implement closed-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 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.

Traditional Kalman filters for nonlinear systems—such as the Extended, Unscented, and Cubature Kalman Filters—suffer from overconfident state estimates, underestimated covariances, and degraded accuracy due to nonlinear measurement functions. This paper identifies, for the first time, the intrinsic bias in covariance propagation underlying these deficiencies and proposes a general, plug-and-play correction framework. Grounded in Bayesian estimation reformulation and explicit covariance propagation calibration, the framework is compatible with mainstream nonlinear Kalman filter variants. Theoretical analysis and extensive experiments across five canonical tasks demonstrate that the method reduces state estimation error by one to three orders of magnitude—particularly under low measurement noise—while significantly improving covariance fidelity and effectively mitigating overconfidence.

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 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 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.

Traditional Kalman filtering is constrained by linear Gaussian assumptions, leading to suboptimal performance in nonlinear sensing scenarios such as Doppler radar and LiDAR, where mere parameter tuning cannot overcome inherent structural limitations. This work proposes the Kalman Evolve framework, which for the first time introduces algorithmic structure discovery into state estimation by jointly optimizing noise parameters and update structures. Leveraging large language models as structured priors over program space, the method employs program synthesis to generate interpretable, non-affine filtering algorithms that retain recursive form while adapting effectively to nonlinear dynamics. Experiments across diverse real-world and synthetic tracking tasks demonstrate up to a 12% reduction in root mean square error (RMSE), significantly outperforming strong existing baselines.

This work addresses the challenge of balancing estimation accuracy and computational cost in robotic state estimation by proposing a Smart Scheduling Hybrid (SSH) framework. The approach integrates an Extended Kalman Filter (EKF) for state propagation with periodic invocations of a fixed-structure batch optimization module. Crucially, the scheduling of optimization updates is explicitly modeled as an independent design variable, revealing its pivotal role in governing the trade-off between accuracy and computational expense. Validation on planar SLAM simulations demonstrates that well-designed scheduling strategies can substantially reduce runtime while effectively mitigating pre-optimization drift and transient errors. This enables the system to retain most of the benefits of global optimization at a significantly lower computational cost.