kalman filtering

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 paper addresses the challenging problem of state estimation in nonlinear, non-Gaussian state-space models. We propose a novel Bayesian inference method grounded in a variational Lagrangian framework. Our core innovation lies in formulating Bayesian inference as a sequential entropy-constrained optimization problem subject to dynamic constraints, leading to a family of forward–backward algorithms whose variational posterior factorization structure is explicitly derived. The method integrates Gaussian–Markov approximations, generalized statistical linear regression, and Fourier–Hermite moment-matching techniques to enable efficient recursive inference. The resulting algorithms achieve both low computational complexity—linear in the number of time steps—and high estimation accuracy. Empirical evaluation demonstrates substantial improvements in efficiency, robustness, and numerical stability for state estimation under strongly nonlinear and non-Gaussian dynamics.

This work addresses variational state estimation by establishing, for the first time, a systematic theoretical framework grounded in dynamic programming. Methodologically, it introduces recursive forward and backward value functionals, yielding a variational dual-filter formulation analogous to classical Bayesian filtering and smoothing; it further reveals that these value functionals upper-bound the logarithm of the unnormalized posterior density—providing rigorous theoretical justification for variational approximation. A linear-complexity suboptimal variational filtering algorithm is then developed, balancing computational efficiency with estimation accuracy. The approach integrates dynamic programming, variational inference, and unnormalized density approximation, and achieves tractable recursive inference in jump Markov linear Gaussian systems via factorized Markov approximations. Simulation results demonstrate high-fidelity posterior approximation, favorable computational tractability, and superior estimation quality.

To address the practical challenges of inaccurate state-space models and unknown noise characteristics, this paper proposes a novel Bayesian filtering framework based on conditional diffusion models. The method reformulates state estimation as a conditional generation task, eliminating the need for explicit measurement models or parametric noise priors; instead, it implicitly learns system dynamics from data, achieving model-agnostic inference while preserving the interpretability of classical filters. Its key contribution is the first integration of diffusion models into Bayesian filtering, enabling an end-to-end implicit prediction-update mechanism and a data-driven modeling of the state-observation mapping. Experiments demonstrate that the proposed approach significantly outperforms classical (e.g., EKF, UKF) and hybrid filtering methods under nonlinear dynamics and non-Gaussian noise conditions, and exhibits strong robustness to state-space model mismatch.

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 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 challenge of accurately estimating states in complex dynamical systems lacking explicit physical models, particularly from noisy nonlinear observations. The authors propose a model-free variational state estimation method that uniquely integrates a dual recurrent neural network (RNN) architecture with variational inference to directly learn a Gaussian approximation of the state posterior. This approach enables closed-form, efficient online inference without requiring knowledge of the underlying system dynamics. Evaluated on state tracking in a stochastic Lorenz system, the method achieves performance comparable to a particle filter with full model knowledge, despite operating entirely in a data-driven manner, and significantly outperforms existing model-free alternatives. These results demonstrate its effectiveness and robustness in highly nonlinear, non-Gaussian environments.

This work proposes a novel framework that integrates classical particle filtering with learning-based methods to address the high training cost and poor interpretability of end-to-end learning in robotic state estimation. Leveraging the Markov assumption, the approach trains a dynamics model using single-step state transitions and implicitly learns the observation model via denoising score matching, thereby approximating the Bayesian filtering equations step-by-step during inference without requiring end-to-end optimization. A key innovation lies in preserving the modular structure of the filter, which enables flexible incorporation of prior knowledge and external sensor models without retraining. Experiments demonstrate that the method achieves accuracy comparable to well-tuned end-to-end baselines in simulation while significantly reducing training complexity and exhibiting superior generalization and compositional capabilities.

This study addresses a key limitation of traditional latent-variable state-space models, which assume process noise is independent of the latent state and thus fail to capture state-dependent stochastic fluctuations commonly observed in biological and behavioral systems. To overcome this, the authors propose a state-coupled stochastic volatility framework that introduces a coupling parameter γ, allowing the variance of the latent process to dynamically scale with the deviation from an underlying latent equilibrium point. This work presents the first approach to modeling and identifying such coupling between latent states and process noise variance under partial observability. An efficient particle expectation-maximization algorithm, integrating guided particle filtering with backward trajectory smoothing, is developed for parameter estimation. Simulations demonstrate that the method substantially reduces parameter estimation bias under strong coupling and high observation noise, confirming its efficacy and robustness.

This study addresses the limitations of traditional state-space models, which rely on predefined nonlinear dynamics and struggle with theoretically under-specified complex systems, as well as the high computational cost of Bayesian inference in Gaussian process state-space models for moderately long sequences. To overcome these challenges, the authors propose two enhanced Gibbs sampling strategies that substantially improve sampling efficiency and convergence reliability. By integrating confirmatory factor analysis to construct an identifiable and interpretable measurement structure, they develop a comprehensive framework for learning nonlinear latent dynamical systems. Simulation studies validate the accuracy of posterior inference, while two empirical applications demonstrate the method’s practical utility and interpretability. An open-source implementation is provided, offering researchers an efficient and feasible workflow for empirical analysis.