information-aided calibration

This work proposes a novel experimental design framework for dynamic systems that addresses two key limitations of existing approaches: the neglect of process noise and the reliance on unknown true parameters for computing the Fisher information matrix (FIM). By integrating Bayesian averaging with an adaptive updating mechanism, the method jointly accounts for both process and measurement noise through Kalman filtering. The FIM is computed via Bayesian averaging over the parameter prior and is continuously updated in real time as new data become available, thereby optimizing subsequent experimental inputs. This approach achieves, for the first time, robust and real-time experimental design in linear dynamic systems with process noise without requiring knowledge of the true system parameters, significantly enhancing both the information efficiency and robustness of system identification.

This work addresses the critical challenge of jointly designing sensor query rates and noise covariance under resource and cost constraints to meet prescribed trajectory estimation accuracy requirements. It presents the first formalization of this problem as a unified optimization model, leveraging semidefinite programming (SDP) within the Kalman filter error covariance framework to simultaneously optimize measurement scheduling and noise parameters. The proposed approach efficiently determines whether a given accuracy target is achievable and, when feasible, synthesizes a corresponding implementation strategy. Experimental validation demonstrates that the computed sensor configurations consistently attain the desired accuracy in both simulated and real-world scenarios, while also reliably identifying infeasible accuracy demands.

This work proposes a data-driven state estimation algorithm that integrates the extended Kalman filter (EKF) with Koopman operator theory to address the challenge of modeling complex or poorly calibrated sensors. By lifting nonlinear observations into a linearly observable Koopman space, the method enables closed-form learning of a linear Gaussian observation model directly from ground-truth data—without requiring an explicit sensor model or iterative optimization. Crucially, Jacobian matrices are computed online to preserve the recursive structure and real-time performance of the EKF. Evaluated on a real-world quadrotor localization task, the approach substantially outperforms conventional EKF implementations reliant on imperfect geometric models and data-driven calibration baselines, achieving significant improvements in estimation accuracy, consistency, and computational efficiency.

Legged robots suffer from sensitivity of state estimation to noise covariances and kinematic parameters in dynamic environments, necessitating labor-intensive manual tuning. To address this, we propose a bi-level differentiable optimization framework: the upper level jointly optimizes process/measurement noise covariances and kinematic model parameters, while the lower level executes a full-information closed-loop estimator; gradients are backpropagated through the estimator via the implicit function theorem to enable end-to-end minimization of trajectory-level estimation error. This work is the first to unify noise statistics calibration and kinematic modeling within a differentiable estimation pipeline, ensuring cross-platform generalizability. Experimental validation on quadrupedal and humanoid robots demonstrates significant improvements in state estimation accuracy and uncertainty calibration consistency over manually tuned baselines.

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 large-scale spatiotemporal systems with unknown or missing sensor models by proposing an inverse sensing architecture that synthesizes measurement likelihoods under prescribed accuracy constraints. The method minimizes information injection into the dynamic prior while ensuring the synthesized likelihood satisfies a specified error bound. Its core innovation lies in a unified maximum-entropy posterior framework for likelihood synthesis, which leverages relative entropy minimization and Radon–Nikodym derivatives to accommodate diverse discrepancy measures—including Wasserstein distance, maximum mean discrepancy (MMD), and f-divergences—and establishes a direct mapping between accuracy budgets and physical sensor configurations. Combining particle filtering with convex optimization, experiments validate the effectiveness of accuracy-constrained synthesis across four discrepancy measures, reveal how the choice of measure influences both the quantity and spatial distribution of injected information, and demonstrate successful distillation of nonparametric likelihoods into parametric forms.

This study addresses the challenge of calibrating Doppler Velocity Logs (DVLs) in GNSS-denied underwater environments, where conventional GNSS-dependent calibration methods fail, leading to degraded navigation accuracy. To overcome this limitation, the authors propose an information-augmented extended Kalman filter framework that integrates external aiding sources to jointly estimate the DVL scale factor and mounting misalignment. This approach enables, for the first time, autonomous DVL self-calibration without GNSS, while further enhancing calibration accuracy when GNSS is available. Experimental validation on real-world autonomous underwater vehicle (AUV) datasets demonstrates an average 20% improvement in calibration accuracy under GNSS coverage and up to a 35% gain in velocity vector estimation precision in GNSS-denied conditions, significantly improving the robustness and reliability of underwater navigation systems.

Traditional Kalman filtering is constrained by linear Gaussian assumptions, leading to suboptimal performance in nonlinear sensing scenarios such as Doppler radar and LiDAR, where mere parameter tuning cannot overcome inherent structural limitations. This work proposes the Kalman Evolve framework, which for the first time introduces algorithmic structure discovery into state estimation by jointly optimizing noise parameters and update structures. Leveraging large language models as structured priors over program space, the method employs program synthesis to generate interpretable, non-affine filtering algorithms that retain recursive form while adapting effectively to nonlinear dynamics. Experiments across diverse real-world and synthetic tracking tasks demonstrate up to a 12% reduction in root mean square error (RMSE), significantly outperforming strong existing baselines.