Accurately predicting the state of health for sodium-ion batteries is crucial for managing battery modules, playing a vital role in ensuring operational safety. However, highly accurate models available thus far are rare due to a lack of aging data for sodium-ion batteries. In this study, we experimentally collected 53 single cells at four temperatures (0, 25, 35, and 45 {\deg}C), along with two battery modules in the lab. By utilizing the charging profiles, we were able to predict the SOC, capacity, and SOH simultaneously. This was achieved by designing a new framework that integrates the neural ordinary differential equation and 2D convolutional neural networks, using the partial charging profile as input. The charging profile is partitioned into segments, and each segment is fed into the network to output the SOC. For capacity and SOH prediction, we first aggregated the extracted features corresponding to segments from one cycle, after which an embedding block for temperature is concatenated for the final prediction. This novel approach eliminates the issue of multiple outputs for a single target. Our model demonstrated an $R^2$ accuracy of 0.998 for SOC and 0.997 for SOH across single cells at various temperatures. Furthermore, the trained model can be employed to predict single cells at temperatures outside the training set and battery modules with different capacity and current levels. The results presented here highlight the high accuracy of our model and its capability to predict multiple targets simultaneously using a partial charging profile.
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.
Event-based sensors (EBS) are a promising new technology for star tracking due to their low latency and power efficiency, but prior work has thus far been evaluated exclusively in simulation with simplified signal models. We propose a novel algorithm for event-based star tracking, grounded in an analysis of the EBS circuit and an extended Kalman filter (EKF). We quantitatively evaluate our method using real night sky data, comparing its results with those from a space-ready active-pixel sensor (APS) star tracker. We demonstrate that our method is an order-of-magnitude more accurate than existing methods due to improved signal modeling and state estimation, while providing more frequent updates and greater motion tolerance than conventional APS trackers. We provide all code and the first dataset of events synchronized with APS solutions.
Gaussian process state-space models (GPSSMs) offer a principled framework for learning and inference in nonlinear dynamical systems with uncertainty quantification. However, existing GPSSMs are limited by the use of multiple independent stationary Gaussian processes (GPs), leading to prohibitive computational and parametric complexity in high-dimensional settings and restricted modeling capacity for non-stationary dynamics. To address these challenges, we propose an efficient transformed Gaussian process state-space model (ETGPSSM) for scalable and flexible modeling of high-dimensional, non-stationary dynamical systems. Specifically, our ETGPSSM integrates a single shared GP with input-dependent normalizing flows, yielding an expressive implicit process prior that captures complex, non-stationary transition dynamics while significantly reducing model complexity. For the inference of the implicit process, we develop a variational inference algorithm that jointly approximates the posterior over the underlying GP and the neural network parameters defining the normalizing flows. To avoid explicit variational parameterization of the latent states, we further incorporate the ensemble Kalman filter (EnKF) into the variational framework, enabling accurate and efficient state estimation. Extensive empirical evaluations on synthetic and real-world datasets demonstrate the superior performance of our ETGPSSM in system dynamics learning, high-dimensional state estimation, and time-series forecasting, outperforming existing GPSSMs and neural network-based SSMs in terms of computational efficiency and accuracy.
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.
Quantum computers offer a promising route to tackling problems that are classically intractable such as in prime-factorization, solving large-scale linear algebra and simulating complex quantum systems, but require fault-tolerant quantum hardware. On the other hand, variational quantum algorithms (VQAs) have the potential to provide a near-term route to quantum utility or advantage, and is usually constructed by using parametrized quantum circuits (PQCs) in combination with a classical optimizer for training. Although VQAs have been proposed for a multitude of tasks such as ground-state estimation, combinatorial optimization and unitary compilation, there remain major challenges in its trainability and resource costs on quantum hardware. Here we address these challenges by adopting Hardware Efficient and dynamical LIe algebra Supported Ansatz (HELIA), and propose two training schemes that combine an existing g-sim method (that uses the underlying group structure of the operators) and the Parameter-Shift Rule (PSR). Our improvement comes from distributing the resources required for gradient estimation and training to both classical and quantum hardware. We numerically test our proposal for ground-state estimation using Variational Quantum Eigensolver (VQE) and classification of quantum phases using quantum neural networks. Our methods show better accuracy and success of trials, and also need fewer calls to the quantum hardware on an average than using only PSR (upto 60% reduction), that runs exclusively on quantum hardware. We also numerically demonstrate the capability of HELIA in mitigating barren plateaus, paving the way for training large-scale quantum models.
Manipulating deformable objects like cloth is challenging due to their complex dynamics, near-infinite degrees of freedom, and frequent self-occlusions, which complicate state estimation and dynamics modeling. Prior work has struggled with robust cloth state estimation, while dynamics models, primarily based on Graph Neural Networks (GNNs), are limited by their locality. Inspired by recent advances in generative models, we hypothesize that these expressive models can effectively capture intricate cloth configurations and deformation patterns from data. Building on this insight, we propose a diffusion-based generative approach for both perception and dynamics modeling. Specifically, we formulate state estimation as reconstructing the full cloth state from sparse RGB-D observations conditioned on a canonical cloth mesh and dynamics modeling as predicting future states given the current state and robot actions. Leveraging a transformer-based diffusion model, our method achieves high-fidelity state reconstruction while reducing long-horizon dynamics prediction errors by an order of magnitude compared to GNN-based approaches. Integrated with model-predictive control (MPC), our framework successfully executes cloth folding on a real robotic system, demonstrating the potential of generative models for manipulation tasks with partial observability and complex dynamics.
We consider the problem of optimal control for partially observed dynamical systems. Despite its prevalence in practical applications, there are still very few algorithms available, which take uncertainties in the current state estimates and future observations into account. In other words, most current approaches separate state estimation from the optimal control problem. In this paper, we extend the popular ensemble Kalman filter to receding horizon optimal control problems in the spirit of nonlinear model predictive control. We provide an interacting particle approximation to the forward-backward stochastic differential equations arising from Pontryagin's maximum principle with the forward stochastic differential equation provided by the time-continuous ensemble Kalman-Bucy filter equations. The receding horizon control laws are approximated as linear and are continuously updated as in nonlinear model predictive control. We illustrate the performance of the proposed methodology for an inverted pendulum example.
This paper introduces a unified approach for state estimation and control of nonlinear dynamic systems, employing the State-Dependent Riccati Equation (SDRE) framework. The proposed approach naturally extends classical linear quadratic Gaussian (LQG) methods into nonlinear scenarios, avoiding linearization by using state-dependent coefficient (SDC) matrices. An SDRE-based Kalman filter (SDRE-KF) is integrated within an SDRE-based control structure, providing a coherent and intuitive strategy for nonlinear system analysis and control design. To evaluate the effectiveness and robustness of the proposed methodology, comparative simulations are conducted on two benchmark nonlinear systems: a simple pendulum and a Van der Pol oscillator. Results demonstrate that the SDRE-KF achieves comparable or superior estimation accuracy compared to traditional methods, including the Extended Kalman Filter (EKF) and Particle Filter (PF). These findings underline the potential of the unified SDRE-based approach as a viable alternative for nonlinear state estimation and control, providing valuable insights for both educational purposes and practical engineering applications.
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 symplectic geometry mode decomposition (SGMD) is a powerful method for analyzing time sequences. The SGMD is based on the upper conversion via embedding and down conversion via diagonal averaging principle (DAP) inherited from the singular spectrum analysis (SSA). However, there are two defects in the DAP: it just hold for the time delay $\tau=1$ in the trajectory matrix and it fails for the time sequence of type-1 with the form $X=\{x[n]\}^N_{n=1}$. In order to overcome these disadvantages, the inverse step for embedding is explored with binary Diophantine equation in number theory. The contributions of this work lie in three aspects: firstly, the pulling back theorem is proposed and proved, which state the general formula for converting the component of trajectory matrix to the component of time sequence for the general representation of time sequence and for any time delay $\tau\ge 1$; secondly a unified framework for decomposing both the deterministic and random time sequences into multiple modes is presented and explained; finally, the guidance of configuring the time delay is suggested, namely the time delay should be selected in a limited range via balancing the efficiency of matrix computation and accuracy of state estimation. It could be expected that the pulling back theorem will help the researchers and engineers to deepen the understanding of the theory and extend the applications of the SGMD and SSA in analyzing time sequences.
The emergence of large language models (LLMs) opens new frontiers for unmanned aerial vehicle (UAVs), yet existing systems remain confined to predefined tasks due to hardware-software co-design challenges. This paper presents the first aerial intelligent agent capable of open-world task execution through tight integration of LLM-based reasoning and robotic autonomy. Our hardware-software co-designed system addresses two fundamental limitations: (1) Onboard LLM operation via an edge-optimized computing platform, achieving 5-6 tokens/sec inference for 14B-parameter models at 220W peak power; (2) A bidirectional cognitive architecture that synergizes slow deliberative planning (LLM task planning) with fast reactive control (state estimation, mapping, obstacle avoidance, and motion planning). Validated through preliminary results using our prototype, the system demonstrates reliable task planning and scene understanding in communication-constrained environments, such as sugarcane monitoring, power grid inspection, mine tunnel exploration, and biological observation applications. This work establishes a novel framework for embodied aerial artificial intelligence, bridging the gap between task planning and robotic autonomy in open environments.
An accurate distribution network model is crucial for monitoring, state estimation and energy management. However, existing data-driven methods often struggle with scalability or impose a heavy computational burden on large distribution networks. In this paper, leveraging natural load dynamics, we propose a two-stage line estimation method for multiphase unbalanced distribution networks. Simulation results using real-life load and PV data show that the proposed method reduces computational time by one to two orders of magnitude compared to existing methods.
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.
Parallel cyber-physical attacks (PCPA) refer to those attacks on power grids by disturbing/cutting off physical transmission lines and meanwhile blocking transmission of measurement data to dwarf or delay the system protection and recovery actions. Such fierce hostile attacks impose critical threats to the modern power grids when there is a fusion of power grids and telecommunication technologies. In this paper, we investigate the fault diagnosis problem of faulty transmission lines under a broader spectrum of PCPA for a linearized (or DC) power flow model. The physical attack mechanism of PCPA includes not only disconnection but also admittance value modification on transmission lines, for example, by invading distributed flexible AC transmission system (D-FACTS). To tackle the problem, we first recover the information of voltage phase angles within the attacked area. Using the information of voltage phase angle and power injection of buses, a graph attention network-based fault localization (GAT-FL) algorithm is proposed to find the locations of the physical attacks. By capitalizing on the feature extraction capability of the GAT on graph data, the fault localization algorithm outperforms the existing results when under cyber attacks, e.g., denial of service (DoS) attacks. A line state identification algorithm is then developed to identify the states of the transmission lines within the attacked area. Specifically, the algorithm restores the power injection of buses within the attacked area and then identities the state of all the transmission lines within the attacked area by solving a linear programming (LP) problem. Experimental simulations are effectiveness of the proposed fault diagnosis algorithms.
This paper describes recursive algorithms for state estimation of linear dynamical systems when measurements are noisy with unknown bias and/or outliers. For situations with noisy and biased measurements, algorithms are proposed that minimize $\epsilon$ insensitive loss function. In this approach which is often used in Support Vector Machines, small errors are ignored making the algorithm less sensitive to measurement bias. Apart from $\epsilon$ insensitive quadratic loss function, estimation algorithms are also presented for $\epsilon$ insensitive Huber M loss function which provides good performance in presence of both small noises as well as outliers. The advantage of Huber cost function based estimator in presence of outliers is due to the fact the error penalty function switches from quadratic to linear for errors beyond a certain threshold. For both objective functions, estimation algorithms are extended to cases when there are additional constraints on states and exogenous signals such as known range of some states or exogenous signals or measurement noises. Interestingly, the filtering algorithms are recursive and structurally similar to Kalman filter with the main difference being that the updates based on the new measurement ("innovation term") are based on solution of a quadratic optimization problem with linear constraints.
This short paper presents research findings on two learning-based methods for quantifying measurement uncertainties in global navigation satellite systems (GNSS). We investigate two learning strategies: offline learning for outlier prediction and online learning for noise distribution approximation, specifically applied to GNSS pseudorange observations. To develop and evaluate these learning methods, we introduce a novel multisensor state estimator that accurately and robustly estimates trajectory from multiple sensor inputs, critical for deriving GNSS measurement residuals used to train the uncertainty models. We validate the proposed learning-based models using real-world sensor data collected in diverse urban environments. Experimental results demonstrate that both models effectively handle GNSS outliers and improve state estimation performance. Furthermore, we provide insightful discussions to motivate future research toward developing a federated framework for robust vehicle localization in challenging environments.
Unmanned ground vehicles operating in complex environments must adaptively adjust to modeling uncertainties and external disturbances to perform tasks such as wall following and obstacle avoidance. This paper introduces an adaptive control approach based on spiking neural networks for wall fitting and tracking, which learns and adapts to unforeseen disturbances. We propose real-time wall-fitting algorithms to model unknown wall shapes and generate corresponding trajectories for the vehicle to follow. A discretized linear quadratic regulator is developed to provide a baseline control signal based on an ideal vehicle model. Point matching algorithms then identify the nearest matching point on the trajectory to generate feedforward control inputs. Finally, an adaptive spiking neural network controller, which adjusts its connection weights online based on error signals, is integrated with the aforementioned control algorithms. Numerical simulations demonstrate that this adaptive control framework outperforms the traditional linear quadratic regulator in tracking complex trajectories and following irregular walls, even in the presence of partial actuator failures and state estimation errors.