physics-informed state estimation

To address the challenges of unmeasurable states, imprecise models, and absence of ground-truth labels in nonlinear systems, this paper proposes a physics-informed adaptive sliding-mode neural observer. The method integrates neural networks with adaptive sliding-mode control, where a neural network dynamically learns time-varying gain matrices—eliminating requirements for system linearization, differentiability assumptions, or exact modeling. Crucially, it introduces the first end-to-end training framework that enforces physical equations as hard constraints without access to true state labels. The resulting architecture exhibits enhanced robustness against severe measurement noise, nonsmooth dynamics, and weak observability. Simulation results demonstrate rapid convergence and high-accuracy state estimation, validating its effectiveness and generalizability under complex operating conditions.

This paper addresses the challenge of state estimation for nonlinear dynamical systems under partial observability and measurement noise. We propose a physics-informed neural network (PINN)-based adaptive observer framework that tightly integrates prior system dynamics with real-time sensor measurements—without requiring linearization or coordinate transformations—and achieves state reconstruction via joint optimization. Crucially, we embed the PINN directly into the observer architecture to adaptively learn time-varying gain matrices, and rigorously prove uniform ultimate boundedness (UUB) of the state estimation error. Evaluations on diverse nonlinear systems—including induction motors and satellite attitude dynamics—demonstrate that the proposed method significantly outperforms conventional approaches such as the extended Kalman filter (EKF) and unscented Kalman filter (UKF) in estimation accuracy, noise robustness, and adaptability to system variations.

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 paper addresses nonlinear state estimation under unknown dynamic and observation models. We propose Neural Kalman Maximum Likelihood Estimation (NK-MLE), a supervised learning framework that jointly learns neural-network-parameterized nonlinear dynamics and observation functions alongside Gaussian noise covariance matrices. Our key innovation is a coordinate ascent optimization strategy that alternately updates neural network parameters and noise parameters, enabling end-to-end differentiability within a Kalman filtering pipeline. Upon training, the learned model can be seamlessly integrated into standard extended or unscented Kalman filters as a drop-in replacement. Experiments across multiple nonlinear dynamical systems demonstrate that NK-MLE significantly improves estimation accuracy and robustness—particularly under model mismatch and uncertain noise statistics—outperforming conventional approaches in both nominal and challenging regimes.

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 the challenge of online state estimation for complex nonlinear dynamical systems under model-form uncertainty and sparse sensor observations. The authors propose PiGGO, a novel framework that integrates physics-informed Graph Neural Ordinary Differential Equations (GNODEs) into an extended Kalman filter, thereby unifying continuous-time dynamics modeling, graph-structured representation, and physical inductive biases within a Bayesian filtering paradigm. PiGGO enables uncertainty-aware virtual sensing and demonstrates structural awareness of unknown nonlinear dynamics along with strong generalization across varying system topologies. Experimental results show that PiGGO significantly outperforms open-loop graph neural models and conventional filtering approaches, achieving superior robustness and estimation accuracy under model mismatch and measurement noise.

This work addresses the absence of computable state estimation error bounds in learning-based Kazantzis–Kravaris/Luenberger (KKL) observers by proposing a physics-informed neural network (PINN) approach that jointly learns the KKL transformation and its left inverse mapping. For the first time, an explicit error bound is derived that depends solely on verifiable quantities associated with the trained neural networks. This bound applies to nonlinear systems subject to bounded additive measurement noise and enables formal performance guarantees for the observer over a specified region of operation. Experimental evaluations on multiple nonlinear benchmark systems demonstrate that the derived error bound is both tight and effective, significantly enhancing the reliability and certifiability of state estimates in noisy settings.

This study addresses the challenge of achieving efficient and accurate state estimation in nonlinear dynamic systems under unknown system dynamics and noise models. To this end, it presents the first systematic comparison of model-free deep learning approaches—including Transformers, state space models (SSMs), and recurrent neural networks—against classical filtering methods such as particle filters and extended/unscented Kalman filters. Experimental results demonstrate that state space neural networks, without requiring any explicit system model, attain estimation accuracy approaching that of strong nonlinear Kalman filters while significantly outperforming weaker baselines. Moreover, these neural architectures achieve substantially higher inference throughput, thereby offering a compelling balance between accuracy and computational efficiency.

This work addresses the challenge of simultaneously estimating states and learning dynamics for soft robots under noisy measurements. The authors propose an online learning framework that integrates marginalized particle filtering with Gaussian process regression. Leveraging a constant-curvature kinematic model and base reaction force observations, the method jointly performs pose estimation and nonparametric online identification of bending stiffness, eliminating the conventional random-walk assumption and thereby significantly enhancing model generalization. Experimental validation on a physical soft robotic platform demonstrates high-accuracy pose estimation and a substantial reduction in multi-step-ahead prediction errors, confirming the effectiveness and superiority of the learned dynamics model.

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.