unscented kalman filtering

This work addresses the challenge that nonlinear Kalman filters—such as the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF)—often struggle to balance robustness and accuracy due to a lack of systematic design principles. To this end, the paper introduces a covariance compensation framework that quantifies the deviation from EKF’s covariance prediction and establishes design criteria for performance improvement. It presents, for the first time, the concept of covariance compensation along with three core guidelines: invariance under orthogonal transformations, sufficient compensation relative to the EKF baseline, and a preference for underconfident compensation magnitudes. Through theoretical analysis and numerical experiments, the study demonstrates that adherence to these principles significantly enhances estimation accuracy and reveals that commonly adopted fixed-parameter strategies in the literature are generally suboptimal.

Standard unscented Kalman filtering (UKF) suffers from modeling inaccuracy and degraded estimation accuracy/stability in navigation systems due to linear propagation of sigma points, which fails to capture strong nonlinearities. To address this, we propose an improved UKF based on a nonlinear error-state propagation model. Our key innovation lies in replacing the conventional linearized sigma-point propagation under the nominal dynamic model with direct evolution of sigma points governed by high-fidelity nonlinear differential equations of the navigation error state—enabling more accurate mean and covariance prediction. The method integrates the unscented transform with multi-sensor measurements from autonomous underwater vehicles (AUVs) and is implemented and validated in realistic oceanic environments. Experimental results demonstrate significant improvements over both standard UKF and extended Kalman filter (EKF) in positioning accuracy, attitude estimation precision, and filter convergence rate—particularly under highly nonlinear, aggressive maneuvering conditions, where robustness and stability are markedly enhanced.

This work addresses the limitations of the conventional unscented Kalman filter (UKF) under time-varying dynamics and heavy-tailed non-Gaussian noise, which stem from its reliance on static parameterization. To overcome this, we propose a memory-augmented meta-learning framework that, for the first time, formulates sigma-point weight generation as a hyperparameter optimization problem. A recurrent context encoder compresses historical innovation sequences, and a policy network dynamically synthesizes weights for the mean and covariance to adaptively balance trust between prediction and measurement. This approach departs from fixed or heuristic tuning paradigms, enabling end-to-end training and out-of-distribution generalization. Evaluated on maneuvering target tracking tasks, the method significantly outperforms standard UKF baselines, demonstrates enhanced robustness to flicker noise, and generalizes effectively to unseen dynamic scenarios.

This work addresses state estimation for discrete-time nonlinear stochastic systems with finite-dimensional states and infinite-dimensional measurements—such as image fields—arising in visual localization and tracking. Conventional methods struggle to rigorously model the relationship between image gradients and the Jacobian of the observation function with respect to the state. To overcome this, we propose an extended Kalman filter (EKF) grounded in infinite-dimensional random field modeling. Crucially, we establish, for the first time from a systems-theoretic perspective, that image gradients correspond precisely to the Fréchet derivative of the observation functional with respect to the state—thereby providing a rigorous mathematical foundation for gradient-based visual state estimation. Evaluated on monocular visual-inertial navigation for unmanned aerial vehicles, our approach reduces root-mean-square error by an order of magnitude compared to VINS-MONO, demonstrating substantial improvements in both estimation accuracy and robustness.

This work addresses the joint online estimation of unknown inputs, time-varying parameters, and dynamic states for linear and nonlinear systems with output-only measurements. We propose a unified recursive framework based on the Unscented Kalman Filter (UKF), which augments the state space to jointly incorporate inputs, parameters, and states. By extending the unscented transform to this augmented space, our method avoids Jacobian computation, enabling robust and computationally efficient handling of strong nonlinearities and unknown input disturbances. A real-time data-driven update mechanism, combined with nonlinear function approximation, ensures rapid convergence and high estimation accuracy. In both simulations and physical experiments, the approach achieves millisecond-level response times and superior estimation precision, consistently outperforming conventional Extended Kalman Filters (EKF) and particle filters.

This work addresses the degraded accuracy and poor covariance calibration of conventional Unscented Kalman Filters (UKF) in nonlinear dynamic systems subject to time-varying noise statistics and model mismatch. To this end, we propose Unscented KalmanNet (UKN), a hybrid recursive estimator that integrates deep learning with the UKF framework. UKN preserves the UKF’s explicit sigma-point covariance propagation and positive definiteness while introducing two neural modules: NoiseNet for bounded multiplicative correction of time-varying noise covariances and GainNet for bounded residual-based adjustment of the analytical gain. A calibration-aware adaptive loss function is designed to jointly optimize state error, covariance consistency, and innovation consistency. Experiments on three synthetic systems and real-world UZH-FPV flight data demonstrate that UKN consistently outperforms UKF, achieving 22.4%–49.7% lower state RMSE and yielding uncertainty estimates—measured by NEES and coverage probability—that are closest to nominal levels, with superior generalization stability.

This work addresses the limitations of conventional local navigation algorithms, which neglect Earth’s curvature, rotation, and gravity variations, thereby failing to meet the demands of high-precision state estimation at a global scale. By leveraging Lie group symmetry and invariant Kalman filtering theory, the paper systematically derives and unifies the global navigation dynamics for four classes of error-state Kalman filters—including standard, left-invariant, and right-invariant formulations. It presents the first comprehensive comparison of ESKF equations under different error-state representations, clarifying their respective applicability conditions and performance characteristics in global scenarios. The proposed framework accommodates complex sensor configurations and dynamic environments, delivering a directly implementable, high-precision, and robust state estimation algorithm that advances the practical deployment of trajectory-independent error propagation theory.

This work addresses the absence of analytical solutions for Bayesian filtering in nonlinear dynamical systems, where existing Gaussian approximation methods often neglect the underlying geometric structure of probability distributions. From an information-geometric perspective, the authors model prediction and measurement update steps as inference processes on the manifold of Gaussian distributions and propose the geometry-aware NANO filter. This approach iteratively refines the posterior mean and covariance via a single-step natural gradient descent, preserving covariance positive definiteness while exactly recovering the Kalman update in the linear Gaussian case. The method demonstrates superior accuracy and robustness across diverse applications, including satellite attitude estimation, SLAM, and state estimation for quadrupedal and humanoid robots.

This work addresses the degraded estimation performance in 3D landmark-aided inertial navigation caused by spurious observability in conventional filters. It introduces, for the first time, the Iterated Invariant Extended Kalman Filter (Iterated Invariant EKF) to this setting. By constraining the state to the observation manifold under low-noise conditions and restricting uncertainty to its tangent space, the method effectively preserves the system’s inherent observability structure. The approach integrates Lie group geometry, group-affine system modeling, and a 3D landmark observation model. Numerical simulations demonstrate that it significantly outperforms classical SO(3)-EKF, iterated SO(3)-EKF, and standard IEKF, achieving notable improvements in both estimation accuracy and consistency.

This work addresses the issue of overconfident filtering in nonlinear state-space models caused by misspecification in either the dynamics or observation model. To mitigate this, the authors propose a Prediction-oriented (PrO) online filtering approach that does not strictly rely on Bayes’ theorem but instead learns only when the overall model is correctly specified. By integrating a linear-Gaussian approximation, the method establishes an efficient iterative update mechanism, yielding a variant of the extended Kalman filter termed EKF-PrO. This framework requires no hyperparameters, is computationally efficient, and automatically adapts to model misspecification. Experimental results demonstrate that, across various scenarios involving both linear and nonlinear model misspecifications, EKF-PrO achieves substantially improved inference robustness while maintaining computational costs comparable to existing methods.