Related papers: The Geometry of Navigation Problems

In this paper, the well-known multiplicative extended Kalman filter (MEKF) is re-investigated for attitude estimation using vector observations. From the Lie group theory, it is shown that the attitude estimation model is group affine and…

Indoor tracking and pose estimation, i.e., determining the position and orientation of a moving target, are increasingly important due to their numerous applications. While Inertial Navigation Systems (INS) provide high update rates, their…

In this paper, we propose and develop a methodology for nonlinear systems health monitoring by modeling the damage and degradation mechanism dynamics as "slow" states that are augmented with the system "fast" dynamical states. This…

This paper presents a novel approach to distributed pose estimation in the multi-agent system based on an invariant Kalman filter with covariance intersection. Our method models uncertainties using Lie algebra and applies object-level…

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 proposes a state estimator for legged robots operating in slippery environments. An Invariant Extended Kalman Filter (InEKF) is implemented to fuse inertial and velocity measurements from a tracking camera and leg kinematic…

This paper introduces a computational framework to reconstruct and forecast a partially observed state that evolves according to an unknown or expensive-to-simulate dynamical system. Our reduced-order autodifferentiable ensemble Kalman…

The Ensemble Kalman Filter (EnKF), as a fundamental data assimilation approach, has been widely used in many fields of the sciences and engineering. When the state variable is of high dimensional accompanied with high resolution…

Forecasting the motion of surrounding obstacles (vehicles, bicycles, pedestrians and etc.) benefits the on-road motion planning for intelligent and autonomous vehicles. Complex scenes always yield great challenges in modeling the patterns…

Aiming to enhance the consistency and thus long-term accuracy of Extended Kalman Filters for terrestrial vehicle localization, this paper introduces the Manifold Error State Extended Kalman Filter (M-ESEKF). By representing the robot's pose…

This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter,…

While LiDAR and cameras are becoming ubiquitous for unmanned aerial vehicles (UAVs) but can be ineffective in challenging environments, 4D millimeter-wave (MMW) radars that can provide robust 3D ranging and Doppler velocity measurements are…

Kalman Filters (KF) are fundamental to real-time state estimation applications, including radar-based tracking systems used in modern driver assistance and safety technologies. In a linear dynamical system with Gaussian noise distributions…

The Ensemble Kalman Filter (EnKF) has achieved great successes in data assimilation in atmospheric and oceanic sciences, but its failure in convergence to the right filtering distribution precludes its use for uncertainty quantification. We…

Inconsistency issue is one crucial challenge for the performance of extended Kalman filter (EKF) based methods for state estimation problems, which is mainly affected by the discrepancy of observability between the EKF model and the…

The Gaussian process state-space models (GPSSMs) represent a versatile class of data-driven nonlinear dynamical system models. However, the presence of numerous latent variables in GPSSM incurs unresolved issues for existing variational…

This paper addresses the issues of unmanned aerial vehicle (UAV) indoor navigation, specifically in areas where GPS and magnetometer sensor measurements are unavailable or unreliable. The proposed solution is to use an error state extended…

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.…

The ensemble Kalman filter (EnKF) is a popular technique for performing inference in state-space models (SSMs), particularly when the dynamic process is high-dimensional. Unlike reweighting methods such as sequential Monte Carlo (SMC, i.e.…

This work studies the state estimation problem of a stochastic nonlinear system with unknown sensor measurement losses. If the estimator knows the sensor measurement losses of a linear Gaussian system, the minimum variance estimate is…