State estimation in stochastic dynamical systems with noisy measurements is a challenge. While the Kalman filter is optimal for linear systems with independent Gaussian white noise, real-world conditions often deviate from these assumptions, prompting the rise of data-driven filtering techniques. This paper introduces Recursive KalmanNet, a Kalman-filter-informed recurrent neural network designed for accurate state estimation with consistent error covariance quantification. Our approach propagates error covariance using the recursive Joseph's formula and optimizes the Gaussian negative log-likelihood. Experiments with non-Gaussian measurement white noise demonstrate that our model outperforms both the conventional Kalman filter and an existing state-of-the-art deep learning based estimator.
Knowledge tracing (KT) aims to predict learners' future performance based on historical learning interactions. However, existing KT models predominantly focus on data from a single course, limiting their ability to capture a comprehensive understanding of learners' knowledge states. In this paper, we propose TransKT, a contrastive cross-course knowledge tracing method that leverages concept graph guided knowledge transfer to model the relationships between learning behaviors across different courses, thereby enhancing knowledge state estimation. Specifically, TransKT constructs a cross-course concept graph by leveraging zero-shot Large Language Model (LLM) prompts to establish implicit links between related concepts across different courses. This graph serves as the foundation for knowledge transfer, enabling the model to integrate and enhance the semantic features of learners' interactions across courses. Furthermore, TransKT includes an LLM-to-LM pipeline for incorporating summarized semantic features, which significantly improves the performance of Graph Convolutional Networks (GCNs) used for knowledge transfer. Additionally, TransKT employs a contrastive objective that aligns single-course and cross-course knowledge states, thereby refining the model's ability to provide a more robust and accurate representation of learners' overall knowledge states.
Spatiotemporal reasoning plays a key role in Cyber-Physical Systems (CPS). Despite advances in Large Language Models (LLMs) and Large Reasoning Models (LRMs), their capacity to reason about complex spatiotemporal signals remains underexplored. This paper proposes a hierarchical SpatioTemporal reAsoning benchmaRK, STARK, to systematically evaluate LLMs across three levels of reasoning complexity: state estimation (e.g., predicting field variables, localizing and tracking events in space and time), spatiotemporal reasoning over states (e.g., inferring spatial-temporal relationships), and world-knowledge-aware reasoning that integrates contextual and domain knowledge (e.g., intent prediction, landmark-aware navigation). We curate 26 distinct spatiotemporal tasks with diverse sensor modalities, comprising 14,552 challenges where models answer directly or by Python Code Interpreter. Evaluating 3 LRMs and 8 LLMs, we find LLMs achieve limited success in tasks requiring geometric reasoning (e.g., multilateration or triangulation), particularly as complexity increases. Surprisingly, LRMs show robust performance across tasks with various levels of difficulty, often competing or surpassing traditional first-principle-based methods. Our results show that in reasoning tasks requiring world knowledge, the performance gap between LLMs and LRMs narrows, with some LLMs even surpassing LRMs. However, the LRM o3 model continues to achieve leading performance across all evaluated tasks, a result attributed primarily to the larger size of the reasoning models. STARK motivates future innovations in model architectures and reasoning paradigms for intelligent CPS by providing a structured framework to identify limitations in the spatiotemporal reasoning of LLMs and LRMs.
Sparse wearable inertial measurement units (IMUs) have gained popularity for estimating 3D human motion. However, challenges such as pose ambiguity, data drift, and limited adaptability to diverse bodies persist. To address these issues, we propose UMotion, an uncertainty-driven, online fusing-all state estimation framework for 3D human shape and pose estimation, supported by six integrated, body-worn ultra-wideband (UWB) distance sensors with IMUs. UWB sensors measure inter-node distances to infer spatial relationships, aiding in resolving pose ambiguities and body shape variations when combined with anthropometric data. Unfortunately, IMUs are prone to drift, and UWB sensors are affected by body occlusions. Consequently, we develop a tightly coupled Unscented Kalman Filter (UKF) framework that fuses uncertainties from sensor data and estimated human motion based on individual body shape. The UKF iteratively refines IMU and UWB measurements by aligning them with uncertain human motion constraints in real-time, producing optimal estimates for each. Experiments on both synthetic and real-world datasets demonstrate the effectiveness of UMotion in stabilizing sensor data and the improvement over state of the art in pose accuracy.
This paper presents a secure safety filter design for nonlinear systems under sensor spoofing attacks. Existing approaches primarily focus on linear systems which limits their applications in real-world scenarios. In this work, we extend these results to nonlinear systems in a principled way. We introduce exact observability maps that abstract specific state estimation algorithms and extend them to a secure version capable of handling sensor attacks. Our generalization also applies to the relaxed observability case, with slightly relaxed guarantees. More importantly, we propose a secure safety filter design in both exact and relaxed cases, which incorporates secure state estimation and a control barrier function-enabled safety filter. The proposed approach provides theoretical safety guarantees for nonlinear systems in the presence of sensor attacks. We numerically validate our analysis on a unicycle vehicle equipped with redundant yet partly compromised sensors.
This paper presents a visual-inertial odometry (VIO) method using long-tracked features. Long-tracked features can constrain more visual frames, reducing localization drift. However, they may also lead to accumulated matching errors and drift in feature tracking. Current VIO methods adjust observation weights based on re-projection errors, yet this approach has flaws. Re-projection errors depend on estimated camera poses and map points, so increased errors might come from estimation inaccuracies, not actual feature tracking errors. This can mislead the optimization process and make long-tracked features ineffective for suppressing localization drift. Furthermore, long-tracked features constrain a larger number of frames, which poses a significant challenge to real-time performance of the system. To tackle these issues, we propose an active decoupling mechanism for accumulated errors in long-tracked feature utilization. We introduce a visual reference frame reset strategy to eliminate accumulated tracking errors and a depth prediction strategy to leverage the long-term constraint. To ensure real time preformane, we implement three strategies for efficient system state estimation: a parallel elimination strategy based on predefined elimination order, an inverse-depth elimination simplification strategy, and an elimination skipping strategy. Experiments on various datasets show that our method offers higher positioning accuracy with relatively short consumption time, making it more suitable for edge-enabled low-altitude IoT navigation, where high-accuracy positioning and real-time operation on edge device are required. The code will be published at github.
Recently, learning-based robotic navigation systems have gained extensive research attention and made significant progress. However, the diversity of open-world scenarios poses a major challenge for the generalization of such systems to practical scenarios. Specifically, learned systems for scene measurement and state estimation tend to degrade when the application scenarios deviate from the training data, resulting to unreliable depth and pose estimation. Toward addressing this problem, this work aims to develop a visual odometry system that can fast adapt to diverse novel environments in an online manner. To this end, we construct a self-supervised online adaptation framework for monocular visual odometry aided by an online-updated depth estimation module. Firstly, we design a monocular depth estimation network with lightweight refiner modules, which enables efficient online adaptation. Then, we construct an objective for self-supervised learning of the depth estimation module based on the output of the visual odometry system and the contextual semantic information of the scene. Specifically, a sparse depth densification module and a dynamic consistency enhancement module are proposed to leverage camera poses and contextual semantics to generate pseudo-depths and valid masks for the online adaptation. Finally, we demonstrate the robustness and generalization capability of the proposed method in comparison with state-of-the-art learning-based approaches on urban, in-house datasets and a robot platform. Code is publicly available at: https://github.com/jixingwu/SOL-SLAM.
The constrained zonotope is a polytopic set representation widely used for set-based analysis and control of dynamic systems. This paper considers the problem of tailoring a quadratic program (QP) optimization algorithm to the particular structure of constrained zonotopes and vice-versa. An alternating direction method of multipliers (ADMM) algorithm is presented that makes efficient use of the constrained zonotope structure. To increase the efficiency of the ADMM iterations, reachability calculations are presented that increase the sparsity of the matrices used to define a constrained zonotope. Numerical results show that the ADMM algorithm solves optimal control problems built using these reachability calculations faster than state-of-the-art QP solvers using conventional problem formulations, especially for large problems. Constrained zonotope reachability and optimization calculations are combined within a set-valued state estimation and moving horizon estimation algorithm, and a projection-based infeasibility detection method is presented for efficient safety verification of system trajectories.
We provide an open-access dataset of phasor & waveform measurement units (PMUs/WMUs) of a real-world electrical distribution network. The network consists of diverse sets of generation resources (including solar panels, fuel cells, natural gas generators, and utility interconnections), loads (including large-scale electric vehicle charging, data centers, central cooling, offices), topology changes (such as line outages and load transfers), as well as a mixture of single- and three-phase networks. We describe a densely deployed PMU sensor network in a distribution grid, in which all buses with non-zero power injections are measured. This approach enables a range of applications such as state estimation, system identification, power flow optimization, and feedback control, several of which are discussed in this paper. Additionally, we provide a synchronized waveform dataset which allows the analysis of harmonics, transient events, dynamic grid impedance, and stability. Data collection started in 2023 while new data is generated continuously and made available online. A characterization of measurement error is provided. Finally, we provide circuit topology and parameters as a part of the dataset. Together, the circuit and timeseries data offer an opportunity for researchers to develop and test algorithms on a real-world system.
Lithium-ion batteries are widely used in transportation, energy storage, and consumer electronics, driving the need for reliable battery management systems (BMS) for state estimation and control. The Single Particle Model (SPM) balances computational efficiency and accuracy but faces challenges in parameter estimation due to numerous parameters. Current SPM models using parabolic approximation introduce intermediate variables and hard to do parameter grouping. This study presents a control-oriented SPM reformulation that employs parameter grouping and parabolic approximation to simplify model parameters while using average and surface lithium-ion concentrations as model output. By parameter grouping, the original 17 parameters were reduced to 9 grouped parameters. The reformulated model achieves a reduced-order ordinary differential equation form while maintaining mathematical accuracy equivalent to the pre-grouped discretized SPM. Through Sobol sensitivity analysis under various current profiles, the grouped parameters were reduced from 9 to 6 highly sensitive parameters. Results demonstrate that estimating these 6 parameters achieves comparable practical accuracy to estimating all 9 parameters, with faster convergence. This control-oriented SPM enhances BMS applications by facilitating state estimation and control while reducing parameter estimation requirements.
Seamless operation of mobile robots in challenging environments requires low-latency local motion estimation (e.g., dynamic maneuvers) and accurate global localization (e.g., wayfinding). While most existing sensor-fusion approaches are designed for specific scenarios, this work introduces a flexible open-source solution for task- and setup-agnostic multimodal sensor fusion that is distinguished by its generality and usability. Holistic Fusion formulates sensor fusion as a combined estimation problem of i) the local and global robot state and ii) a (theoretically unlimited) number of dynamic context variables, including automatic alignment of reference frames; this formulation fits countless real-world applications without any conceptual modifications. The proposed factor-graph solution enables the direct fusion of an arbitrary number of absolute, local, and landmark measurements expressed with respect to different reference frames by explicitly including them as states in the optimization and modeling their evolution as random walks. Moreover, local smoothness and consistency receive particular attention to prevent jumps in the robot state belief. HF enables low-latency and smooth online state estimation on typical robot hardware while simultaneously providing low-drift global localization at the IMU measurement rate. The efficacy of this released framework is demonstrated in five real-world scenarios on three robotic platforms, each with distinct task requirements.
This paper introduces ZETA, a new MATLAB library for Zonotope-based EsTimation and fAult diagnosis of discrete-time systems. It features user-friendly implementations of set representations based on zonotopes, namely zonotopes, constrained zonotopes, and line zonotopes, in addition to a basic implementation of interval arithmetic. This library has capabilities starting from the basic set operations with these sets, including propagations through nonlinear functions using various approximation methods. The features of ZETA allow for reachability analysis and state estimation of discrete-time linear, nonlinear, and descriptor systems, in addition to active fault diagnosis of linear systems. Efficient order reduction methods are also implemented for the respective set representations. Some examples are presented in order to illustrate the functionalities of the new library.
Visual-inertial odometry (VIO) is widely used for state estimation in autonomous micro aerial vehicles using onboard sensors. Current methods improve VIO by incorporating a model of the translational vehicle dynamics, yet their performance degrades when faced with low-accuracy vehicle models or continuous external disturbances, like wind. Additionally, incorporating rotational dynamics in these models is computationally intractable when they are deployed in online applications, e.g., in a closed-loop control system. We present HDVIO2.0, which models full 6-DoF, translational and rotational, vehicle dynamics and tightly incorporates them into a VIO with minimal impact on the runtime. HDVIO2.0 builds upon the previous work, HDVIO, and addresses these challenges through a hybrid dynamics model combining a point-mass vehicle model with a learning-based component, with access to control commands and IMU history, to capture complex aerodynamic effects. The key idea behind modeling the rotational dynamics is to represent them with continuous-time functions. HDVIO2.0 leverages the divergence between the actual motion and the predicted motion from the hybrid dynamics model to estimate external forces as well as the robot state. Our system surpasses the performance of state-of-the-art methods in experiments using public and new drone dynamics datasets, as well as real-world flights in winds up to 25 km/h. Unlike existing approaches, we also show that accurate vehicle dynamics predictions are achievable without precise knowledge of the full vehicle state.
State estimation in the presence of uncertain or data-driven noise distributions remains a critical challenge in control and robotics. Although the Kalman filter is the most popular choice, its performance degrades significantly when distributional mismatches occur, potentially leading to instability or divergence. To address this limitation, we introduce a novel steady-state distributionally robust (DR) Kalman filter that leverages Wasserstein ambiguity sets to explicitly account for uncertainties in both process and measurement noise distributions. Our filter achieves computational efficiency by requiring merely the offline solution of a single convex semidefinite program, which yields a constant DR Kalman gain for robust state estimation under distributional mismatches. Additionally, we derive explicit theoretical conditions on the ambiguity set radius that ensure the asymptotic convergence of the time-varying DR Kalman filter to the proposed steady-state solution. Numerical simulations demonstrate that our approach outperforms existing baseline filters in terms of robustness and accuracy across both Gaussian and non-Gaussian uncertainty scenarios, highlighting its significant potential for real-world control and estimation applications.
Event cameras asynchronously output low-latency event streams, promising for state estimation in high-speed motion and challenging lighting conditions. As opposed to frame-based cameras, the motion-dependent nature of event cameras presents persistent challenges in achieving robust event feature detection and matching. In recent years, learning-based approaches have demonstrated superior robustness over traditional handcrafted methods in feature detection and matching, particularly under aggressive motion and HDR scenarios. In this paper, we propose SuperEIO, a novel framework that leverages the learning-based event-only detection and IMU measurements to achieve event-inertial odometry. Our event-only feature detection employs a convolutional neural network under continuous event streams. Moreover, our system adopts the graph neural network to achieve event descriptor matching for loop closure. The proposed system utilizes TensorRT to accelerate the inference speed of deep networks, which ensures low-latency processing and robust real-time operation on resource-limited platforms. Besides, we evaluate our method extensively on multiple public datasets, demonstrating its superior accuracy and robustness compared to other state-of-the-art event-based methods. We have also open-sourced our pipeline to facilitate research in the field: https://github.com/arclab-hku/SuperEIO.
Linear quadratic Gaussian (LQG) control is a well-established method for optimal control through state estimation, particularly in stabilizing an inverted pendulum on a cart. In standard laboratory setups, sensor redundancy enables direct measurement of configuration variables using displacement sensors and rotary encoders. However, in outdoor environments, dynamically stable mobile platforms-such as Segways, hoverboards, and bipedal robots-often have limited sensor availability, restricting state estimation primarily to attitude stabilization. Since the tilt angle cannot be directly measured, it is typically estimated through sensor fusion, increasing reliance on inertial sensors and necessitating a lightweight, self-contained perception module. Prior research has not incorporated accelerometer data into the LQG framework for stabilizing pendulum-like systems, as jerk states are not explicitly modeled in the Newton-Euler formalism. In this paper, we address this gap by leveraging local differential flatness to incorporate higher-order dynamics into the system model. This refinement enhances state estimation, enabling a more robust LQG controller that predicts accelerations for dynamically stable mobile platforms.
Network-wide Traffic State Estimation (TSE), which aims to infer a complete image of network traffic states with sparsely deployed sensors, plays a vital role in intelligent transportation systems. With the development of data-driven methods, traffic dynamics modeling has advanced significantly. However, TSE poses fundamental challenges for data-driven approaches, since historical patterns cannot be learned locally at sensor-free segments. Although inductive graph learning shows promise in estimating states at locations without sensor, existing methods typically handle unobserved locations by filling them with zeros, introducing bias to the sensitive graph message propagation. The recently proposed Dirichlet Energy-based Feature Propagation (DEFP) method achieves State-Of-The-Art (SOTA) performance in unobserved node classification by eliminating the need for zero-filling. However, applying it to TSE faces three key challenges: inability to handle directed traffic networks, strong assumptions in traffic spatial correlation modeling, and overlooks distinct propagation rules of different patterns (e.g., congestion and free flow). We propose DGAE, a novel inductive graph representation model that addresses these challenges through theoretically derived DEFP for Directed graph (DEFP4D), enhanced spatial representation learning via DEFP4D-guided latent space encoding, and physics-guided propagation mechanisms that separately handles congested and free-flow patterns. Experiments on three traffic datasets demonstrate that DGAE outperforms existing SOTA methods and exhibits strong cross-city transferability. Furthermore, DEFP4D can serve as a standalone lightweight solution, showing superior performance under extremely sparse sensor conditions.
This article proposes numerically robust algorithms for Gaussian state estimation with singular observation noise. Our approach combines a series of basis changes with Bayes' rule, transforming the singular estimation problem into a nonsingular one with reduced state dimension. In addition to ensuring low runtime and numerical stability, our proposal facilitates marginal-likelihood computations and Gauss-Markov representations of the posterior process. We analyse the proposed method's computational savings and numerical robustness and validate our findings in a series of simulations.
The Shallow Recurrent Decoder networks are a novel paradigm recently introduced for state estimation, combining sparse observations with high-dimensional model data. This architecture features important advantages compared to standard data-driven methods including: the ability to use only three sensors (even randomly selected) for reconstructing the entire dynamics of a physical system; the ability to train on compressed data spanned by a reduced basis; the ability to measure a single field variable (easy to measure) and reconstruct coupled spatio-temporal fields that are not observable and minimal hyper-parameter tuning. This approach has been verified on different test cases within different fields including nuclear reactors, even though an application to a real experimental facility, adopting the employment of in-situ observed quantities, is missing. This work aims to fill this gap by applying the Shallow Recurrent Decoder architecture to the DYNASTY facility, built at Politecnico di Milano, which studies the natural circulation established by internally heated fluids for Generation IV applications, especially in the case of Circulating Fuel reactors. The RELAP5 code is used to generate the high-fidelity data, and temperature measurements extracted by the facility are used as input for the state estimation. The results of this work will provide a validation of the Shallow Recurrent Decoder architecture to engineering systems, showing the capabilities of this approach to provide and accurate state estimation.
The recent developments in data-driven methods have paved the way to new methodologies to provide accurate state reconstruction of engineering systems; nuclear reactors represent particularly challenging applications for this task due to the complexity of the strongly coupled physics involved and the extremely harsh and hostile environments, especially for new technologies such as Generation-IV reactors. Data-driven techniques can combine different sources of information, including computational proxy models and local noisy measurements on the system, to robustly estimate the state. This work leverages the novel Shallow Recurrent Decoder architecture to infer the entire state vector (including neutron fluxes, precursors concentrations, temperature, pressure and velocity) of a reactor from three out-of-core time-series neutron flux measurements alone. In particular, this work extends the standard architecture to treat parametric time-series data, ensuring the possibility of investigating different accidental scenarios and showing the capabilities of this approach to provide an accurate state estimation in various operating conditions. This paper considers as a test case the Molten Salt Fast Reactor (MSFR), a Generation-IV reactor concept, characterised by strong coupling between the neutronics and the thermal hydraulics due to the liquid nature of the fuel. The promising results of this work are further strengthened by the possibility of quantifying the uncertainty associated with the state estimation, due to the considerably low training cost. The accurate reconstruction of every characteristic field in real-time makes this approach suitable for monitoring and control purposes in the framework of a reactor digital twin.