augmented-state ekf

To address degraded tracking performance of mechanical systems—such as exoskeletons—under unknown dynamic disturbances, this paper proposes a novel disturbance observer framework that jointly optimizes estimation speed and uncertainty quantification. We theoretically reveal an inherent trade-off between estimation responsiveness and uncertainty in disturbance reconstruction, and accordingly design two observers: the Interacting Multiple Model Extended Kalman Filter (IMM-EKF) and the Multi-Kernel Correntropy Extended Kalman Filter (MKCE-EKF). The IMM-EKF achieves adaptive model-set switching to accommodate time-varying interaction forces, while the MKCE-EKF employs an information-entropy-driven covariance adaptation mechanism to enhance robustness against non-Gaussian uncertainties. Experimental validation on a lower-limb exoskeleton demonstrates significant improvements: hip joint tracking errors are reduced by 36.3% and 16.2%, and knee joint errors by 46.3% and 24.4%, respectively—both metrics outperforming conventional EKF-based methods.

Traditional Kalman filtering lacks robustness against systems subject to unmodeled process and measurement noise. To address this, we propose a novel generalized Bayesian robust filtering framework that, for the first time, extends the weighted observation likelihood mechanism to the process noise modeling component, enabling joint suppression of process and measurement outliers. Our method constructs a dual-weighted likelihood function to uniformly characterize non-Gaussian anomalies in both process dynamics and observations, and performs robust recursive state estimation within a generalized Bayesian inference framework. Experimental results demonstrate that, under significant process or measurement outliers, the proposed approach achieves substantially higher estimation accuracy and stability compared to the standard Kalman filter and existing robust filters. These findings validate both the theoretical soundness and practical applicability of the method.

Traditional Kalman filtering (KF) suffers from limited state estimation accuracy due to oversimplified state-space models. To address this, we propose an AI-enhanced filtering framework that deeply integrates model-driven and data-driven paradigms. We systematically introduce two novel AI-KF fusion paradigms—task-oriented and state-space-model-oriented—and embed deep neural networks directly into the KF architecture, enabling adaptive modeling of unknown dynamics while preserving physical interpretability. Our method supports partial state-space modeling and end-to-end joint training. Experiments across diverse nonlinear and time-varying systems demonstrate significant improvements in tracking accuracy and robustness over conventional approaches. Furthermore, we fully open-source the implementation, establishing the first reproducible benchmark and design paradigm for AI-augmented filtering.

This paper addresses state estimation under Stiefel manifold geometric constraints. We propose an extended Kalman filter (EKF) framework rigorously defined on the Stiefel manifold, departing from conventional Euclidean-space EKFs. Our method performs linearization in the tangent space, and employs exponential and logarithmic maps for observation updates—thereby preserving orthogonality constraints exactly. Theoretically, we derive the recursive filtering equations and covariance propagation rules intrinsic to the Stiefel manifold. Algorithmically, the framework supports arbitrary St(n,p) manifolds and accommodates common subcases including the unit sphere S² and the 4×2 orthogonal matrix manifold. Simulation results demonstrate that, compared to standard EKF applied naively in the ambient Euclidean embedding space, our approach achieves significantly higher estimation accuracy and superior constraint satisfaction—validating its effectiveness and robustness for non-Euclidean state estimation.

Robot state estimation faces growing challenges from platform diversity and task complexity, while traditional discrete-time filtering and smoothing methods suffer from sampling-rate limitations and temporal misalignment. This paper proposes a unified formal framework for continuous-time state estimation, systematically integrating major modeling paradigms—including spline interpolation, Gaussian process regression, Bayesian smoothing, and continuous-time optimization—for the first time. We present the most comprehensive survey and taxonomy to date, clarifying methodological evolution, state representation strategies, and application-specific advancements. Furthermore, we identify and formally characterize key open problems, highlighting emerging research directions: differentiable modeling, asynchronous multi-sensor fusion, and real-time computation. Our framework significantly improves estimation accuracy, temporal resolution flexibility, and downstream planning and control performance. By bridging theoretical rigor with practical applicability, this work advances both the foundations and deployment of continuous-time estimation in robotics.

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.

This work addresses the sensitivity of conventional Kalman filters to model mismatch and inaccurate noise covariance specifications, as well as the limitations of existing learning-based approaches that require extensive labeled data and struggle to deliver consistent uncertainty estimates. The authors propose a self-supervised hybrid adaptive Kalman filter that leverages only observational data to online-learn structured corrections to both system dynamics and process noise covariances, while preserving the probabilistic framework of the filter to enable joint state estimation and model classification. This approach is the first to achieve adaptive Kalman filtering with statistically consistent uncertainty quantification without requiring labeled data, and it employs generalized Bayesian inference for data-efficient classification. Experiments demonstrate substantial improvements in estimation accuracy on both real-world and simulated datasets, along with robust classification performance across both small-sample and large-data regimes.

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.

This study addresses online learning of the Kalman filter for output and state estimation in partially observable linear dynamical systems with unknown system models. The authors propose a unified algorithmic framework based on online optimization, incorporating a stochastic querying mechanism to handle limited observability. Their theoretical analysis establishes, for the first time, that sublinear regret in state estimation is unattainable without queries, yet a √T regret bound becomes achievable with a finite number of stochastic queries, revealing a fundamental trade-off between query complexity and regret. The proposed algorithm attains a logarithmic regret bound (log T) for output estimation and a √T regret bound for state estimation. Numerical experiments corroborate the theoretical findings and demonstrate the algorithm’s empirical effectiveness.