open-loop filtering

This study addresses the lack of quantitative criteria for selecting between closed-loop and open-loop Kalman filter architectures in airborne aided inertial navigation. To this end, the authors propose a unified simulation framework to systematically evaluate the performance differences of these two error-state Kalman filtering approaches under varying inertial sensor accuracy levels. The methodology employs standard inertial mechanization in the geodetic frame combined with direct position aiding, enabling a comprehensive analysis of the trade-off between fusion smoothness and long-term stability. The work provides the first quantitative evidence that, with high-accuracy IMUs, the open-loop architecture yields smoother state fusion, whereas the closed-loop configuration offers superior long-term navigation stability, thereby offering empirical guidance for filter architecture selection.

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.

Conventional Kalman filtering and minimum-variance unbiased (MVU) estimation fail in structural health monitoring when sensor configurations are non-ideal—e.g., rank-deficient feedthrough matrices, direct transmission paths, or unmodeled noise/parameter uncertainties. Method: This paper proposes a general adaptive filtering and smoothing framework integrating MVU principles, state-augmented filtering, and online self-calibration—without requiring fictitious input models or full-rank feedthrough assumptions. Contribution/Results: Validated for the first time in physical experiments using a five-story shear-frame shake-table setup under multiple impact excitations, the method demonstrates robustness and real-time adaptability under realistic sensor noise and structural parameter uncertainty. It achieves high-accuracy joint estimation of system states and unknown inputs, significantly extending the engineering applicability boundary of general unknown-input estimation 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.

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 proposes a novel experimental design framework for dynamic systems that addresses two key limitations of existing approaches: the neglect of process noise and the reliance on unknown true parameters for computing the Fisher information matrix (FIM). By integrating Bayesian averaging with an adaptive updating mechanism, the method jointly accounts for both process and measurement noise through Kalman filtering. The FIM is computed via Bayesian averaging over the parameter prior and is continuously updated in real time as new data become available, thereby optimizing subsequent experimental inputs. This approach achieves, for the first time, robust and real-time experimental design in linear dynamic systems with process noise without requiring knowledge of the true system parameters, significantly enhancing both the information efficiency and robustness of system identification.

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.

We study online prediction for marginally stable, partially observed linear dynamical systems under nonstochastic disturbances. Our objective is to minimize the cumulative squared prediction loss and compete with the best-in-hindsight Luenberger predictor. Standard online learning methods typically rely on bounded domains/gradients, and thus their guarantees may fail to deal with potentially unbounded trajectories in marginally stable systems. In this paper, we introduce an unconstrained online least squares method that stabilizes the learning process via tailored predictive hints. With model knowledge, we prove that hints constructed from any stabilizing Luenberger predictor render the hint residuals uniformly bounded, achieving logarithmic regret despite unbounded trajectory growth. We also discuss model-free prediction and introduce a simple universal hint for symmetric systems, under which logarithmic regret is maintained without model knowledge. Our results provide an adaptive, instance-wise optimal online predictor compared to classical fixed-gain observers under nonstochastic disturbances.

This study addresses the challenge of achieving efficient and accurate state estimation in nonlinear dynamic systems under unknown system dynamics and noise models. To this end, it presents the first systematic comparison of model-free deep learning approaches—including Transformers, state space models (SSMs), and recurrent neural networks—against classical filtering methods such as particle filters and extended/unscented Kalman filters. Experimental results demonstrate that state space neural networks, without requiring any explicit system model, attain estimation accuracy approaching that of strong nonlinear Kalman filters while significantly outperforming weaker baselines. Moreover, these neural architectures achieve substantially higher inference throughput, thereby offering a compelling balance between accuracy and computational efficiency.