state estimation

Accurate estimation of latent object states and motion dynamics from image observations remains challenging due to occlusions, clutter, and nonlinear observation processes. Method: This paper proposes an end-to-end joint learning framework that simultaneously performs latent-state filtering and identifies linear dynamical equations directly from raw images—marking the first such approach. It integrates deep generative modeling, variational Bayesian inference, and latent-space linear system identification within a fully differentiable architecture, circumventing error propagation inherent in conventional staged modeling. Contribution/Results: The framework unifies nonlinear observation mapping, latent-state dynamics modeling, and linear dynamical structure discovery, balancing estimation accuracy with model interpretability. Evaluated on simulated visual dynamical environments, it reduces filtering error by 32% compared to baseline methods; the identified dynamical parameters retain clear physical meaning. Consequently, the method significantly enhances both robustness and interpretability of state estimation under complex, realistic visual observations.

This work addresses the limitations of existing conformal prediction methods, which struggle to distinguish regions in the state-action space with varying degrees of model mismatch and rely heavily on environment-specific data, hindering generalization to unseen test scenarios. The paper proposes OCULAR, the first algorithm to integrate semantic visual perception with conformal prediction for locally calibrating linear Gaussian dynamics models at arbitrary precision. Without requiring strong distributional assumptions, OCULAR provides non-asymptotic, distribution-free probabilistic coverage guarantees for future states. By leveraging visually similar environmental data, it adaptively quantifies uncertainty levels across different inputs, enabling probabilistic safety-aware planning. Experiments on a double integrator system demonstrate that OCULAR accurately captures uncertainty both in-distribution and out-of-distribution, achieving significantly higher volumetric efficiency in prediction regions compared to baseline methods that depend on environment-specific data.

Real-world sensor data in autonomous driving and healthcare monitoring often exhibit unknown or partially known noise statistics, alongside outliers, biases, drifts, and missing observations—challenging conventional Bayesian filtering. Method: This paper proposes a novel robust nonlinear Bayesian filtering framework that unifies variational inference and particle filtering within a robust Bayesian paradigm. It introduces an anomaly-aware smoothing extension mechanism and establishes a computable Bayesian Cramér–Rao bound (BCRB) for theoretical performance analysis. Furthermore, it extends robustness beyond traditional filtering to learning and generative modeling—e.g., robust diffusion models. Contribution/Results: Evaluated on target tracking, indoor localization, 3D point-cloud registration, and pose-graph optimization, the framework significantly improves estimation accuracy and anomaly tolerance. It provides both theoretical foundations and practical tools for high-reliability intelligent decision-making under complex, real-world sensing uncertainties.

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.

Safety certification for unknown polynomial dynamical systems with latent states, where only input-output data—not full state measurements—are available. Method: We propose a data-driven barrier certificate synthesis framework that jointly integrates Bayesian state-space modeling with sum-of-squares (SOS) optimization. Latent-state uncertainty is quantified via marginal Metropolis–Hastings sampling; a parameterized barrier function is constructed using SOS programming; and statistical safety verification is performed on finite data samples to guarantee safety of the true system with high probability. Contribution/Results: This is the first approach to synthesize provably safe barrier certificates without requiring full-state measurements. It provides rigorous probabilistic safety guarantees under model uncertainty, bridging Bayesian learning and formal verification. Numerical experiments demonstrate both efficacy and reliability of the method in synthesizing high-confidence safety certificates from purely input-output data.

Existing Kalman filters struggle to simultaneously achieve robustness against outliers and adaptability to time-varying process/observation noise. Method: This paper proposes a robust adaptive Kalman filtering framework integrating Student’s t-loss and variational Bayesian inference. It establishes—novelly—that “robustness is a prerequisite for adaptability,” and introduces a switchable fusion mechanism to jointly model temporal variations in process/observation noise and outlier contamination. The framework unifies classical, robust, and adaptive KF variants within a single architecture. Robustness is induced via the heavy-tailed t-distribution; noise hyperparameters are estimated via variational inference; and estimation is refined through fixed-point iteration. Results: The method significantly improves estimation accuracy and stability across diverse complex noise scenarios—including non-Gaussian, heavy-tailed, and mixed-noise settings. Simulations demonstrate superior performance over state-of-the-art robust and adaptive KF methods in both robustness and adaptability.

Inaccurate calibration of sensor noise covariances severely degrades the robustness of state estimation in multi-sensor fusion. Method: This paper proposes a novel bi-level collaborative optimization framework. It innovatively decomposes the Bayesian joint likelihood into a chain structure, decoupling the nested dependency between odometry and supervisory measurements to enable parallel optimization of trajectory estimation (lower level) and noise covariance adaptation (upper level). The lower level employs an augmented-state invariant extended Kalman filter; the upper level leverages a derivative filter to efficiently compute analytical gradients for iterative covariance refinement. Results: Extensive experiments on both synthetic and real-world datasets demonstrate significant improvements in covariance estimation accuracy and convergence speed, while maintaining favorable computational scalability. The method provides a robust, efficient, and adaptive solution for heterogeneous sensor fusion, particularly under uncertain or time-varying noise statistics.

This work addresses the core challenge in reinforcement learning of accurately estimating environmental states from high-dimensional, multimodal, and noisy observations. It proposes a geometric representation of uncertainty that obviates the need for explicit noise modeling or prior assumptions about noise distributions. By constructing a structured latent space where distances between states correspond to the minimum number of actions required to transition between them, the method embeds state-transition dynamics directly into the metric geometry of the space. A multimodal latent transition model, coupled with an inverse-distance-weighted sensor fusion mechanism, enables adaptive integration of heterogeneous perceptual inputs. Empirical results demonstrate that this approach significantly improves state estimation accuracy and agent decision-making performance across diverse multimodal reinforcement learning tasks, while exhibiting enhanced robustness to observation noise.

This paper addresses the problem of selecting appropriate belief state approximations for sample-based planning and calibration in latent-state simulators accessible only via sampling. Methodologically, it reformulates belief selection as a conditional distribution selection problem, uncovering a fundamental theoretical distinction between observation and latent-state spaces regarding identifiability and learnability. It precisely characterizes the applicability boundaries of single-reset versus repeated-reset strategies and proposes a theoretically grounded distribution selection algorithm that explicitly accounts for distribution shift and coupling with rollout policies. Contributions include: (i) a rigorous analysis of how distribution selection affects rollout performance; (ii) identification of a sharp success/failure dichotomy between two conditional distribution selection paradigms under different reset mechanisms; and (iii) novel principled criteria for trustworthy planning in latent-state simulators. The results establish formal guarantees on approximation quality and planning reliability under sampling constraints.

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.