian Network-based Extended Kalman Filter (GBN-EKF) for non-linear state estimators on stiff and ill-conditioned continuous-discrete stochastic systems, with a further analysis on systems with…

In real-world applications the Perspective-n-Point (PnP) problem should generally be applied in a sequence of images which a set of drift-prone features are tracked over time. In this paper, we consider both the temporal dependency of…

Autonomous vehicles have gained significant attention due to technological advancements and their potential to transform transportation. A critical challenge in this domain is precise localization, particularly in LiDAR-based map matching,…

Modern autonomous navigation for unmanned ground vehicles relies on different estimators to fuse inertial sensors and GNSS measurements. However, the constant noise covariance matrices often struggle to account for dynamic real-world…

The Ensemble Kalman Filter (EnKF) belongs to the class of iterative particle filtering methods and can be used for solving control--to--observable inverse problems. In this context, the EnKF is known as Ensemble Kalman Inversion (EKI). In…

In a recent methodological paper, we showed how to learn chaotic dynamics along with the state trajectory from sequentially acquired observations, using local ensemble Kalman filters. Here, we more systematically investigate the possibility…

Many filters have been proposed in recent decades for the nonlinear state estimation problem. The linearization-based extended Kalman filter (EKF) is widely applied to nonlinear industrial systems. As EKF is limited in accuracy and…

The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion. Despite its widespread use, there has been little analysis of its theoretical properties. Many of the algorithmic innovations…

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 studies the distributed state estimation problem for a class of discrete time-varying systems over sensor networks. Firstly, it is shown that a networked Kalman filter with optimal gain parameter is actually a centralized filter,…

Vision-aided localization for low-cost mobile robots in diverse environments has attracted widespread attention recently. Although many current systems are applicable in daytime environments, nocturnal visual localization is still an open…

The traditional GNSS-aided inertial navigation system (INS) usually exploits the extended Kalman filter (EKF) for state estimation, and the initial attitude accuracy is key to the filtering performance. To spare the reliance on the initial…

This paper extends the ensemble Kalman filter (EnKF) for inverse problems to identify trending model coefficients. This is done by repeatedly inflating the ensemble while maintaining the mean of the particles. As a benchmark serves a…

LiDAR odometry is a pivotal technology in the fields of autonomous driving and autonomous mobile robotics. However, most of the current works focus on nonlinear optimization methods, and still existing many challenges in using the…

Advanced driver assistance systems are critically dependent on reliable and accurate information regarding a vehicles' driving state. For estimation of unknown quantities, model-based and learning-based methods exist, but both suffer from…

To enhance accuracy of robot state estimation, active sensing (or perception-aware) methods seek trajectories that maximize the information gathered by the sensors. To this aim, one possibility is to seek trajectories that minimize the…

This paper investigates the state estimation problem for unknown linear systems subject to both process and measurement noise. Based on a prior input-output trajectory sampled at a higher frequency and a prior state trajectory sampled at a…

Due to the state trajectory-independent features of invariant Kalman filtering (InEKF), it has attracted widespread attention in the research community for its significantly improved state estimation accuracy and convergence under…

The Kalman filter (KF) and the extended Kalman filter (EKF) are well established techniques for state estimation. However, the choice of the filter tuning parameters still poses a major challenge for the engineers [1]. In the present work,…