joint state and parameter estimation

This work addresses the challenge of nonlinear parameter estimation in Wiener-type state-space models by proposing a fixed-point iteration-based dual estimator framework. The approach couples two affine minimum mean square error (MMSE) estimators to separately handle unknown parameters and latent states, while introducing dynamic basis statistics (DBS) to efficiently summarize information from nonlinear basis functions. The resulting dual state-parameter and dual basis-parameter estimators alternately update their prior information, enabling stable and efficient nonlinear learning. Extensive Monte Carlo experiments demonstrate that the dual state-parameter estimator significantly outperforms existing methods—including purely affine estimators, particle Gibbs, and expectation-maximization (EM) variants of sequential Monte Carlo algorithms—in terms of parameter mean square error.

Modeling nonlinear dynamical systems from limited data remains challenging due to difficulties in integrating prior knowledge—such as partially known governing equations and smoothness assumptions on unknown components—as well as the complexity of joint latent-state inference and nested function learning. Method: This paper proposes a unified Bayesian system identification framework that enables end-to-end co-modeling of explicit physical constraints and implicit Gaussian process priors, without requiring manual coordinate transformations or model inversion. It supports both online and offline latent-state estimation and joint learning of unknown dynamics, enhanced by closed-form density derivation and analytical parameter marginalization for improved robustness. Results: Evaluated on three real-world experimental case studies, the method achieves significantly higher modeling accuracy than baselines under small-sample regimes and demonstrates strong generalization capability.

This work proposes a continuous-time stochastic state-space model grounded in Lagrangian mechanics for partially observed and noisy physical systems. The approach parameterizes kinetic and potential energy using neural networks, models unknown external forces as Gaussian white noise, and uniquely integrates Bayesian filtering with Lagrangian neural networks to jointly estimate system states and dynamical parameters. By combining Gaussian approximations with maximum likelihood learning, the method significantly outperforms conventional Lagrangian neural networks in experiments on the simple pendulum and Duffing oscillator, and achieves performance approaching that of Bayesian filters with known dynamics—even when the true model is unavailable.

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 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 addresses the longstanding computational barrier that has hindered the application of non-Gaussian filtering to parameter estimation and Bayesian inference in state-space models, primarily due to the high cost of numerical integration. Leveraging modern computational capabilities, the authors embed unknown parameters into the state vector and integrate self-organizing state-space modeling with deterministic numerical integration to jointly estimate parameters and latent states. This approach overcomes the computational bottleneck of non-Gaussian filtering and yields stable, smooth log-likelihood estimates across low- to moderate-dimensional linear, nonlinear, and radar tracking models. The method demonstrably outperforms particle filters, whose performance is degraded by Monte Carlo noise, thereby affirming the practicality and superiority of non-Gaussian filtering under contemporary hardware conditions.

This study addresses the problem of jointly recovering an unknown system matrix and low-rank initial states from partially observed trajectories. We propose a local identifiability theory grounded in the rank certificate principle, establishing necessary and sufficient conditions for global recovery along with a closed-form solution. The original problem is reformulated as a nonlinear least-squares model, which is efficiently solved by integrating low-rank factorization theory with the Adam optimizer. Experimental evaluations on both synthetic and real-world datasets demonstrate that the proposed method achieves superior recovery performance across varying sampling rates.

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.

This work addresses the instability of conventional Gaussian sum filters and the high computational cost of particle filters in nonlinear or non-Gaussian state-space models by proposing an Augmented Gaussian Sum Filter (AGSF). The method introduces latent variables and tunable covariance parameters to construct a unified framework that enables continuous interpolation and adaptive switching between Gaussian approximation and particle filtering behaviors. By innovatively integrating augmented Gaussian approximation, adaptive mechanisms, and sequential Monte Carlo principles, AGSF dynamically adjusts its approximation strategy based on the local degree of nonlinearity. Experimental results demonstrate that the proposed approach achieves both efficiency and robustness in target tracking tasks, effectively avoiding failure modes of traditional methods, while toy experiments validate the efficacy of its adaptive mechanism.

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.