bayesian filtering

This work addresses inference failure in Bayesian filtering caused by misspecification of the state-space model (SSM) transition kernel. We propose a robust filtering framework based on nudging, treating it as a data-driven, implicit model correction mechanism that adaptively constructs an equivalent SSM with higher marginal likelihood via optimization of the observation marginal likelihood. Theoretically, we provide the first rigorous guarantee for nudging from a marginal likelihood perspective, proving that it implicitly mitigates dynamical misspecification and enhances filtering robustness. Experiments on both linear Gaussian SSMs and the stochastic Lorenz-63 nonlinear system demonstrate that our method significantly improves estimation accuracy and numerical stability over standard filters. These results validate nudging as a general-purpose, self-calibrating strategy for model correction in sequential inference.

This work addresses the challenge of inaccurate state estimation in cyber-physical systems caused by false data injection attacks. The authors propose a unified framework that integrates active probing with Bayesian inference to dynamically identify compromised sensors and maintain robust control. By modeling the sensing process as a bipartite graph and constructing a Bayesian network incorporating anomaly alerts, the method enables real-time inference of sensor integrity. Leveraging system nonlinearities, an active probing strategy is designed to enhance the distinguishability among competing attack hypotheses, allowing selective disabling of corrupted nodes. Notably, this approach achieves progressively improving attack identifiability and reliable state estimation even during ongoing attacks. Experimental results on an inverted pendulum system under both single- and multi-sensor attacks demonstrate significant performance gains over baseline methods based on outlier robustness and prediction, with particularly pronounced advantages in long-duration attack scenarios.

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 inefficiency, high latency, and unbounded memory consumption associated with likelihood computation in Bayesian state estimation by introducing a novel Bayesian filtering approach grounded in native processor operations. For the first time, it integrates native uncertainty tracking into Bayesian inference and combines it with deterministic stratified importance resampling, enabling online inference for arbitrary procedural dynamic models. The proposed method achieves root mean square error (RMSE) accuracy comparable to particle filters while delivering up to an 805× average speedup over Monte Carlo methods. It further guarantees deterministic latency, bounded memory usage, and attains Pareto optimality in the trade-off between accuracy and latency.

This work addresses the challenge of accurately estimating the filtering distribution (i.e., the state posterior) in high-dimensional nonlinear dynamical systems. To overcome the bias inherent in traditional ensemble Kalman filters (EnKF) under strong nonlinearity and their reliance on labor-intensive manual tuning, we propose an end-to-end learning framework grounded in variational inference. Specifically, the filter’s analysis step is modeled as a learnable, parameterized analysis mapping; key components—including gain computation, covariance inflation, and localization—are jointly optimized via a variational objective. This constitutes the first systematic integration of variational inference into filter design, enabling unified modeling and automatic calibration of the analysis process. Experiments across diverse linear and nonlinear systems demonstrate that our method significantly reduces filtering bias, improves posterior estimation accuracy, and drastically diminishes dependence on manual parameter tuning.

This work proposes a novel particle filtering framework tailored for discrete-time state-space models under severely degraded or vanishing observation noise, specifically when the observation equation is a linear function of the latent state with degenerate additive noise. The method preserves desirable filtering properties even as the noise approaches its degenerate limit and, for the first time, extends this approach to continuous-time models where the hidden state is driven by a diffusion process. By integrating state-space modeling, specialized handling of degenerate noise, and refined time-discretization analysis, the proposed algorithm demonstrates strong robustness and high accuracy in multiple numerical experiments, particularly under low-noise regimes and fine temporal resolutions.

Online Bayesian filtering for high-dimensional nonlinear dynamical systems remains challenging due to numerical instability, approximation errors, and computational intractability—especially under state constraints. Method: This paper proposes a novel constrained Bayesian filtering framework incorporating compact-state-set constraints to jointly ensure stability, accuracy, and computational feasibility. We establish, for the first time, a stability theory and explicit error bounds for constrained Bayesian filtering. A data-driven drift correction mechanism based on barrier functions is introduced, integrating the Doob *h*-transform with Itô process control, and continuous–discrete filtering is realized via constrained Markov transition kernels. Results: Evaluated on the partially observed Lorenz-96 system, the method demonstrates numerical stability and bounded estimation error in high dimensions, while exhibiting strong robustness to model mismatch and sparse observations.

This work addresses the performance degradation and miscalibrated uncertainty quantification of traditional Kalman filters under misspecified observation noise, particularly in the presence of heavy-tailed outliers. It introduces diffusion score matching into the ensemble Kalman filter framework for the first time, refining the analysis step to achieve robustness against non-Gaussian observation noise while preserving reliable uncertainty quantification. The approach is developed for linear Gaussian systems, yielding conjugate closed-form updates, and is extended through generalized Bayesian inference, stochastic–deterministic coupling, and localization to produce robust variants of EnKF, ESRF, and LETKF. Experiments on target tracking and Lorenz-63/96 systems demonstrate superior data assimilation performance under nonlinear dynamics and heavy-tailed noise, supported by theoretical guarantees of high-dimensional consistency.

This work addresses the challenge of reliably inferring latent environmental states and their associated uncertainties in reinforcement learning under partially observable or adversarially perturbed observations. It introduces, for the first time, adversarial observation perturbations that satisfy likelihood consistency constraints into linear probabilistic state-space models. By combining Bayesian inference with constrained optimization, the study analyzes how such perturbations affect latent state estimation and subsequent policy decisions. The research elucidates the propagation pathways through which observation perturbations influence both latent state beliefs and policy outputs, enabling the development of a more robust reinforcement learning framework. This approach provides a theoretical foundation and an effective design paradigm for safety-critical applications—such as robotics—to withstand sensor noise, failures, and adversarial attacks.

This work addresses the degraded performance of conventional filtering methods in joint state and parameter estimation for nonlinear systems subject to non-Gaussian, multimodal uncertainties. To this end, we propose a forward–backward estimation framework based on conditional normalizing flows. Conditional embeddings are generated using MLPs, Transformers, or Mamba-SSMs, and their efficacy is systematically evaluated for the first time in time-reversal and sequential prediction tasks. Furthermore, we introduce a kinetic-energy regularization term derived from optimal transport theory to mitigate over-parameterization and enhance training stability in deep flow models. Empirical evaluations on real-world scenarios—including autonomous driving and a COVID-19 SIR epidemiological model—demonstrate that the proposed method significantly outperforms traditional filters, achieving notably higher estimation accuracy under complex, non-Gaussian uncertainty distributions.