Extended Kalman Filter

Recursive state estimation often executes approximate numerical solutions inside a feedback loop, where highly accurate local steps do not guarantee better overall results. For a fixed linear Kalman model, we characterize when a correction within a prescribed subspace and norm budget can meet a local admissibility tolerance, and how the defects actually executed affect the finite-horizon covariance response. Centering each defect on the exact gain for the implemented covariance separates current solve error from inherited gain drift. Expanding the exact residual-drift identity reveals opposing quartic contributions beyond the quadratic response: innovation-covariance inflation enters positively, while local-gain reoptimization enters subtractively. Under matched initialization, an absolute sixth-order remainder bound, uniform over bounded defect sequences at fixed horizon, gives sufficient conditions for quadratic under- or overprediction. Machine learning proposes bounded corrections, while a learner-independent residual certificate and verified fallback govern execution of classical and quantum candidates without changing the reference estimator. In a power-grid tolerance study, learned correction lowers the minimum conjugate-gradient iteration count for deployment without fallback relative to uncorrected solves under the same residual certificate. Gains reconstructed from a variational quantum linear solver and from an annealing-based binary encoding, with small-scale terminal measurements on superconducting hardware and sampling on a quantum annealer, are executed through the same interface. By linking local repairability to nonlinear error propagation, the framework evaluates approximate solvers and learned corrections through independent certification and finite-horizon response, providing a practical basis for studying hybrid quantum--classical computation.

Data assimilation estimates a dynamical state from partial and noisy observations. Classical ensemble filters are efficient but restrict analysis updates through finite sample covariance and affine Gaussian distribution. We introduce the Flow Ensemble Filter (FlowEF), which uses conditional flow matching to transport the forecast ensemble from a classical baseline filter to an analysis ensemble. FlowEF uses a localized Gaussian source during training, transports forecast ensemble members from a baseline filter at deployment, and conditions its velocity field on ensembles from that baseline filter and the observation. The proposed model therefore learns a nonlinear update while mapping each baseline ensemble independently. For sparsely observed dynamical systems, FlowEF improves both deterministic and probabilistic metrics over all four classical ensemble filters. It also achieves the best performance among the state-of-the-art generative data assimilation models.

Bioinspired feedback controls for pursuit, tracking, and collective motion are often expressed in terms of the relative configuration between interacting agents. In practice, however, onboard sensors may not directly provide all quantities required for feedback control, necessitating estimation of unobserved quantities. This paper develops a bioinspired internal model-based estimator for reconstructing those quantities from partial sensory observations and known self-motion. State reconstruction is posed as an optimization problem that treats the relative kinematics as constraints and minimizes the disagreement between the internal model outputs and measurements from onboard sensors. Pontryagin's Maximum Principle is used to derive the necessary optimality conditions. A forward-backward algorithm is used to provide a numerical solution and a moving horizon formulation is employed for online implementation. The estimator is evaluated numerically against classical state estimators. Real-time implementation of the proposed framework on robotic hardware is demonstrated through two pursuit strategies.

Bayesian filtering provides a principled framework for online state estimation under uncertainty, yet its application to systems with high-dimensional states and complicated posterior distributions remains challenging. Recent generative models, such as flow matching, have shown potential in Bayesian filtering. However, they still rely on particle-based representations of the posterior, which lose the rich information of the full distribution, or tackle a trajectory-level inverse problem that conflicts with the recursive structure of Bayesian filtering. To address this, we propose a new perspective of directly encoding the evolving distribution into flow matching model weights, namely, the Belief Flow Filter (BFF). It is a generative filtering framework that updates model weights via gradient descent at test time to track the posterior evolution. Thereby, BFF bypasses the scalability issue of particle representations or the flexibility limitation of Gaussian assumptions in conventional filters. We theoretically justify that the BFF design is structurally aligned with Bayesian filtering, and its training objective targets the recursive filtering operator. BFF is empirically verified across 5 different physical systems, including ones with chaotic dynamics and highly sparse, non-linear observations. The results show that BFF attains the best score in 8 of 9 metric-benchmark cells across the three standard 1D and 2D PDE benchmarks, and similarly leads on the extreme single-moving-sensor setting and on a real-world-grounded tokamak plasma estimation task, demonstrating its potential to accurately approximate the Bayesian filtering operator in high-dimensional probability space.

Recent factor graph approaches to continuum robot state estimation have been successful for quasi-static applications and spatiotemporal estimation using white-noise kinematic motion priors. However, when inertial effects are significant, these approximations may fail to capture the underlying physics, limiting accuracy during dynamic motions. In contrast, our approach approximates the Cosserat rod dynamics of continuum robots. We write inertia and damping as equivalent applied loads, so that the dynamic balance retains the algebraic form of the static one from prior work with quasi-static robots. Without backbone observations, the framework reduces to a stochastic forward simulation of the robot's motion. Given observations, it jointly refines kinematic and dynamic states and infers external loads, among other states. We validate the approach through simulation and experiments, demonstrating stochastic forward simulation as well as state estimation on tendon-driven continuum robots.

In this paper, we tackle the problem of jointly estimating the system states and partially unknown dynamics within distributed sensor-equipped networks, particularly in scenarios where only partial state observations are available. To address this issue, we propose an observer-based dynamic cooperative learning framework incorporating online distributed Gaussian Process (GP) regression, which enables accurate estimation despite incomplete in measurements and deficient GP models. In addition, a novel data collection strategy is introduced, with theoretical conditions ensuring feasible data acquisition. Moreover, we also derive an error upper bound encompassing state estimation and model estimation, leveraging the deterministic error bounds of GPs. Empirical simulations demonstrate the superiority of our approach compared to existing distributed GP-based methods.

This work proposes a physics-enhanced machine learning approach for the system identification of Linear Time-Varying (LTV) systems under time-varying operating conditions in terms of fast-varying natural frequencies and damping ratios by combining a long short-term memory network with an Extended Kalman Filter (EKF). The proposed approach uses vibration data (displacement and velocity measurements), domain knowledge of modal damping ratios, and a physics-based model that can yield an approximate natural frequencies time-dependency model. The approach is validated using synthetic data generated from a finite element model of a 2-blade offshore wind turbine under realistic environmental and operating conditions. This system displays fast time-varying frequencies due to operating conditions, whose identification is particularly challenging because of the wind and wave loading. The robustness of the proposed approach is assessed under assumed incorrect system information (e.g. damping ratio). The proposed approach is evaluated across different environmental and operating conditions to show its applicability to different operating regimes. The results show the approach can accurately identify the selected fast-varying natural frequency, 1st Fore-Aft (FA-1) mode, with a maximum root mean square error of 0.0012 Hz. The results demonstrate that the model trained on EKF estimates depends on accurate damping values, whereas the model trained on physics-based data exhibits robustness to incorrect damping assumptions. The approach is extended to damping ratio identification for the selected mode by estimating the root mean square error between models trained on EKF estimates and physics-based data. The results show that the approach can yield a good approximation of the FA-1 mode damping ratio using grid search, offering an improvement over covariance-driven stochastic subspace identification.

Predicting the future trajectories of surrounding vehicles in autonomous driving is important for collision risk assessment and safe ego-vehicle path planning. Conventional neural network-based trajectory predictors typically achieve strong prediction performance by exploiting agent history, dynamic scene graphs, and semantic maps. However, in specific motion regimes such as acceleration, deceleration, and turning, these predictors may fail to reflect physically feasible trajectories. To address this issue, this study proposes a framework that fuses the output of Trajectron++, a neural network-based trajectory predictor, with extended Kalman filter (EKF)-based multiple trajectory candidates at a late stage. On the nuScenes dataset, the proposed method reduces the average displacement error and final displacement error of the Trajectron++ robot baseline by 13.7% and 14.6%, respectively, without modifying the baseline architecture. These results indicate that EKF-based trajectory candidates can effectively complement neural trajectory prediction through learned fusion.

Physical teleoperation integrates human cognitive flexibility with robotic precision, yet demanding manipulation tasks frequently induce severe cognitive workload, acute frustration, and execution breakdown. Conventional shared autonomy paradigms rely primarily on task-based rules, such as spatial error boundaries, which disregard the operator's transient affective state and risk misaligned control interventions. To address this limitation, we propose an affect-aware shared autonomy teleoperation framework that dynamically modulates robotic assistance based on real-time operator state estimation. The system estimates operator affective states from synchronized facial video, cardiac signals, and bilateral arm kinematics, outputting a seven-state affective distribution and a three-category operational abstraction (neutral, productive, adverse). Affect-aware assistance is selectively triggered when the user is detected in a continuous adverse state, preserving task-positive engagement without unnecessary disruption. The empirical user study ($N = 30$) confirms that the proposed affective assistance increases the productive states by up to 39.7% without compromising user agency. The collected dataset represents the first multimodal dataset that provides continuous visual, physiological, and operator's bilateral motion tracking of temporal affective state shifts during bimanual teleoperation. Our multimodal fusion model outperforms zero-shot baselines (Qwen, MiniCPM-V) in tracking temporal state dynamics. This real-world deployment offers a new human-centric framework that integrates visual, physiological, and motion tracking for physical human-robot interaction.

Autonomous Underwater Vehicles (AUVs) navigating without GPS typically fuse inertial measurements with acoustic Doppler Velocity Log (DVL) velocities and pressure-derived depth. Posing the navigation state on a Lie group improves accuracy and consistency. However, state-of-the-art filters based on the Invariant Extended Kalman Filter (IEKF) append the Inertial Measurement Unit (IMU) biases as a Euclidean extension, which breaks the group-affine structure required for exact log-linear error dynamics, causing the reported covariance to degrade alongside the estimate. We apply the Tangent-Group (TG) symmetry, which carries the biases within the geometry of the state space, to derive an Equivariant Filter (EqF) for this system, leaving zero linearization error in the navigation states and second-order error only in the biases. We develop an equivariant output model for the DVL, whose update incurs only third-order linearization error, together with a direct pressure output. Monte Carlo simulations benchmark the TG-EqF against a Two-Frame-Group IEKF and a Multiplicative EKF. The TG-EqF reduces error by 18--25% against both alternatives in each of attitude, velocity, and position. The main benefit is in the covariance it estimates: its Average Normalized Estimation Error Squared (ANEES) stays closer to its nominal value of one than that of the others. Offline analysis on AUV field data corroborates the findings of the simulations, demonstrating reduced position drift.

This paper proposes Dynamic-LIVO, a dynamic-aware LiDAR-Inertial-Visual Odometry (LIVO) system for robust state estimation and static colored mapping in dynamic environments. Dynamic-LIVO employs Spatio-Temporal (S-T) normal analysis to identify dynamic LiDAR points and propagates the resulting classification to both LiDAR-inertial and visual-inertial updates, preventing dynamic LiDAR measurements and their associated visual observations from affecting state estimation and mapping. However, S-T normal estimation can be unreliable in newly observed and spatially sparse regions due to insufficient spatio-temporal observations. To address this issue, we introduce a time-delayed S-T normal estimation strategy that defers the classification of insufficiently constrained points and re-evaluates them as additional observations become available. This strategy improves dynamic classification reliability while preserving valid static points for map construction. Extensive experiments on public and self-collected datasets with diverse sensor configurations demonstrate that Dynamic-LIVO improves localization accuracy and produces cleaner static colored maps in challenging dynamic environments. The source code and self-collected dataset will be publicly released upon acceptance.

Vehicle tracking is fundamental to applications ranging from urban mobility and public safety to security and defense. Conventional tracking relies on direct access to sensors that provide strong observations such as vehicle identity and location. In practice, however, factors such as ownership, privacy, cost, and operational constraints may limit directly accessible sensors, leaving sparse observations and long tracking gaps. Meanwhile, many additional third-party sensing assets may be present across the environment but remain inaccessible at the raw-data level, preventing their direct integration into the tracking system. In this work, we investigate whether weak, indirect observations with uncertain spatial and temporal cues can complement sparse direct sensing for vehicle tracking. Specifically, we propose GrayTrack, which fuses weak anonymous events with sparse direct observations using a road-constrained particle filter. We build a CARLA-Mininet-WiFi pipeline to evaluate the system under controlled conditions, generating direct observations from accessible cameras and indirect observations from third-party cameras. Our learning-based detector achieves an F1 score of 0.989 for anonymous vehicle passages. Further, incorporating indirect third-party observations reduces trajectory RMSE by 60.1% and catastrophic track loss from 35.8% to 0.3%. These results demonstrate that GrayTrack can effectively exploit weak indirect observations to extend tracking capabilities.

The Koopman operator has been widely used for time-series prediction in dynamical systems. However, prior work that learns latent ``Koopman spaces'' using neural networks often did not construct a valid Koopman space for forecasting, as these representations may be mathematically inconsistent with the operator-theoretic formulation and fail to capture the intrinsic low-rank structure of system dynamics. To address this issue, we introduce K$^2$SVD, a method that explicitly learns the leading singular functions of the Koopman operator by optimizing a Hilbert-Schmidt objective. This yields a well-defined low-rank approximation of the Koopman operator with an interpretable linear combination, featuring a compact latent space with less than $10\%$ of the dimensions used in previous work. In the learned Koopman space, K$^2$SVD further captures temporal evolution with a linear Gaussian state-space model and performs inference via Kalman filtering, mitigating noise accumulation during multi-step prediction. Empirical results show that K$^2$SVD outperforms state-of-the-art methods across multiple datasets, with significantly faster prediction speeds and lower computational cost than previous efficiency-focused models. This highlights the benefits of principled low-rank Koopman representations and opens up broader potential for applications.

In partially observable settings, agents must act without full knowledge of the world state and rely on uncertain state-estimation pipelines. Obtaining grounded and verifiable symbolic plans under such uncertainty remains a key challenge. Recent work has integrated Vision-Language Models (VLMs) to bridge perception and symbolic reasoning, following two main paradigms. The first, VLM-as-planner, maps images directly to action sequences, and the second, VLM-as-grounder, grounds observations into symbolic predicates used as the initial state by off-the-shelf planners. Both approaches ignore uncertainty in the planning process, compromising robustness. We introduce a third paradigm, VLM-as-probabilistic-grounder, a novel approach that captures the uncertainty of VLM predicate groundings as a probability distribution over symbolic states. This enables planning in belief space and producing robust plans under uncertainty. Experiments in simulated household robot settings show improved robustness and task success over deterministic grounding, underscoring how our approach leverages foundation models for reliable planning under uncertainty.

Power Flow (PF), Optimal Power Flow (OPF), and State Estimation (SE) are fundamental problems in power system analysis, but solving them is computationally expensive. Graph Neural Networks (GNNs) have been proposed as fast surrogates, yet existing solvers are trained for a single problem at a time, producing narrow models that must be rebuilt for each new task. We propose a more general approach: a single Heterogeneous Residual Gated Graph Convolutional Network that solves all three problems with one shared backbone. Rather than learning one mapping, the model learns a reusable representation of how the network behaves, from which PF, OPF, and SE can each be estimated. Trained jointly on the three problems across diverse topologies and loading conditions, and evaluated on the IEEE 14-bus and 118-bus systems, the shared model matches the accuracy of task-specific GNN solvers and stays robust on unseen loading levels and topologies. These results show that a single model can capture the basic operation of a power network and serve several analysis tasks at once, a first step toward a foundation model for power systems.

Estimating deformable object states remains a fundamental challenge in robotics and simulation. We propose a novel factor graph-based framework for probabilistic mesh state estimation of deformable objects. The method directly updates a tetrahedral mesh, a rich and physically-grounded representation of an environment, by combining physics priors, noisy sensor measurements, and temporal smoothness constraints within a unified probabilistic formulation. The estimation problem is posed as a nonlinear least-squares optimization and solved using Levenberg-Marquardt. Ex vivo central-airway obstruction experiments and simulations on deforming cube models demonstrate reliable and accurate reconstruction under both rigid motion and deformation, highlighting the potential of this probabilistic approach for principled, measurement-driven mesh state estimation in deformable object reconstruction.

This letter presents a unified formulation and a controlled numerical comparison of generative-model approaches to the nonlinear filtering problem. Under this formulation the analysis step is realized by a transport of the forecast distribution to the posterior, the approaches differing only in how that transport is selected and learned. We derive three new filters, based on stochastic interpolants, their deterministic flow-matching limit, and Schrödinger bridges realized through forward--backward SDEs. We develop a two-stage tuning procedure that separates the training of the generative model from its online refinement. The resulting methods are compared against the optimal transport filter (OTF), the Knothe--Rosenblatt filter (KRF), the sequential importance resampling (SIR) particle filter and the ensemble Kalman filter (EnKF), in terms of accuracy, computational time, and sensitivity to ensemble size and state dimension. The results indicate that every generative filter resolves multimodal posteriors that the EnKF and SIR do not, that no single generative framework dominates, the preferred method being set by the available online budget and ensemble size, and that the filters differ in the regularity of the particle trajectories they produce.

This paper presents the iterative equivariant filter (IterEqF). The iterative extended Kalman filter (IterEKF) replaces the standard EKF correction step with an iterative correction step that is the Gauss-Newton solution to a nonlinear weighted least squares problem. The standard equivariant filter (EqF) exploits and respects the underlying symmetry of state estimation problems posed on homogeneous spaces and Lie groups. The motivation behind the IterEqF is to combine the features of both the IterEKF and the EqF, thus leading to a high-performance state estimation solution that is well suited to navigation problems. This paper derives the iteration procedure for the IterEqF update step and shows how the intrinsic nonlinearity of the approach naturally results in a `reset' of the filter's covariance into new coordinates. Monte-Carlo simulations of range-based localisation for a mobile robot demonstrate the improvement in performance relative to a standard EqF, especially during the transient convergence.

Reliable online autonomy is critical for quadrotor operation in urban airspaces, where global navigation satellite systems (GNSS) measurements suffer from multipath, blockage, and latency issues, introducing non-stationary, temporally correlated errors that degrade conventional GNSS-IMU fusion. This paper presents a belief-adaptive online autonomy framework that augments an extended Kalman filter (EKF) with explicit GNSS trust modelling, second-order online belief adaptation, and latency-aware out-of-sequence measurement handling. GNSS trust is represented as a latent belief state that modulates measurement weighting and multipath bias uncertainty, and is updated online using EKF consistency signals. Unlike reactive covariance tuning, the proposed approach enables proactive and stable sensor trust adaptation without prior environmental knowledge or offline training. Evaluation in simulated urban air mobility scenarios with correlated multipath, stochastic latency, and obstacle constraints demonstrates improved belief convergence, smoother trajectories, and reduced estimation and tracking errors compared to naive, adaptive, and first-order baselines. The framework preserves classical GNSS-IMU fusion structure and can be integrated directly into existing flight control pipelines, supporting robust online autonomy in GNSS degraded environments.

Accurate posterior prediction need not require accurate approximation of Bayesian updates. We prove that an unbounded gap between the update maps can coexist with vanishing predictive KL for every fixed finite $K\ge2$ in a stationary symmetric Gaussian HMM. Exact Bayesian mixing and an explicit deterministic radial filter act on the same $K-1$ belief coordinates. As $q\to0^+$, their separation in centered logits in the worst case grows at least linearly in the natural confidence scale $L_K(q)$, while their categorical $D_{\mathrm{KL}}(\mathrm{exact}\|\mathrm{radial})$ vanishes at the same explicit witness. Along stationary HMM trajectories, the expected terminal KL between filtered posteriors also converges to zero at $H(q)=\lceil-\log(q)/c\rceil+1$. Typical blocks without switches drive both filters into a common confidence cone, where softmax curvature suppresses their disagreement; a single Gaussian maximal event controls adaptive noise. A sweep with equally spaced Gaussians over $K\in\{2,4,8\}$ illustrates the opposing trends, and binary controls at long horizons compare saturating and nonsaturating recurrences. The result isolates two missing links between internal update gaps and predictive cost: the contribution of separating states to expected loss and decoder sensitivity. Thus even an unbounded internal update gap does not by itself certify predictive failure. The construction is fixed in $K$ and does not provide a universal criterion for when compression is harmless or characterize when internal gaps must incur task loss.

Manipulating deformable objects (DOs) is challenging due to their high-dimensional state space, underactuated dynamics, and partial observability. In this paper, we propose cRVAE, a lightweight conditional recurrent variational autoencoder that estimates the full DO state from only partial corner-node observations during inference. The resulting model is used as the forward model in a receding-horizon optimal control framework for obstacle-aware collaborative DO manipulation. In simulation on rope and fabric, cRVAE estimates the full DO state from the available corner-node measurements alone, matching the accuracy of a parameter-identified XPBD model. At inference it uses no physical parameters as model inputs and performs no online parameter identification. It also runs approximately 350 times faster on the rope and over 1500 times faster on the fabric per forward pass, keeping horizon-based planning within the 100 ms control budget where XPBD exceeds it already at short horizons. Full-shape estimation from corner sensing at in-loop speed is what makes the model deployable on hardware, which we demonstrate on a Unitree Go2 robot.

Maritime target tracking over large distances often requires multi-agent teams without centralized coordination, and intermittent communication. Each agent must maintain an independent estimate that can take advantage of opportunistic communications availability when possible. This can lead to overly confident local estimates in the absence of external data. In this work, we propose an augmentation to a classical particle filter implementation that accounts for this potential source of error by forcing particles to spread strategically in the absence of informative updates from other sensor nodes. We demonstrate our method using Unmanned Surface Vessels (USVs) on a lake, and show that our augmentations do not deteriorate nominal performance, and provide an advantage in some specific edge cases.

Linear attention is increasingly used in frontier language models for efficient long-context inference and constant-memory decoding. Its fixed-size recurrent memory, however, requires an online decision at each token: what to write and how strongly to overwrite existing associations before knowing which information future queries will require. Delta-rule models learn this strength from the current token embedding but do not track confidence in the memory estimate, preventing each write from adapting to accumulated evidence. To represent this uncertainty explicitly, we reformulate recurrent associative memory as a linear--Gaussian state-space model, for which the Kalman filter is the optimal recursive estimator, and introduce a new family of models, Kalman Delta Networks (KDNs). Within KDNs, the transition propagates both the memory state and its uncertainty, allowing the Kalman gain to weight each residual write by accumulated evidence and observation reliability. Under this formulation, Delta-style updates emerge as a special case that substitutes a token-wise isotropic surrogate for predictive covariance and omits covariance tracking. Exact tracking, however, entails a dense, state-dependent Riccati recursion that is poorly suited to GPU-parallel linear-attention scans. To address this issue, we introduce two scan-compatible KDN approximations. Diagonal KDN projects each one-step posterior onto the diagonal Gaussian family through online mean-field variational inference, whereas Isotropic KDN uses an isotropic approximation with a single uncertainty scalar per head. Their uncertainty recurrences are Mobius maps, enabling associative scans with logarithmic parallel depth. Across controlled pretraining at 750M and 1.3B parameters, KDN variants consistently improve perplexity and mean downstream accuracy over state-of-the-art linear-attention models.

Data-driven process simulation aims to generate realistic case trajectories from historical event logs without requiring an explicitly specified model of the underlying dynamics. Deep sequence models can capture complex temporal dependencies through next-activity probabilities and conditional time distributions. However, event logs provide only a partial view of the underlying process state, often recording activity completions without the corresponding service-start times. Consequently, the same observed process history may be consistent with multiple plausible latent process conditions, whereas standard recurrent models compress each process prefix into a single deterministic recurrent state. We propose a Unified Particle Filter LSTM (Unified PF-LSTM) that maintains and sequentially updates a weighted set of recurrent-state hypotheses. We summarize this particle belief using its weighted mean and learned features based on the moment-generating function. The resulting representation is used to predict a categorical distribution over the next activity and conditional quantiles of the current activity's sojourn time. The framework is trained end-to-end from event-log data and evaluated on three real-world emergency department datasets. The results show that the proposed framework consistently outperforms the considered data-driven baselines in reproducing routing, duration, and system-level behavior across all datasets, with particularly strong gains in settings where complex process dynamics are only partially reflected in the available event logs.

We study short- and mid-horizon UAV bounding-box forecasting on the FRED event-camera dataset. We use a constant-velocity Kalman filter over a full center-size box state as a strong physical baseline, and train a residual model to predict acceleration-like corrections from recent box history, filtered state features, and local event representations. This simple residual formulation consistently improves over the Kalman baseline, with event-conditioned models giving the strongest results among the evaluated methods. We further show that part of the residual target is predictable from anchor position and velocity alone, indicating that canonical FRED results can reflect both visual evidence and dataset-specific motion priors. To analyze this effect, we introduce decorrelated subsets as a diagnostic stress test, showing that event-conditioned residual models retain useful predictive signal even when measured position- and velocity-based shortcuts are weakened.

The rapid advancement of large language models (LLMs) has made AI-generated text detection increasingly critical. Existing zero-shot detectors assume that more token-level evidence leads to more reliable detection. However, our empirical study challenges this consensus: fewer tokens sometimes work better, retaining only 40% can yield optimal performance, yet this benefit is not universal. Using the Entropy Gap Score (EGS), we introduce top-$k$ cumulative probability filtering as a diagnostic probe. Across three representative settings, filtering exhibits strikingly different behaviors. We analyze EGS via typical set theory and quantify its dynamics through entropy calibration and distribution analysis. We find that filtering helps for weak source LMs, where low-entropy tokens are harmful, but fails for strong source LMs, where they are not notably harmful. Our work provides the first systematic analysis showing that some tokens are not merely uninformative but systematically harmful due to entropy miscalibration, revealing a two-sided trade-off in token-level detection.

Reliable onboard state estimation is essential for safe robotic operation, yet unmodeled disturbances, such as sensor aliasing or out-of-distribution noise, still cause estimators to degrade or fail completely. While many methods aim to improve estimator robustness, only a few provide introspective mechanisms to assess estimate quality. Existing uncertainty measures, such as covariances, rely on idealized assumptions and tend to be overconfident, and more recent data-driven approaches are typically tied to their training data distributions. We propose a sensor-agnostic introspective method that assesses estimator health by analyzing the frequency-domain power distribution of recent velocity estimates. The method is evaluated using outdoor flight data from an aerial robot running visual-inertial, LiDAR-inertial, and radar-inertial odometry. The dataset includes multiple estimator failures, enabling analysis of several frequency-domain indicators, such as signal power, spectral bandwidth, and entropy. We observe consistent spectral power differences between healthy and degraded estimates, allowing detection of 51%-58% of labeled failures with 60%-84% precision across three fundamentally different state estimation frameworks. Our results show that even a simple frequency-domain analysis of a state estimator's output can serve as a lightweight introspective tool to complement existing robustness techniques in real-world robotic deployments, and opens promising avenues for future investigation.

Robotic localization under changing sensing conditions can suffer from biased errors and miscalibrated covariances. We present WRAP, an adapter-agnostic Wasserstein-robust plug-in for nonlinear extended Kalman filter (EKF) and error-state Kalman filter (ESKF) stacks. A causal module supplies time-varying effective process and measurement statistics; a mean-preserving Wasserstein local update then computes least-favorable covariances and a robust gain without changing the propagation model, residual, or retraction. This separates mean adaptation from covariance robustification and uses distinct radii for propagation and sensing. On 18 UWB--IMU sequences held out from adapter training, adapter-only and WRAP reduce mean 3-D position RMSE by $19.8\%$ and $27.4\%$ relative to the nominal ESKF; an isotropic ablation reaches $19.5\%$, linking the incremental gain to directional process-covariance redistribution. An in-sample GNSS--INS study shows that mean adaptation provides most of the accuracy gain, while DR improves consistency and mitigates over-tightened classical covariance estimates. The robust solve takes 0.05 ms for UWB and 2.92 ms for GNSS on a Jetson Orin Nano.

We present an attitude-only framework for estimating a spacecraft's normalized inertia tensor from torque-free rotational motion. Our method supports both continuous single-arc observations and the joint use of multiple short torque-free arcs, while requiring neither gyroscope measurements nor known control torques. A Karush-Kuhn-Tucker formulation provides a fast linear initialization, which is refined by nonlinear shooting using the exact Jacobi-elliptic solution of Euler's equations and a Magnus-expansion quaternion map. Under controlled attitude noise, tests using a single 500-second arc reduced inertia-tensor error by approximately one order of magnitude relative to an Extended Kalman Filter initialized from the same estimate, while requiring nearly two orders of magnitude less computation. Joint estimation from three 100-second arcs provided a similar improvement in accuracy and remained more than one order of magnitude faster. Photorealistic proximity-operations simulations further evaluated both strategies using monocular image-derived attitudes. The 2000-second single-arc cases achieved sub-thousandth median inertia-tensor error and supported 10-hour attitude predictions with single-digit-degree median error. In three-arc cases using 30-300 seconds per arc, our method consistently outperformed the EKF refinement, with performance governed by rotational excitation and temporal sampling.

Data-driven health-state estimators for SiC (Silica-Carbide) power modules typically report their performance on a single accelerated-aging campaign, and how that performance transfers to a different failure mechanism is rarely tested. We benchmark five reference methods from the prognostics and condition-monitoring literature against a physics-informed NODE (Neural Ordinary Differential Equation) on two SiC power-cycling campaigns driven by structurally different failure mechanisms, solder-layer fatigue and wire-bond lift-off, under a per-module $k$-fold protocol. The NODE is evaluated under two input regimes that share the rest of the pipeline: the baseline electrical precursors and a set of cumulative thermoelectric features. Every reference method degrades on the wire-bond campaign, with average errors growing and precision decreasing with respect to their performance on the soldered campaign. The NODE fed with the cumulative features keeps its soldered-campaign metrics on both mechanisms, with differences inside the fold-to-fold variance, while the same architecture fed with the baseline precursors falls back to the reference-method cluster. The input representation contributes at least as much as the architecture to failure-mechanism transferability of a health-state estimator.

This paper presents a collaborative UAV-UGV navigation framework for high-altitude, snow-covered terrain, where reduced visibility and unstable ground render conventional methods ineffective. We introduce a custom efficient U-Net architecture that falls under the computational constraints for real-time road segmentation, utilizing a novel synthetic snow data augmentation technique to achieve 96.5% segmentation accuracy. For UAV localization, we implement an Extended Kalman Filter (EKF) fusing onboard GPS and IMU data, achieving a maximum observed positional error of +-0.5 meters. The UGV position is determined via a visual tracking pipeline using YOLOv5 and depth data from the UAV's RGB-D camera. A dynamic path planning algorithm utilizes this segmentation to adjust for snow drifts, enabling successful navigation in obscured test environment with minimal deviation.

This article presents a kinematic-inertial-LiDAR-visual odometry for humanoid robots, called KILVO. Tailored to the platform features, requirements, and real-world complexity, it fully utilizes the sensors commonly equipped on humanoid robots, including joint encoders, IMU, LiDAR, and camera, within an asynchronous-sequential hybrid error-state iterated Kalman filter (ESIKF). Specifically, inertial data are used for prediction, leg kinematics are processed asynchronously at a high rate and provide proprioceptive constraints, while exteroception is updated sequentially, first by registering LiDAR points for geometric priors and then by updating the visual component via photometric errors. Moreover, the framework is elaborately designed with multimodal adaptation for resilience to sensor failures. A compact contact estimation module is also developed, sharing information with state estimation without additional sensors. Extensive experiments on public datasets and in the real world across multiple humanoid robots, gait patterns, and scenarios demonstrate that KILVO achieves highly competitive accuracy, efficiency, and output rates, with strong robustness against sensor degradation and failures, making it more suitable for humanoid robots than state-of-the-art fusion methods. Our code and datasets are released on GitHub.

Continuum robots often operate in uncertain environments, where accurate state estimation is essential for safe interactions. Estimate uncertainty is inherently spatially non-uniform: confidence varies depending on where measurements are available. Global estimation accuracy is not always the top priority, but rather achieving sufficient confidence at task-relevant locations along the robot. This extended abstract introduces mechanically reconfigurable sensing enabling uncertainty-shaping in state estimation for continuum robots. We present a concept hardware design demonstrating the feasibility of longitudinal translation of a sensor within a continuum robot. We demonstrate that state estimation confidence can be reconfigured by varying the sensor location, and show a reduction of full-body shape estimation errors when sliding the sensor back and forth over time, compared to a single fixed tip sensor.

Nonlinear state estimation requires sequentially fusing model-based predictions with noisy measurements. Under imperfect dynamics and unknown, time-varying noise statistics, this fusion can degrade in both accuracy and statistical consistency. Existing learning-aided filters largely treat accuracy and uncertainty estimation separately, limiting their ability to correct model-mismatch-induced bias while retaining an explicit, calibrated posterior covariance. This paper introduces Unscented KalmanNet (UKN), a model-based deep learning architecture that extends the Unscented Kalman Filter (UKF) with learned mechanisms for these two sources of filtering error while preserving explicit posterior covariance propagation. NoiseNet learns time-varying process and measurement covariances as bounded multiplicative corrections to baseline covariances, guaranteeing positive definiteness, while GainNet learns a bounded residual correction to the analytical UKF gain to compensate for model-mismatch-induced bias. A calibration-aware training objective couples state error with posterior covariance and innovation consistency terms through adaptive weighting, jointly optimizing accuracy and calibration. UKN is benchmarked against UKF, KalmanNet, and Bayesian KalmanNet on three synthetic systems and real-flight UZH-FPV data. It achieves the lowest state-estimation error in all four examples and reduces RMSE by 26.4-49.7% compared with UKF in the synthetic cases. Leave-one-sequence-out cross-validation over 11 flights shows 22.4% and 34.3% reductions in mean position and velocity RMSE, respectively. UKN also yields the lowest fold-to-fold variability, with dimension-normalized NEES and empirical coverage closest to nominal values among covariance-reporting filters. These results show that structured learned adaptation improves estimation accuracy while retaining calibrated uncertainty.

State estimation is a key component in model-based control of walking robots and, more broadly, applicable wherever hidden variables must be inferred. The Kalman filter is widely used to estimate floating-base position and velocity by fusing multiple sensing modalities. However, tuning noise parameters is challenging and typically requires expert knowledge. Moreover, fixed noise parameters are unsuitable for varying gaits and environments. We propose an online adaptation strategy for the process noise covariance matrix Q and the measurement noise covariance matrix R. Specifically, we introduce a filter residual and innovation-based covariance adaptation method for legged robot state estimation and evaluate it against a baseline approach relying on IMU and foot force measurements. The proposed adaptation is implemented within an Invariant Extended Kalman Filter (InEKF) fusing IMU and leg kinematics. Experiments on indoor and outdoor datasets with a Unitree Go2 quadruped show that adapting R is sufficient and improves accuracy by 25% for the trotting gait compared to the fixed-tuned InEKF. Finally, the proposed residual-based adaptation achieves comparable performance to the foot force approach, without requiring foot force measurements or additional parameter tuning.

More than 70% of the people that fell overboard cruise ships in the period 2010-2019 lost their lives. This paper presents a strategy for reliably predicting the area a person may be in after a man overboard incident, and describes in detail the search methods to find them utilizing UAV technology. The search area prediction method employs an Extended Kalman Filter that capitalizes on the information from the Leeway model to track the missing person in the sea by taking into account the uncertainty of the movement of the person and the weather conditions in the area. Then, a UAV uses this information to search for the person. Five different methods for searching in this dynamic area are presented and evaluated - the Zigzag, the Boustrophedon, the Spiral, the Probability Informed Search and the Improved Probability Informed Search (IPIS) methods. The IPIS method provides success rate of over 80% on average for finding a person, even if the UAV initiates the search mission 20 minutes after the man overboard incident and even assuming a detection method with a success rate of 30%. All code for the simulation environment and the evaluation of the methods is available on our GitHub page at https://github.com/diangeli/pdms-man-overboard.

In vision-aided navigation and visual-inertial odometry, the quality of triangulated three-dimensional feature positions is a fundamental prerequisite for state estimation accuracy. Triangulation becomes ill-conditioned or even impossible when a camera undergoes pure rotation without translation, or when the observed bearing vectors provide insufficient parallax. Even though visual-inertial odometry has been extensively studied, the active maintenance of feature-observability during navigation has not been sufficiently addressed in the literature. To address this gap, this study presents TANGO-VIO, a triangulation-aware navigation framework that embeds a log-determinant metric of the feature-wise stacked-bearing matrix into a control barrier function. In this proposed method, the observability guarantee is established in the feature-geometric sense by enforcing a lower bound on the aggregate triangulation-information metric through a nominal-direction-weighted minimum-deviation velocity correction. The proposed architecture is evaluated through software-inthe- loop simulations and real flight experiments. The results show improved triangulation conditioning under low-parallax motion, while the flight response closely reproduces the corresponding simulation behavior and confirms the practical realizability of the proposed safety filter. Supplementary materials are available on the project webpage.

This paper proposes a localization framework that uses spatiotemporal fields governed by partial differential equations (PDEs) as localization signatures. Two PDE classes are considered: the shallow water equations, which describe free-surface flows in coastal and riverine environments, and the advection-diffusion equation, which models the transport and mixing of scalar quantities such as temperature, salinity, and dissolved oxygen. A numerical PDE solver provides predicted fields over the domain, and multiple field channels are fused as multimodal measurements to improve localization accuracy. We formulate the problem within a Rao-Blackwellized particle filter (RBPF) that partitions the vehicle state into a nonlinear component sampled by particles and a linear sensor bias component tracked analytically via per-particle Kalman filters. This factorization reduces the required number of particles compared to a standard particle filter while accounting for realistic sensor drift. Simulation studies on both PDE scenarios show that the RBPF consistently outperforms a standard particle filter in terms of final position error and Root Mean Square Error (RMSE) across varying particle counts. Field experiments with an autonomous surface vehicle measuring salinity, temperature, and dissolved oxygen validate that PDE-governed environmental fields provide sufficient spatial variability for practical localization. Related experimental videos are available at https://localization-environmental-pdes.github.io/.

Reinforcement learning (RL) finetuning significantly enhances the reasoning capabilities of large language models (LLMs), yet its effectiveness critically depends on selecting prompts of appropriate difficulty for the current policy. This is challenging because prompt difficulty evolves throughout training. Existing online methods therefore face a trade-off: evaluation-based approaches are accurate but expensive, while prediction-based approaches are efficient but typically assume stationary difficulty, making them ill-suited to RL's non-stationary training dynamics. To address these issues, we propose a Kalman-Guided Prompt Selection method (KGPS), which reformulates prompt selection as a dynamic state estimation problem rather than static difficulty prediction. KGPS models each prompt's latent success rate in logit space using a linear-Gaussian state-space model, with process noise coupled to the magnitude of policy updates so that uncertainty increases when the policy changes more substantially. A Kalman filter then maintains a calibrated Gaussian posterior over prompt difficulty, and prompts are selected by maximizing a posterior-expected training utility that favors intermediate-difficulty prompts while naturally revisiting uncertain ones. The resulting procedure is adaptive to policy drift and requires no additional rollouts beyond standard policy training. Extensive experiments across mathematics, planning, and geometry reasoning benchmarks, as well as multiple RL algorithms, show that KGPS consistently improves both final accuracy and rollout efficiency over strong baselines, establishing state-of-the-art performance among online prompt selection methods. For example, on DeepSeek-R1-Distill-7B, KGPS uses 83% fewer rollouts than DS while even improving the average performance by 0.12 point across six math reasoning benchmarks.

Attitude estimation based on inertial sensing requires measurements of local angular velocities and local gravity via gyroscopes and accelerometers. However, during the motion of a mobile system the inertial measurement unit (IMU) will be subject to additional accelerations which skews the measurement of local gravity. This effect gets amplified the further away the IMU is from the base of the system. Many attitude estimation filters, such as "Madgwick" or "Mahony", account for this by relying more on gyroscope integration for periods of high angular velocity. However, this approach is prone to accumulate long term error especially around the gravity vector. In this work we utilize the gyroscope measurements to compensate the additional accelerations induced by the motion of the system, i.e., centripetal- and tangential-accelerations. Additionally, we introduce a calibration method that estimates intrinsic IMU parameters such as axes misalignment, bias, scale, as well as the extrinsic base-to-IMU vector without the necessity for additional external equipment. Our evaluation in simulation as well as in the real-world shows that this method improves any attitude filter that relies on the direction of gravity. Furthermore we demonstrate the effectivenes on highly dynamic systems, and systems that are unable to put the IMU at the center of rotation, using our real-world spherical mobile mapping system.

Repeated human-robot interaction (HRI) requires proactively accounting for humans who continually adapt to evolving beliefs about the robot. Prior frameworks often treat encounters as isolated events, suffering cumulative task performance decay as human perception drifts, or maintain long-term influence through erratic, unpredictable behavior that erodes perceived human trust and relies on computationally unscalable formulations. To address these gaps, we introduce the Belief- Aware Influence and Trust (BAIT) controller. BAIT integrates a hierarchical particle filter, which infers both fast human strategic shifts and slow perceptual belief updates, with a belief-aware Model Predictive Path Integral planner. BAIT explicitly optimizes the trade-off between long-horizon influence and human trust, while enforcing immediate task performance as a strict constraint. Across simulations, a human-subject study, and a real-world GEM vehicle deployments in repeated lane-merging scenarios, BAIT achieves task performance comparable to baselines that optimize long-term influence through unpredictability while yielding significantly higher user trust. The video demonstrating our experiments is available at https://youtu.be/9o4GqKLWDCw.

This work investigates uncertainty decomposition and explainability in a deep learning-based framework for gyroscope bias correction. A 1-D Convolutional Neural Network is trained to predict residual angular rate corrections from multi-sensor inputs, including gyroscope and star tracker measurements. The bias corrections are sent to a flight-representative Gyro-Stellar Estimator. The network produces both mean corrections and input-dependent (heteroscedastic) aleatoric uncertainty, while epistemic uncertainty is estimated via an ensemble of independently trained models. The proposed approach is trained under nominal conditions and evaluated in both nominal and structured perturbations that include additive and temporally correlated noise. Gradient-based attribution methods are applied to both the correction and uncertainty outputs, enabling a decomposition of the evidence that drives state updates and uncertainty estimates. By aggregating attribution patterns across rotational axes and regimes, we reveal axis-specific behaviors and characterize how structured perturbations influence the collaboration between aleatoric and epistemic uncertainty. Uncertainty analysis shows that aleatoric uncertainty increases with perturbation intensity, but the distributions overlap and the calibration is not consistent across regimes. On the other hand, epistemic uncertainty gives a clear signal that gets clearer as the distributional shift happens, showing that the models disagree more. These results show that aleatoric and epistemic uncertainty work well together and that epistemic uncertainty is better at distinguishing between nominal and perturbed operating conditions. The results provide insight into the behavior of hybrid learning-based state estimation components and motivate the use of uncertainty for downstream monitoring and fault detection.

The presence of UAVs in military operations has recently increased, also increasing the demand for defense systems against UAV attacks. UAVs can also be used as countermeasures. Most available methods rely on UAV-to-UAV communication and global positioning. However, such resources may not be available in modern warfare scenarios. To address these limitations, we propose a pipeline for ground-target protection against UAV attacks that employs autonomous swarms of UAVs. We assume a communication- and GPS-denied environment in which the UAVs use onboard sensors to track the target and coordinate as a swarm. We developed Kalman filters to estimate the states of unknown targets and the positions of UAVs in the swarm using only relative measurements. Also, our strategy is to encircle the target of interest to maximize coverage. To achieve that, we propose a decentralized swarm encirclement technique that adapts to the target's motion. Our approach was extensively validated using real robots, demonstrating its effectiveness in detecting, encircling, and intercepting hostile UAVs.

In this paper, we present a generalized temporal-difference (TD) reinforcement learning framework based on the theory of conditional expectations. The value and action-value (Q-value) functions are treated as uncertain quantities, and their estimation is formulated as a stochastic inference problem. Unlike classical Kalman-based temporal-difference learning, which relies on linear-Gaussian assumptions, the proposed formulation is derived directly from the conditional expectation framework and naturally extends to nonlinear models and non-Gaussian probability distributions. The proposed method recursively estimates not only the conditional expectation of the value function but also its second probabilistic moment, thereby quantifying the uncertainty associated with the learned value function throughout the learning process. To obtain a computationally tractable algorithm, the stochastic problem is discretized using either polynomial chaos expansions or ensemble-based approximations, providing efficient representations of the underlying random variables. The proposed framework is demonstrated on two optimal control problems: a linear mass--spring--damper system and a nonlinear heat conduction problem in a closed cavity. The numerical examples illustrate the capability of the proposed method to accurately estimate both the value function and its associated uncertainty, while extending classical Kalman-based temporal-difference learning to a broader class of stochastic systems.

PairUAV relative localization maps two UAV images to a polar navigation command. Although heading and range share the same pairwise pose context, treating them as homogeneous coordinates forces both outputs to use the same decoder evidence and optimization state. Controlled readout probes reveal a different structure: the two axes favor different decoder-depth combinations, their best checkpoints disagree on 80.8% of a validation trajectory, and range errors exhibit a distinct high-error tail. We introduce method, Polar Axis-Conditioned Estimation, which retains a shared Reloc3r-style pair representation while assigning axis-specific readout interfaces. Heading uses mid/late relational evidence, whereas range remains attached to a direct late metric path. On the official hidden test, the strongest released raw predictor scores 0.002460; the complementary PAAER predictor scores 0.002514 with a slightly lower angle error. Deterministic challenge packaging, reported separately from learned estimation, yields the final score of 0.001874. Code, checkpoints, predictions, and reconstruction tools are available at https://github.com/zerong7777-boop/PairUAV-PACE.

The deployment of reliable lithium-ion battery management systems is crucial for accelerating electrification, yet the joint prognosis of State of Health (SOH) and Remaining Useful Life (RUL) remains severely hindered by task heteroscedasticity. Conventional multi-task learning frameworks fail to balance the bounded, low-variance noise of SOH estimation with the unbounded, nonlinearly expanding uncertainty of long-term RUL predictions. Here, we present the Rotary SOH-Injected Prior Battery Transformer (RoSIP-Batt), a unified co-estimation framework that resolves these optimization conflicts. By formulating joint prediction as a Bayesian multi-task objective, RoSIP-Batt introduces a homoscedastic uncertainty weighting mechanism to dynamically scale task-specific gradients based on learned residual noise levels. The architecture leverages decoupled dual classification tokens and a per-dimension gated fusion mechanism, secured by a gradient-detachment operator to prevent high-variance RUL updates from corrupting the stable SOH representation space. To capture electrochemical degradation patterns without relying on absolute cycle steps, Rotary Position Embedding (RoPE) is incorporated into a shared Transformer backbone to model translation-invariant relative temporal profiles. Crucially, the intermediate SOH estimate is directly injected into the RUL regression head as a physical degradation prior. Evaluations across the NASA, MIT-Stanford, and HUST datasets show that RoSIP-Batt significantly outperforms state-of-the-art baselines, reducing SOH estimation error to 1.994% MAE on NASA and restricting RUL prediction error to 62.85 cycles on Stanford. These findings establish RoSIP-Batt as a highly generalizable, computationally efficient solution suitable for real-time embedded BMS deployment.

The deployment of reliable lithium-ion battery management systems is crucial for accelerating electrification, yet the joint prognosis of State of Health (SOH) and Remaining Useful Life (RUL) remains severely hindered by task heteroscedasticity. Conventional multi-task learning frameworks fail to balance the bounded, low-variance noise of SOH estimation with the unbounded, nonlinearly expanding uncertainty of long-term RUL predictions. Here, we present the Rotary SOH-Injected Prior Battery Transformer (RoSIP-Batt), a unified co-estimation framework that resolves these optimization conflicts. By formulating joint prediction as a Bayesian multi-task objective, RoSIP-Batt introduces a homoscedastic uncertainty weighting mechanism to dynamically scale task-specific gradients based on learned residual noise levels. The architecture leverages decoupled dual classification tokens and a per-dimension gated fusion mechanism, secured by a gradient-detachment operator to prevent high-variance RUL updates from corrupting the stable SOH representation space. To capture electrochemical degradation patterns without relying on absolute cycle steps, Rotary Position Embedding (RoPE) is incorporated into a shared Transformer backbone to model translation-invariant relative temporal profiles. Crucially, the intermediate SOH estimate is directly injected into the RUL regression head as a physical degradation prior. Evaluations across the NASA, MIT-Stanford, and HUST datasets show that RoSIP-Batt significantly outperforms state-of-the-art baselines, reducing SOH estimation error to 1.994% MAE on NASA and restricting RUL prediction error to 62.85 cycles on Stanford. These findings establish RoSIP-Batt as a highly generalizable, computationally efficient solution suitable for real-time embedded BMS deployment.

This paper presents a method for user-driven robot Learning from Demonstration (LfD) that reduces user effort while ensuring compliant and precise reproduction. The method eliminates repeated teaching for the same task and enables real-time learning from a single demonstration. Demonstrated motions are reproduced with high precision, while impedance variations are learned in real time to provide both compliance and robustness against perturbations. This mitigates potential safety issues in Human-Robot Interaction (HRI) that arise from conventional time-indexed trajectories lacking compliance. The proposed approach integrates a three-dimensional (3D) Fast Diffeomorphic Matching (FDM) algorithm with a Dynamical System (DS)-based motion generator to achieve real-time single-shot demonstration learning and reproduction. An Extended Kalman Filter (EKF) framework compensates for reproduction errors and recovers from external interactions. Furthermore, an impedance parameterization function is incorporated to learn impedance variations from demonstrations and maintain surface contact for specific applications. The proposed approach is validated through comprehensive experiments on a 7 Degree-of-Freedom (DOF) KUKA LWR IV+ robot.

Accurate articulation angle estimation of trucks with trailers is critical for autonomous driving and advanced driver assistance system (ADAS). Existing methods either require manual initialization, additional sensors, or prior knowledge and signals from trailers, or they lack real-world validation, limiting practical deployment. This paper presents multiple learning-based models to directly estimate articulation angles from visual and kinematic inputs, eliminating the need for dedicated driving maneuvers for initialization, bounding box annotations, trailer-mounted sensor signals, or prior knowledge of trailer parameters. Two learning-based models are integrated with a kinematic model within an extended Kalman filter (EKF) framework, and an adaptive weighting scheme based on uncertainty quantification is applied for measurements involving visual input. Extensive real-world experiments with different trailer types demonstrate the approaches' robustness and generalization under out-of-domain conditions, including new trailers, varying colors, and lighting conditions. Results show that the hybrid method achieves accurate and reliable articulation angle estimation while maintaining reduced implementation requirements and practical deployment advantages.

Ultra-Wideband (UWB) ranging has become a viable option for industrial Autonomous Mobile Robot (AMR) localization due to improved accuracy and low cost. However, real-world deployments remain limited by two recurring challenges: calibrating static anchors can be time-consuming and error-prone, and integrating UWB with existing onboard sensors requires careful design to ensure robust and consistent pose estimation. Addressing these challenges, this paper presents an end-to-end pipeline that combines automatic anchor calibration with a generic multi-sensor estimator tailored to surface-bound vehicle motion. It targets existing AMR stacks in scenarios where robot pose priors are available for initialization. The calibration stage estimates anchor positions and range biases, while the localization stage fuses UWB with proprioceptive sensing in a bias-aware Extended Kalman Filter to improve consistency without extensive parameter tuning. Experiments on a commercial logistics AMR in a warehouse setting demonstrate accurate positioning indoors and across outdoor transitions, with improved consistency compared to an earlier estimator formulation. Evaluation on an independent forklift dataset further indicates transferability to other platforms. The method remains effective in test cases with limited line-of-sight and sparse anchor coverage. These results show that UWB localization can be deployed with substantially reduced manual effort while preserving the accuracy required for industrial AMRs. The collected warehouse dataset is made publicly available.

Battery health estimation is fundamental for battery management in battery-powered systems, where inaccurate health states may affect control, maintenance, and service life. It becomes even more critical in intelligent connected systems, where estimation errors can propagate across interconnected devices and downstream decisions. In this paper, we propose TIDE, a trustworthy and interpretable battery degradation estimator for reliable battery health estimation. TIDE jointly considers accuracy, trustworthiness, and interpretability, which are all essential for practical deployment and downstream decision making. To realize these objectives, TIDE combines battery-domain knowledge with operational measurements in a three-component backbone. A knowledge-guided degradation prior promotes trustworthy estimation, a monotone residual component provides interpretable aging-consistent refinement, and a contextual learning component captures battery-specific operational effects for improved accuracy. The trained backbone is then distilled into a compact symbolic surrogate to provide model-level interpretability and support deployment. Experiments show that TIDE achieves strong estimation accuracy, improving overall estimation fidelity by an average of 19.7% over representative baselines. Its knowledge-guided prior and monotone residual modelling substantially reduce aging-consistency violations, supporting trustworthy estimation. Meanwhile, the backbone enables component-level interpretation, while symbolic distillation provides a compact model-level representation of the learned estimation logic. These results support the practical use of TIDE for battery health monitoring and decision support in intelligent connected systems.

Quorum Sensing (QS) is a key capability for robot swarms, useful for coordination of activities at the group level. Effective communication is instrumental for individuals to estimate the quorum level of the entire swarm. Anonymous communication protocols where individuals exchange local information without revealing unique identities are helpful to support quorum estimates by sampling information from neighbours and maintain scalability of the QS process. However, because anonymous protocols cannot distinguish message sources, repeated messages from the same sender may be double-counted, thereby biasing collective quorum estimates. In this study, we introduce a stochastic filtering protocol inspired by $k$-priority sampling to improve estimate stability (\ANTk), and we compare it with a baseline anonymous protocols (\AN) and a randomised variant designed to improve accuracy (\ANT). We find that the baseline protocol \AN provides a parsimonious and fast solution, but remains highly inaccurate due to double-counting bias. The \ANT variant improves accuracy but suffers from information inertia, resulting in slower convergence. Finally, actively filtering the message buffer via the \ANTk protocol successfully decreases temporary errors and stabilises the estimate, at the cost of an increased time of recovery from errors.

Surgical tissue retraction requires effective manipulation planning under partial and noisy perception. We study state estimation for deformable tissue retraction, where only sparse observations of the tissue surface are available at decision time. We propose a learned state estimator that reconstructs the full deformable mesh state from 40 noisy vertex observations. The estimator combines a multilayer perceptron with a low-dimensional PCA latent representation and is trained using geometry-aware regularization that encourages smooth and physically plausible deformations. We evaluate the approach in a 2D deformable sheet simulation using single-step and multi-step retraction planning. Results show that the learned estimator achieves 98.1% of oracle performance in multi-step retraction while supporting efficient inference. These results demonstrate that learned, geometry-regularized state estimation can support effective deformable manipulation under realistic perception constraints.

LiDAR-inertial odometry (LIO) is a key component of autonomous navigation, but high-dynamic driving exposes two coupled challenges: intra-scan motion distortion and vibration-contaminated inertial measurements. Most real-time LiDAR-inertial pipelines propagate the system state by integrating raw IMU measurements and then use the propagated trajectory for point cloud de-distortion, thereby propagating inertial noise into both the corrected scan and the subsequent scan-to-map registration. This paper presents WNOJ-LIO, a LiDAR-IMU fusion framework based on a White-Noise-on-Jerk (WNOJ) Extended Kalman Filter (EKF). WNOJ-LIO employs a decoupled WNOJ prior on $\R^3 \times \SO(3)$ for state prediction and treats the IMU as a high-frequency measurement source rather than the driver of state propagation. The resulting posterior state history is then used for LiDAR scan de-distortion and subsequent point-to-plane LiDAR updates. The decoupled process model enables closed-form covariance propagation, thereby bridging the gap between batch WNOJ Gaussian process (GP) trajectory priors and recursive filtering. Simulation results demonstrate improvements in acceleration and angular-velocity denoising, scan de-distortion, and localization accuracy over a FAST-LIO-style baseline. Real-world experiments were conducted using an autonomous racing car on four driving segments with maximum speeds ranging from 53 to 208~km/h, covering a wide range of vehicle vibration levels. The experiments further validate the proposed method and provide a comprehensive evaluation of its performance in estimating acceleration, angular velocity, body-frame linear velocity, attitude, and position under highly dynamic driving. The source code of WNOJ-LIO is publicly available at https://github.com/LvJohny/wnoj-ekf-lio.git.

Data assimilation estimates the state of a dynamical system from model forecasts and incoming observations. Many observation mechanisms, however, are many-to-one, implicit, non-smooth, or accessible only through simulation, and need not provide the residual structures or likelihood guidance required by existing ensemble filters. We introduce implicit data assimilation, in which the analysis law is defined as an energy tilt of the forecast distribution. We then propose the Ensemble Controlled-flow Filter (EnCF), which realizes this update through a stochastic controlled flow and learns the observation-dependent control by adjoint matching from terminal energy gradients. For simulator-defined observations, EnCF-LF learns a surrogate conditional energy from samples and applies the same controlled-flow solver. We prove ideal exactness, derive a one-step error decomposition, and establish non-accumulation of local errors under filter stability. Numerical results show that Kalman-type filters remain preferable for smooth additive-Gaussian observations, while the proposed methods are better suited to non-Gaussian, many-to-one, multimodal, and implicit observation models.

Thermal infrared (TIR) imaging is essential for UAV swarm operations in visually degraded environments. However, tracking tiny UAVs remains challenging due to limited appearance cues, frequent occlusions, and rapid maneuvers. Despite significant progress driven by benchmarks such as the Anti-UAV challenge, existing methods primarily prioritize accuracy while overlooking the computational constraints of real-time edge deployment. The standard Kalman Filter (KF) offers the efficiency required for edge devices, yet its constant-velocity assumption often breaks down under highly dynamic UAV motion and thermal sensor jitter. More sophisticated nonlinear estimators can improve robustness but often introduce additional computational costs. To address this gap, we propose an edge-aware online tracking pipeline centered on the Adaptive Kinematic Kalman Filter (AKKF), which augments the linear KF with state-dependent kinematic modeling while preserving real-time efficiency. Combined with transient false-positive suppression and kinematics-driven predictive coasting, the presented pipeline improves trajectory continuity under challenging TIR conditions. Experiments on the Beyond Strong Baseline (BSB) benchmark provide a starting point for edge-aware UAV tracking by jointly evaluating tracking performance and computational efficiency, offering insights toward future real-time deployment.

This paper investigates the control of discrete-time linear time-invariant (LTI) systems subject to incomplete and corrupted measurements. Specifically, we focus on designing a Linear Quadratic Gaussian (LQG) controller without relying on explicit state estimation. By leveraging minimum variance duality, our approach allows the current control input to be represented as a linear function of available measurements and previously applied inputs, successfully reducing the task to a tractable deterministic optimization problem. We provide theoretical justification for this framework and demonstrate its practical effectiveness through numerical experiments.

Sensor-rich data-driven applications increasingly use Bayesian approaches to infer latent states of dynamic systems from noisy sensor measurements and physical models. Yet the computation of the likelihood remains an essential bottleneck for accurate posteriors and performant inference. This paper presents a Bayesian filtering technique that uses processor-native uncertainty tracking for both uncertainty propagation and inference. The technique implements deterministic hierarchical importance restructuring through a native operation, giving deterministic latency and bounded memory use for arbitrary models written as program code. Benchmarks across three nonlinear state-space systems compare the approach against particle filters and Monte-Carlo-based likelihood estimators. The technique enables deterministic approximate filtering with as high as 805$\times$ average speedup against direct Monte Carlo work at matched result quality for model evaluation, and Pareto-dominant accuracy-latency trade-offs for posterior inference while remaining competitive in RMSE with baseline particle filters.

Underwater dead reckoning estimates vehicle position when vision is unavailable and external positioning cannot be assumed. A single set of filter parameters can work well in many situations, but fixed tuning may be poorly matched during turns, motion transitions, or periods when sensor measurements are less reliable. This paper presents the Situation-Triggered Calibrated Adaptive Robust Extended Kalman Filter for a BlueROV2. An onboard probabilistic trigger identifies the current motion situation while one error-state filter runs continuously. When the trigger is confident, the filter changes only to the corresponding pre-calibrated process- and measurement-noise matrices; the state estimate, covariance history, dynamics, and measurement models are not reset or replaced. The trigger, noise profiles, and a one-time Doppler velocity log yaw-alignment correction are calibrated offline using sparse AprilTag-supervised pool runs. A separate validation set selects the scheduling policy, which is then fixed before held-out testing. Across four held-out pool runs, the method reduces label-weighted mean per-run translation root-mean-square error from 0.488 m to 0.471 m relative to the same filter backbone with one global noise profile, and every held-out run favors the scheduled method. A paired bootstrap over 10-second segments gives a candidate-minus-baseline difference of -0.017 m with a 95% confidence interval of [-0.024, -0.008] m, while orientation error remains essentially unchanged. These results indicate that situation-aware covariance scheduling provides a modest but consistent vision-free dead-reckoning improvement without switching estimators or resetting the filter.

State estimation is essential for quadruped robots, enabling robust locomotion, navigation, and control. While many estimators have been proposed in the literature, existing implementations are often tied to specific robots or software stacks, making fair comparisons difficult. This lack of a general-purpose benchmarking framework hinders reproducibility and slows down algorithmic innovation. In this paper, we introduce Chalito, an extensible MATLAB/Python library for benchmarking filter-based state estimation algorithms in quadruped robots. Chalito imports robot models directly from URDF, supports multiple filtering approaches, and is designed to be easily extended with new methods. The framework runs on both simulated and real datasets, enabling systematic evaluation across robots and filters. To the best of our knowledge, this is the first open-source library exclusively dedicated to benchmarking filtering algorithms for quadruped robots.