State Estimation

While homographies are fundamental to many computer vision tasks, the majority of conventional estimation techniques provide only point estimates without directly quantifying uncertainty introduced by noisy observations. Uncertainty, though, propagates to subsequent processing steps such as camera calibration and 3D reconstruction and is particularly relevant in safety-critical and socially relevant fields including medical imaging, autonomous driving, and defense. We present a fast Bayesian formulation for homography estimation from point correspondences that explicitly incorporates measurement uncertainty and prior knowledge while providing a posterior distribution over the homography parameters. A closed-form solution of the posterior mean of the homography is derived in homogeneous coordinates and supplemented by an iterative Bayesian approach to handle non-linearities. Synthetic experiments demonstrate the applicability to projective transformations and show improved estimation accuracy over DLT under varying noise conditions. Image stitching experiments further demonstrate applicability to real image correspondences while additionally providing uncertainty information.

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.

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.

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.

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.

Robotic systems must operate under uncertainty while satisfying complex task and safety specifications. Monitoring such specifications under uncertainty remains challenging, as existing formulations typically require extensive data or explicit uncertainty distributions. In this paper, we propose a real-time monitoring framework that reduces data requirements by leveraging data-driven reachable sets for specification evaluation. We instantiate the framework for maritime navigation, where complex specifications arise from traffic rules. We develop a data-efficient pipeline for constructing reachable sets and derive a monitoring formulation suitable for real-time deployment. Simulation and hardware experiments demonstrate robust monitoring under realistic disturbances, achieving improved risk detection compared to state-of-the-art metrics.

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 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.

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.

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.

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.

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.

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.

Dynamic environments remain a fundamental challenge for visual SLAM, where unreliable observations from moving objects and rapid motion degrade state estimation accuracy. Although event cameras preserve fine-grained spatio-temporal information, most existing event-based SLAM frameworks still assume static scenes and lack approaches to estimate the reliability of features. To this end, we propose PLED-VINS, a monocular event camera-based visual-inertial SLAM framework that enables robust state estimation in dynamic environments. We propose an entropy-recency score map to characterize the temporal reliability of both point and line features based on event temporal statistics. Concurrently, geometric reliability is estimated via a unified point-line robust bundle adjustment. Building upon these, we design an adaptive weighting strategy that fuses temporal and geometric reliability, including motion-conditioned reliability modeling for line features, to suppress unreliable observations. Experimental results demonstrate that PLED-VINS improves state estimation on the evaluated dynamic sequences with moving objects.

A learning-enabled disturbance-rejection framework based on a Neural Extended State Observer (Neural-ESO) is presented in this letter. Unlike existing learning-based control methods that largely rely on the learned model once deployed, Neural-ESO adopts a dual-pathway architecture: a predictive pathway uses a neural network to provide a feedforward disturbance estimate that accelerates convergence, while a corrective pathway employs a conventional ESO to compensate prediction errors and prevent over-reliance on the neural component. Using Lyapunov theory and a small-gain analysis, we show that enforcing a Lipschitz bound on the learning component guarantees uniform ultimate boundedness of the closed-loop error dynamics. The proposed framework is validated on a quadrotor landing task subject to strong ground-effect disturbances across normal and out-of-distribution scenarios, demonstrating accuracy-robustness trade-off and greater operational reliability during training, deployment, and transfer compared with state-of-the-art baselines.

In many multisensor systems, measurements from different sensors are subject to unknown relative time delays. Accurate state estimation requires that delays be accounted for and, when possible, calibrated online. We consider the case of aided navigation, where measurements from a single aiding sensor are subject to an unknown but constant delay relative to the inertial measurement stream, and study the identifiability of the resulting system. Critically, identifiability depends not only on the temporal structure of the measurements, but also on the shape of the vehicle trajectory: some trajectories are sufficiently informative to support unique recovery of the delay and the navigation state, while others are not. Using the special Galilean group, we characterize these uninformative (or degenerate) trajectories and relate them to a continuous symmetry of the delayed measurement model, providing geometric insight into identifiability failures. We show that the class of trajectories for which identifiability fails is larger than previously reported, and connect our characterization to the familiar linearized, Jacobian-based analysis. Although our development is motivated by aided navigation, the underlying ideas apply more broadly to estimation problems on Lie groups with delayed measurements.

The accuracy of consumer-grade inertial navigation is bottlenecked by the stochastic noise of Micro-Electro-Mechanical Systems (MEMS). Traditional deterministic neural architectures often succumb to ``estimation jittering,'' sacrificing high-frequency kinematic fidelity for numerical stability. We propose PedestrianDiffusion, a multimodal spectral-domain generative framework reformulating dense 6D state estimation as a continuous conditional denoising process. By operating in the frequency domain, our formulation bounds the spectral covariance, acting as a mathematical preconditioner to stabilize the reverse diffusion trajectory. Furthermore, we introduce a zero-shot semantic conditioning mechanism leveraging vision-language embeddings as categorical priors to generalize across heterogeneous sensor noise profiles. To address the computational intractability of generative tracking, we deploy a single-step deterministic probability flow ODE solver ($T=1$). This yields high-capacity asynchronous batch trajectory refinement, establishing the viability of generative architectures for asynchronous batch trajectory refinement on edge hardware. Extensive evaluations on the OxIOD, RIDI, RoNIN, and TLIO benchmarks demonstrate that PedestrianDiffusion achieves state-of-the-art performance, exhibiting unprecedented robustness to impulse perturbations and coupled 6D kinematic drift. This work provides a rigorous algorithmic blueprint for next-generation Neural Inertial Measurement Units (N-IMUs).

Distributed trajectory estimation arises in many applications across robotics, but existing implementations typically do not consider asynchrony in agents' communications and computations. Therefore, we propose an asynchronous block coordinate descent algorithm for distributed trajectory estimation. We consider a team of agents that observes a team of robots and estimates the robots' states over a sliding window. The agents solve an approximation of the maximum a posteriori estimation problem, which we derive. We show this approximation introduces negligible errors and eliminates up to 96.9% of communications among agents. Next, we prove that agents' iterates converge exponentially fast to the optimal estimate of the robots' states. Simulations show that this approach has up to 64% less error than a comparable state-of-the-art algorithm. Experiments on mobile robots show this approach is robust to delays whose lengths span three orders of magnitude.

Domain adaptive visual object tracking under adverse weather conditions has garnered significant attention in recent years. Despite the impressive performance, existing methods heavily rely on the large-scale video frames from both source and target domains, which is impractical under rigid resource constraints where source data is unavailable. To overcome this limitation, we propose SFDATrack, a generalized source-free domain adaptive tracker that merely leverages adverse weather samples from the target domain for robust state estimation. Specifically, SFDATrack first employs a mean-teacher backbone with Dual Interactive Mamba (DIM) blocks to distill the candidate target tokens that are resilient to weather variations from classified, augmented samples. Afterwards, we introduce a hyperspherical prototype projection (HPP) module to project these tokens onto multi-domain prototypes within a latent hyperspherical space. By enforcing both domain-specific and domain-invariant properties of the multi-domain prototypes, SFDATrack can be seamlessly adapted to diverse weather conditions with powerful generalizability. Extensive experiments evaluated on various benchmarks demonstrate that SFDATrack achieves superior performance compared to state-of-the-art approaches. The code is available at https://github.com/watcherBR0/sfdatrack.

Use of quadrotor UAVs for wind velocity estimation is gaining popularity in recent studies, leveraging their maneuverability, compact size and low cost. Among available approaches, model-based wind velocity estimation is most commonly used, since it relies only on onboard sensors. However, as the quadrotor is a highly nonlinear system, thus making this task challenging. This study evaluate the use of both discrete and continuous dynamic equations of the quadrotor UAV for wind velocity estimation on SE(3), rather than commonly adapted continuous or discretized form. Lie Group Variational Integrator, developed on discrete Lagrangian is used as the discrete model without any approximation or discritization. The study assess both the discrete and continuous form of the quadrotor dynamics on SE(3) using Extended Kalman filter (EKF), and Unscented Kalman filter (UKF). The quadrotor UAV performance is evaluated in both MATLAB-based numerical simulations and free outdoor flight. The numerical simulations are conducted during both hovering and trajectory-tracking flights. Results demonstrate that, by using discrete SE(3) dynamics coupled with UKF, the quadrotor achieves higher estimation accuracy while maintaining trajectory tracking, even with low-cost sensors. These findings highlight the potential of discrete quadrotor models with UKF not only for wind velocity estimation but also for other high-accuracy tasks, even when relying on low-cost onboard sensors.

Standard stereo VIO focuses exclusively on the benefit of metric scale via single-spectrum baselines, often overlooking the risks of spectral redundancy. This structural limitation leads to correlated failures, where both sensors simultaneously fail in degraded environments that affect their shared spectrum. Leveraging a cross-spectral system presents a complementary solution to this issue, yet the significant appearance gap between modalities renders standard matching ineffective. Existing deep learning-based matchers, while effective, introduce inference latencies that violate real-time constraints. To bridge this gap, we present an asynchronous real-time cross-spectral visual-thermal-inertial (VTI) system that temporally decouples high-latency deep matching from high-rate state estimation. Our architecture incorporates a spectral-aware weighting scheme that dynamically balances modality reliance based on photometric entropy and thermal noise, ensuring robustness against both abrupt lighting changes and thermal artifacts. Furthermore, we introduce a seamless handling mechanism for thermal Non-uniformity Correction (NUC) to maintain tracking continuity. Extensive experiments across diverse scenarios confirm that our system overcomes spectral redundancy, yielding superior accuracy in nominal daylight while ensuring robustness in visually degraded environments. We will open source our code and data: https://github.com/seungsang07/cross-spectral-stereo-inertial-odometry

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving nonlinear partial differential equations (PDEs), including battery electrochemical models. They typically en-force conservation laws within the loss function to ensure physically consistent solutions. Tradi-tional numerical methods such as finite difference, finite volume, and finite element techniques, re-ly on discretization and can be computationally expensive for nonlinear systems. To address this challenge, PINNs offer improved scalability, particularly for reduced-order models like the single particle model with electrolyte (SPMe). The SPMe describes lithium-ion battery dynamics through coupled diffusion, transport, reaction kinetics, and voltage equations. Despite these advantages, training SPMe-based PINNs from scratch for different battery chemistries or operating conditions is demanding and often leads to slow convergence. To overcome this limitation, this work introduces a transfer learning framework for SPMe-PINNs. The model is first pretrained to learn general elec-trochemical dynamics and then adapted to a target battery by transferring weights, freezing se-lected layers, and fine tuning the remaining parameters, including estimating key electrochemical variables. Validation using PyBaMM demonstrates accurate voltage prediction, indicating that the proposed approach preserves electrochemical consistency while reducing training time and ena-bling efficient generalization across batteries.

Robotic table tennis has emerged as a compelling benchmark for real-time robotic perception due to its fast ball dynamics and stringent timing requirements. Accurate, high-frequency, and low-latency ball state estimation is critical for reliable trajectory prediction and timely control. Traditional frame-based cameras face an inherent trade-off: low frame rates leave temporal blind spots that miss fast-moving objects and high frame rates raise data and computational cost. Event cameras instead offer microsecond temporal resolution and, under sufficient illumination, remain largely free of motion blur even at high ball speeds. However, the community lacks large-scale datasets to develop and benchmark event-based perception in realistic sports scenarios. We address this gap by introducing the first large-scale event-camera dataset for table tennis, comprising over 1000 rallies from a diverse group of players ranging from amateurs to elite-level athletes. Each recording captures the event stream alongside 14 synchronized high-speed frame-based cameras at 200 FPS, which we use to produce 1 kHz pseudo ground-truth labels for ball position, velocity, and spin. Building on this dataset, we train a convolutional neural network robust to background player motion that jointly estimates the ball's position and velocity in the image-plane from events. Treating the predicted velocity as an additional measurement in the Kalman filter reduces bounce-point prediction error by 36% relative to a position-only baseline. Finally, we close the perception-action loop by integrating the event-based system with a Stäubli robotic arm, enabling the first real-time human-robot table tennis rallies driven by event-based perception.

An invariant extended Kalman filter (IEKF) is developed for state estimation of serial rigid manipulators with an arbitrary number of links, formulated entirely within the Lie group SE(3). The group-affine property of the kinematic equations makes the linearised error dynamics autonomous, so the Riccati equation governs the true error covariance rather than a local approximation. A physically separated noise model treats gyroscope and accelerometer channels independently: the accelerometer provides translational twist via gravity-compensated integration, yielding a measurement covariance that scales with the sample interval in exact analogy with process noise discretisation; a state-dependent Coriolis noise term captures gyroscope noise propagating through the nonlinear dynamics, vanishing at rest and growing with twist magnitude. The filter is structured as a modular chain of per-link IEKFs in which the predicted covariance of each link depends on its predecessor only through the Adjoint-transformed posterior, giving linear computational cost in link count. Exponential ultimate boundedness in mean square is established via a Lie algebra Lyapunov function, with per-link bounds chained through the Adjoint operator norm to yield a stability certificate that is modular and scalable to arbitrary chain length. Numerical results validate the design.

We study trajectory optimization in mobile sensing systems that must identify which member of a finite candidate set is the true target, while maintaining reachability to all potential candidate targets, under resource constraints. Deferred-Decision Trajectory Optimization (DDTO) addresses this setting by computing trajectories that reach individual targets but remain coincident for as long as possible before separating toward different targets. We propose Active-Sensing DDTO (AS-DDTO), which extends DDTO by adding a trajectory-dependent information-acquisition term to the planning objective. The resulting planner maintains reachability to candidate targets while biasing the coincident portion of the trajectories toward regions that enable earlier target identification. The framework supports Bayesian updates and conformal candidate-set updates for distance-dependent sensing. We derive a mixed-integer conic reformulation and provide guarantees on recursive feasibility, belief concentration, and fixed-time coverage for the raw conformal candidate set. Numerical simulations show improved target identification compared with standard DDTO under distance-dependent sensing uncertainty and limited sensing budget.

Trajectory prediction allows autonomous vehicles to anticipate the future behavior of surrounding objects (or agents) and, accordingly, maximize the safety and efficiency of their driving. State-of-the-art Transformed-based interaction-aware trajectory prediction models, which rely on attention mechanisms to capture multi-agent interactions and maximize prediction accuracy, are commonly trained and evaluated on long-range high-quality datasets. These datasets are typically obtained by aggregating data from multiple vehicles or drones and removing any object detection or tracking noise offline. Yet, information about a surrounding object's state (its position, speed, heading) is far from being noiseless in real-world deployments. Object state estimation is affected by perception uncertainties and localization errors that can be particularly large for objects received via Vehicle-to-Everything (V2X) communications. In this paper, we analyze the impact of noisy object state information on the trajectory prediction accuracy of a state-of-the-art Transformer-based interaction-aware trajectory prediction model. Our study demonstrates that trajectory prediction accuracy can rapidly deteriorate as the noise intensity increases. Numerical results show that the prediction accuracy can reduce by a 1.3x factor under small noise levels and by as much as a 3.9x factor under the highest (yet realistic) noise conditions. These findings reveal the strong sensitivity of trajectory prediction models to noisy data, underscoring the need for more realistic training and evaluation datasets as well as noise mitigation strategies.

In this paper, we present a fully discrete approach for the accurate and numerically efficient dynamical modeling and state estimation of continuum robots. The model is based on geometrically exact beams in a minimal, strain-based formulation and derived in the framework of Lie group variational integrators, allowing to preserve important geometric properties that we exploit to achieve high accuracy and numerical efficiency. We then propose a disturbance observer based on an extended Kalman filter formulation that reliably estimates system states as well as model uncertainties and external disturbances. Experiments on a real system validate the accuracy and efficiency of the proposed model and observer.

Sensor measurements are frequently corrupted by outliers and non-Gaussian noise. These imperfections in the sensor data can cause classical state estimators to generate biased and unreliable state and uncertainty estimates. Robust estimators reject or downweight outliers but do not perform measurement covariance estimation, whereas joint state and covariance estimators assume Gaussian residuals and fixed loss shape parameters. Integrating these two capabilities into a single framework is an opportunity to simultaneously estimate both state and covariance in the presence of outliers. This paper proposes a unified Block-Coordinate Descent framework that combines a norm-aware adaptive robust loss, an Iteratively Reweighted Least-Squares state update, and a Minimum Weighted Covariance Determinant covariance estimator, yielding a self-tuning joint state and covariance estimator. The framework is evaluated in a Monte-Carlo simulation and on real-world ultra-wideband localization experiments in cluttered non-line-of-sight environments. Results show that the proposed estimator consistently recovers the true inlier measurement covariance and matches or exceeds the state estimation accuracy of all baselines, without requiring any manual parameter tuning.

A precise state estimate is crucial for a tight feedback control that enables agile and near-obstacle flights of UAVs. The state-of-the-art methods fuse slow pose measurements with high-frequency inertial measurements to obtain a precise state estimate. However, the inertial measurements from the IMU onboard the UAV are degraded by vibrations from spinning propellers and the precision of the estimated state suffers. We propose a novel approach based on the preintegration of accelerations obtained from motor speeds. We show that the accelerations obtained in this manner can be used for state propagation on their own to achieve better precision without including the IMU. Further, we propose a factor composed of the preintegrated motor speeds that can be directly employed in factor graph optimization frameworks. We combine our factor with LiDAR measurements into the proposed Motor Angular Speed LiDAR Odometry (MAS-LO) algorithm for precise state estimation, which we open-source. Lastly, we evaluate the estimation precision against a state-of-the-art inertial algorithm LIO-SAM to show 28% improvement in position and 65% in velocity estimation accuracy, 14% lower measurement lag, and high robustness to wrong parameter values.

To address cumulative localization drift of unmanned ground vehicles in structured road environments under severe Global Navigation Satellite System signal occlusion, this paper proposes a robust route-constrained state estimation method. During periods without satellite signals, the proposed method establishes the correspondence between the historical dead reckoning trajectory and local segments of the mission route extracted from a high-definition map, and estimates a route-referenced position via a two-dimensional rigid transformation. The estimated position is then formulated as a pseudo-position observation and incorporated into an Extended Kalman Filter update. In this way, route constraints at the road level can be continuously injected into a unified state estimation framework, thereby suppressing position deviation relative to the mission route while indirectly improving azimuth estimation. To enhance practical applicability, engineering strategies, such as trigger control, matching quality validation, route offset compensation, and single update correction limiting, are further introduced. Experiments in three representative scenarios, including a long tunnel, a multi-segment tunnel, and a curved tunnel, show that the proposed method effectively suppresses error accumulation during satellite outages, reduces the risk of large maximum deviation, and improves localization continuity and road-level usability.

Robust state estimation and mapping in long-term, large-scale, and highly dynamic environments remains a key challenge in robotics. Existing LiDAR-Inertial-Visual Odometry (LIVO) systems achieve strong local accuracy but suffer from accumulated drift over long distances and may fail in geometrically degraded or textureless scenes. Meanwhile, GNSS-aided fusion frameworks often rely on LiDAR or visual odometry for state prediction and outlier rejection, making them vulnerable when odometry degenerates. To address these limitations, we propose a tightly coupled LiDAR-Inertial-Visual-GNSS fusion framework based on an Error-State Iterated Kalman Filter. An online spatiotemporal alignment module using Dynamic Time Warping is introduced for highly dynamic conditions. To better exploit GNSS precision, we develop observation models based on Doppler shifts and fixed-anchor Time-Differenced Carrier Phase, providing millimeter-level relative constraints without augmenting historical anchor states. We further design a degeneracy-aware dual-mode outlier rejection strategy that switches between LIVO-prior-guided rejection and GNSS-aided recovery according to the LIVO degeneracy level. Experiments on the public M3DGR dataset and a custom 20~m/s fixed-wing UAV dataset demonstrate that our system reduces accumulated drift and map ghosting, outperforming state-of-the-art methods in accuracy and robustness.

Autonomous fall recovery is a critical capability for quadrotors operating in real-world environments, where collisions or failures may leave the vehicle resting on the ground in an arbitrary attitude. This problem is challenging because recovery must be achieved under limited onboard sensing, in constrained free space, with ground contact, and in the presence of unknown disturbances. In this letter, we present an RL-based framework for autonomous fall recovery of a quadrotor from arbitrary ground attitudes to stable hover using only lightweight onboard sensors. To address severe partial observability and intermittent sensor invalidity, we train a recurrent policy within an asymmetric actor--critic architecture, leveraging an Incremental Nonlinear Dynamic Inversion (INDI) controller to track the policy output. Combined with high-fidelity simulations of motor response and optical flow, the overall training framework significantly reduces the sim-to-real gap. Simulation ablation studies validate the importance of the main design choices, while real-world experiments demonstrate zero-shot transfer and robust recovery under different initial attitudes, wind disturbances, and additional payloads. These results demonstrate that agile quadrotor fall recovery can be achieved without explicit state estimation using only limited and unreliable onboard sensing.

Reliable state estimation in robotics and control re quires balancing estimation accuracy against computational cost. While filtering-based methods such as the Extended Kalman Filter (EKF) provide efficient real-time updates, and optimisation based formulations using factor graphs improve global consistency, the role of optimisation scheduling is often treated implicitly rather than examined as an explicit design variable. This paper presents an experimental study that explicitly isolates optimisation scheduling using a Smart Scheduled Hybrid (SSH) EKF-FGO framework as a controlled testbed. By combining EKF-based state propagation with periodically invoked batch optimisation and holding solver structure and effort fixed, the main contribution of this work is the experimental characterisation of optimisation scheduling as an independent design variable governing the trade-off between intermediate estimation accuracy and computational cost. Simulation results in a planar SLAM environment show that scheduling strongly influences pre optimisation drift, transient error behaviour, and runtime. In particular, the results identify operating regimes in which most of the benefit of global optimisation can be retained at a fraction of the computational cost, highlighting optimisation scheduling as an under-explored yet critical consideration in hybrid state estimation systems.

Seams encode rich structural information about garments but are frequently partially observable in robotic manipulation scenarios. To robustly leverage seam information, we propose a Seam-to-Graph network based on graph neural networks and attention mechanisms. This network maps unstructured seam observations to a topology-encoded structural skeleton graph for real-time garment state estimation. Using this skeleton-graph-based state estimation, we design a deformation-aware, hierarchical visual servoing controller for garment configuration alignment. We implement this controller on a bimanual robot system to load a garment onto a screen printing platen and to align it to the desired configuration precisely. Real-robot experiments demonstrate that the robot using the proposed method not only achieves human-level alignment accuracy with reduced variance in alignment error but is also robust to different garments. These results demonstrate that the use of seam information is effective for garment manipulation.

State estimation is the closed-loop core of every real-time tracking system, from radar surveillance and counter-UAV defense to autonomous driving and robotics. These deployments run on edge platforms, where defense systems mount on vehicles and drones, and civilian pipelines live on cars and handheld devices. Here, every additional watt of compute erodes mission duration or operational range. Two hard constraints follow: each new measurement must be fused before the next control cycle, and the total compute must fit within a strict battery and thermal power envelope. The Linear and Extended Kalman Filters (LKF, EKF) are dominant estimators on these systems, but today they execute almost exclusively on CPUs, which serialize multi-object tracking (MOT) updates, or on custom FPGA/ASIC accelerators that lengthen design cycles. Contemporary AI-PC SoCs, like the Intel Core Ultra Series 1 and 2, integrate a low-power, data-parallel Neural Processing Unit (NPU). We therefore ask whether the Kalman filter can be mapped onto this existing matrix engine to meet real-time and low-power budgets simultaneously, avoiding a dedicated accelerator and keeping the CPU and GPU free for primary workloads. We present KATANA, an NPU-aware optimization framework delivering the first end-to-end mapping of the LKF and EKF onto a commercial NPU, alongside a cross-platform characterization on shipping AI-PC silicon. KATANA applies three algebraic graph rewrites: subtract-to-add reformulation via a precomputed negative-projection matrix H_neg, static-shape tensor fusion, and block-diagonal batched parallelization, ensuring 100% of operations execute on the DPU matrix engine. On the Series 2, the optimized batched EKF reaches 223.35 FPS at 13.43 W active power, and the LKF reaches 408.73 FPS at 14.05 W, delivering up to a 97.9% reduction in dynamic energy versus the CPU implementation.

Kalman filters based on the Embedded Latent Transfer Operators (ELTO) emerge as novel statistical tools for sequential state estimation. However, a critical limitation stems from their use of simplified noise models, which fail to dynamically adapt to non-stationary processes. To address this limitation, we introduce an ELTO-based Bayesian filtering approach with a new structured parameterization for the filter's noise model. This parameterization enables structured noise adaptation, which couples the data-driven learning of an optimal time-invariant noise model with dynamic parameter adaptation that responds to changes in dynamics within non-stationary processes. Empirical results show that our structured noise adaptation improves the filter's dynamic state estimation performance in noisy, time-varying environments.

In this paper, we propose a method that applies Inertial-Leg (IL) tokenization to an attention-based network for proprioceptive state estimation in legged robots. Unlike existing learning-based state estimators that concatenate all sensor measurements into a single flat vector, the proposed architecture represents inertial measurements and leg-wise measurements as individual tokens and uses an attention mechanism to learn the relative importance of each measurement.This design allows the network to reweight each measurement according to the current contact condition, reflecting the fact that the reliability of forward kinematic measurements depends on whether the corresponding foot is in contact. Unlike conventional contact-aided estimators, however, the proposed method learns this behavior without relying on an explicit contact estimator or on explicit measurement updates based on a stationary contact assumption. To validate the proposed method, we conducted experiments on a Unitree Go1 robot, including debris terrain not modeled in simulation and gait patterns not seen during training. Experimental results show that the proposed method achieves better estimation performance than existing learning-based state estimators under unseen gait patterns and also improves performance over contact-aided model-based methods.

We introduce Equilibrium State Estimation (ESE), a novel paradigm for simultaneous prediction, where multiple interacting systems require separate yet coordinated forecasts. Such scenarios often arise in real-world settings such as economics and healthcare modeling. Unlike existing approaches that predict one system at a time, ESE forecasts all systems in a single pass. It first estimates the equilibrium state across systems, then generates holistic forecasts based on the difference between the current state and the estimated equilibrium. Extensive experiments on synthetic and real-world datasets, including currency exchange and COVID-19 spread modeling, demonstrate that ESE is at least as accurate as state-of-the-art (SOTA) methods while being significantly faster. In addition, ESE integrates seamlessly with conventional predictors, combining their accuracy with its exceptional efficiency and delivering a 10-70x speedup. With linear-time complexity, ESE scales far better than SOTA methods as the number of systems increases. Moreover, it remains accurate under diverse perturbations, establishing ESE as a fast, generalizable, robust, and scalable multi-prediction method.

This paper presents a nonlinear parameter estimator for Wiener-type state-space models obtained as a fixed-point architecture that couples two affine minimum mean-squared error (MMSE) estimators: one for the unknown parameters and one for latent variables. The architecture retains the functional structure of the optimal affine MMSE parameter estimator while incorporating Dynamic Basis Statistics (DBS) estimates that summarize nonlinear basis-function evaluations. Two DBS construction strategies are developed, leading to two nonlinear estimator frameworks. The dual basis-parameter estimator combines an affine basis estimator with the affine parameter estimator, whereas the dual state-parameter estimator first computes affine state estimates and their covariances, then maps these state-estimate statistics through a Gaussian DBS operator to obtain DBS estimates. Both dual estimators admit fixed-point characterizations that alternate between estimating each component using the updated prior of the other, obtained from that component's plug-in estimate statistics from the previous iteration. The efficacy of the proposed methods is examined via extensive Monte Carlo experiments, showing that the dual basis-parameter estimator attains parameter mean-squared errors comparable to those of the purely affine parameter estimator, while the dual state-parameter estimator achieves the lowest parameter mean-squared error, outperforming both the dual basis-parameter and purely affine parameter estimators, as well as sequential Monte Carlo variants of classical Particle Gibbs and Expectation-Maximization schemes.

False data injection attacks (FDIAs) introducing small measurement perturbations can still cause large deviations in power system state estimation when the injected signals align with the pseudo-null space of the system model. Existing model- and data-driven detectors may fail to identify such low-magnitude but high-impact attacks because residual tests ignore changes hidden in the pseudo-null space, while subspace learning methods capture correlation patterns without enforcing physical consistency. This paper proposes Physically Consistent Null Space Alignment (PCNSA), a framework that detects stealthy FDIAs by preserving, through preprocessing, the geometric correspondence between the physical null space and the measurement-derived pseudo-null space. The key point is a Pseudo-null Space Conserved data Preprocessing (PSCP) step that re-expresses measurements in the physical coordinate frame before subspace extraction. We prove that PSCP preserves the separation between row space and its orthogonal complement, a property that conventional per-feature standardization violates. This keeps the singular value decomposition (SVD)-derived pseudo-null subspace aligned with the physical residual space without explicit knowledge of H. Experiments on IEEE 14-, 30-, 57-, and 118-bus systems confirm this principle in practice: stealthy attacks that evade XTM, LSTM, AE and Isolation Forest baselines appear as clear deviations in the aligned subspace, yielding higher F1-score and detection accuracy while remaining robust under partial observability and realistic PMU noise.

This letter proposes a novel distributed bearing-based pose estimator for time-varying multi-robot systems. The method uses angles computed from body-frame bearings to estimate the robots' positions in $\mathbb{R}^3$ without knowledge of their orientations. The orientations in $\mathrm{SO}(3)$ are recovered from the estimated positions, the bearings, and the bearing derivatives. The proposed observer only requires the (directed) sensing topology to be \textit{angle-rigid}, a weaker condition than the commonly used ones like bearing rigidity. Local uniform exponential stability of the proposed observer is established under the assumption of persistently exciting motions for a subset of robots. Simulations are presented and discussed to evaluate the scheme's effectiveness and practicality.

Knowledge of real-time road slipperiness, or even better, a refined estimate of peak grip potential, is a critical input for vehicle warning and intervention control systems. Typically, friction is estimated through dynamics-based recursive estimators by calculating the slip slope; however, its efficacy is heavily constrained by the vehicle dynamic scenario. When the vehicle is cruising and there is little to no slip, these methods become ineffective due to the inability of present-day production-grade sensors, such as wheel speed sensors, and methods to either measure or accurately estimate micro slip, which is crucial for distinguishing different surfaces. To address this challenge, the correlation between vehicle signals and road surface condition during cruising needs to be uncovered using machine learning. In this paper, a feature-based framework and an end-to-end data-driven framework are used to correlate the statistics of vehicle dynamics behavior with the condition of the road surface and perform binary classification into grip, dry or damp, and slip, snow or ice, conditions. A sliding-window approach is adopted to batch a short buffered window of wheel speeds, wheel torques, longitudinal acceleration, steering angle, and yaw rate, which are fed into a machine learning module for predicting the road state. Validation results on public-road data show scenarios where the data-driven method identifies the road surface correctly even during cruising, showing promise for accurate data-driven friction-related state estimators in the field of tire and vehicle dynamics.

Robust and efficient state estimation is crucial for perception, navigation, and control in robotics. State estimation problems are conveniently modeled using the factor-graph framework as enabled by modern software packages such as GTSAM or g2o. However, the standard solvers included in such frameworks are local and may converge to poor local minima, posing significant safety concerns. Conversely, techniques based on convex relaxations have been shown to provide a means of globally solving or certifying many state estimation problems. However, these relaxations 1) often require substantial effort to formulate, and 2) may incur significantly higher cost compared to efficient local solvers, as they require solving a large semidefinite program (SDP). In this work, we address both shortcomings by 1) creating a new procedure within the GTSAM framework for automatically constructing convex SDP relaxations for any factor graphs with common factor and variable types, and by 2) exploiting the Bayes tree constructions native to GTSAM to decompose the SDP problem, leading to significant speedup in solver time for chordally sparse problems. We demonstrate the favorable scaling of this structure-exploiting global estimator compared to standard local solvers for two case studies: A 3D pose-graph SLAM problem with a ring factor graph and a 2D localization problem with a chain factor graph. The software framework is available at https://github.com/borglab/gtsam.

Reinforcement learning (RL) refines large language models (LLMs) by directly optimizing model behavior through reward signals. While accurate state value estimation is critical for stable training in classical RL, it remains an underexplored challenge in LLM post-training. In this work, we introduce the State Value Estimation Benchmark (SVEB) to assess state estimation within existing RL frameworks and show that critics in standard approaches like PPO collapse to a coarse group-average baseline. To address this, we propose two techniques: Numca, which leverages numerical spans as gradable milestones for state value estimation, and Hista, a framework that uses LLM's hidden states as representation to weighted average disjoint rollouts and their return. Extensive experiments demonstrate that both methods yield more accurate state value estimates and enhance training performance across different RL algorithms and model sizes without incurring significant computational overhead.

State estimation is a fundamental problem in control and signal processing, for which the Kalman Filter provides an optimal solution under linear dynamics, Gaussian noise, and known noise covariances. However, these assumptions often fail in realistic sensing settings such as Doppler radar and LiDAR. In these cases, the optimal estimator is inherently nonlinear, which leads to systematic performance degradation. This creates a performance gap that cannot be eliminated by tuning the noise covariance parameters (i.e., the process and measurement noise in the Kalman Filter) alone. To address this limitation, we propose Kalman Evolve, a framework for discovering improved filtering algorithms by jointly optimizing both noise parameters and the update structure. Our approach leverages large language models (LLMs) as a structured prior over program space, enabling the generation of interpretable, non-affine modifications to the classical Kalman filter while preserving its recursive form. We provide analytical results establishing the suboptimality of affine estimators under common nonlinear sensing models, motivating the need for structure-aware updates. Across a range of synthetic and real-world tracking benchmarks, including Doppler radar, LiDAR-based localization, and pedestrian tracking, the discovered algorithms consistently improve over strong baselines such as the Optimized Kalman Filter, achieving up to 12% reduction in RMSE. These results suggest that optimizing the structure of the Kalman filter, rather than only its parameters, provides a practical and interpretable way to improve state estimation.

Robustness is a critical requirement for deploying autonomous driving systems in the real world. Existing robustness benchmarks for autonomous driving have made important progress in studying the effects of image-level corruptions, such as adverse weather or camera degradation, on perception modules and open-loop planning outputs. However, deployment can also involve system-level imperfections, such as inference latency and ego-state estimation errors, which remain less studied in closed-loop E2E-AD evaluation. These imperfections can accumulate through the feedback loop and destabilize control. In this work, we present Bench2Drive-Robust, to our knowledge the first device-centric robustness benchmark for closed-loop end-to-end autonomous driving under realistic deployment perturbations. We systematically evaluate deployment-oriented perturbations arising from three major sources: camera-stream failures (frame drop, partial observation), ego-state estimation errors (GPS noise, and speed or odometry errors), and compute-induced control delay (model inference delay). We evaluate representative end-to-end driving methods and analyze their robustness under different perturbation severities. Our results show that these deployment-related perturbations can substantially degrade closed-loop driving performance, revealing robustness challenges that are not fully captured by conventional image-level corruption evaluations. By establishing a closed-loop evaluation protocol and demonstrating the substantial impact of these deployment-oriented perturbations, Bench2Drive-Robust defines practical robustness problems for end-to-end autonomous driving and encourages further research on deployment-aware robust driving systems.

Tightly coupled SLAM formulations under mixed-rate sensing often bind temporal processing, local geometric association, estimator formulation, and map-update policy into method-specific designs. Such binding makes it difficult to vary one design choice without re-engineering the rest of the state-estimation process. This paper presents FUSE, a framework for unified state estimation in vehicular and robotic SLAM systems. FUSE organizes the state-estimation interface around observation ingestion, propagation, update, and state query, and uses this interface to separate temporal processing, residual-ready local geometric association, estimator formulation, and map-update policy. A LiDAR--IMU instantiation is developed to examine the framework under mixed-rate sensing and directional degeneracy, where high-rate inertial propagation, LiDAR-triggered geometric update, residual screening, and degeneracy-aware correction operate through the same interface boundaries. On a 418~m loop-corridor sequence, the instantiation reports a 1.626 m end-to-end trajectory error, corresponding to a 7.9% relative error reduction compared with Faster-LIO, the lowest-error baseline on this sequence. The results support FUSE as a framework for organizing state-estimation design choices and show how the evaluated instantiation regularizes updates along weakly observable directions.

Accurate visual state estimation has been a central topic in robotics with a wide range of applications in robot navigation, autonomous driving, and autonomous flight. Recent advances in robot perception have led to significant improvements in the accuracy and robustness of state estimation, yet a fundamental challenge remains in how to quantify and calibrate its precision, i.e., how confident we are in an estimate and whether failures can be detected. This issue is particularly pronounced in visual-inertial odometry (VIO), where the heteroscedastic and multimodal nature of the problem makes uncertainty quantification especially difficult. This paper introduces MUSE (Multimodal Uncertainty Quantification of State Estimation), a novel real-time learning-based framework that leverages the strong and efficient sequential modeling capacity of Mamba to estimate localization uncertainty from multiple asynchronous sensor streams. Experiments on both public and in-house datasets demonstrate that MUSE achieves superior reliability and robustness compared to existing uncertainty quantification methods, and ablation studies justify the benefits of its key design choices.

Fast and reliable initialization is critical for monocular visual-inertial navigation systems (VINS), as it establishes the starting conditions for subsequent state estimation. Despite steady progress, most existing methods heavily rely on visual feature correspondences and require 3-4 seconds of sensory data for successful initialization, which limits their applicability and efficiency. With the advent of feed-forward 3D models that can directly predict point clouds from images, we revisit the visual-inertial initialization problem from a concise perspective. In this work, we propose a feature-free initialization framework that leverages up-to-scale point clouds predicted by a feed-forward 3D model, thereby obviating the need for visual feature tracking and estimation. This design substantially reduces system complexity and improves the reliability of initialization. Experiments on public datasets demonstrate that the proposed feature-free initialization method achieves the highest success rate, exceeding 90%, and significantly reduces the data duration required for successful initialization, typically to under 1.2 s. We further validate our method on a self-collected dataset covering various indoor and outdoor scenarios, demonstrating robust performance, particularly in visually degraded environments where existing methods often fail. The code and dataset are available at https://github.com/Yuantai-Z/FF-VIO-Init.

Robust state estimation for highly dynamic motion of legged robots remains challenging, especially in dynamic, contact-rich scenarios. Traditional approaches often rely on binary contact states that fail to capture the nuances of partial contact or directional slippage. This paper presents CoCo-InEKF, a differentiable invariant extended Kalman filter that utilizes continuous contact velocity covariances instead of binary contact states. These learned covariances allow the method to dynamically modulate contact confidence, accounting for more nuanced conditions ranging from firm contact to directional slippage or no contact. To predict these covariances for a set of predefined contact candidate points, we employ a lightweight neural network trained end-to-end using a state-error loss. This approach eliminates the need for heuristic ground-truth contact labels. In addition, we propose an automated contact candidate selection procedure and demonstrate that our method is insensitive to their exact placement. Experiments on a bipedal robot demonstrate a superior accuracy-efficiency tradeoff for linear velocity estimation, as well as improved filter consistency compared to baseline methods. This enables the robust execution of challenging motions, including dancing and complex ground interactions -- both in simulation and in the real world.

Many Inertial Navigation Systems (INS) use Global Navigation Satellite System (GNSS) position as the primary measurement to drive filter performance and bound error growth. However, commercial-grade GNSS receivers introduce unknown measurement delays ranging from 50 ms to 300 ms depending on sensor quality and operating mode. Such time delays can significantly degrade INS performance unless they are explicitly compensated for. Existing algorithms commonly estimate this delay offline, run the filter concurrently with GNSS measurements using buffered Inertial Measurement Unit (IMU) data, and predict the current state by forward-integrating buffered inertial measurements via IMU preintegration. The state-of-the-art online method is an Extended Kalman Filter (EKF) that explicitly models the time delay as a state parameter, which defines the preintegration duration. This paper introduces a novel geometric framework for modeling time-delayed INS, in which Galilean symmetry is leveraged to provide a joint representation of space and time for consistent state estimation. An Equivariant Filter (EqF) is derived for the coupled estimation of navigation states and time delay. Validation is performed on two fixed-wing Uncrewed Aerial Vehicles (UAV) with GNSS time lags of 90 ms and 120 ms. The test flights last two to three minutes. Simulations further investigate delays up to 500 ms and provide a statistical comparison against the state-of-the-art EKF. Results show that the EqF preserves accuracy and consistency, while the EKF lacks consistency and its performance degrades significantly with increasing measurement delays.

When people share the same documents and observations yet reach different conclusions, the disagreement often shifts into a judgment that the other party is cognitively defective, irrational, or acting in bad faith. This paper argues that such divergence is better described as a form of non-identifiability inherent in inference and learning, rather than as a defect of the other party. We organize the phenomenon into two levels: (i) $θ$-level non-identifiability, where conclusions diverge under the same world model $W$ because inference settings differ; and (ii) $W$-level non-identifiability, where repeated use of an inference setting $θ$ biases data exposure and update rules, causing the learned world model $W$ itself to diverge. We introduce an inference profile $θ= (R, E, S, D)$, consisting of Reference, Exploration, Stabilization, and Horizon, and show how outputs can split even for the same observation $o$ and the same $W$. We further explain why disagreements tend to project onto a small number of bases -- abstract versus concrete, externalizability, and order versus freedom -- as a consequence of general constraints on learning systems: computational, observational, and coordination constraints. Finally, we relate the framework to deep representation learning, including representation hierarchy, latent-state estimation, and regularization-exploration trade-offs, and illustrate the framework through a case study on AI regulation debates.

We compare three state-of-the-art proprioceptive state estimators for quadruped robots: MUSE [1], the Invariant Extended Kalman Filter (IEKF) [2], and the Invariant Smoother (IS) [3], on the CYN-1 sequence of the GrandTour Dataset [4]. Our goal is to give practitioners clear guidance on accuracy and computation time: we report long-term accuracy (Absolute Trajectory Error, ATE), short-term accuracy (translational and rotational Relative Pose Error, RPE), and per-update computation time on a fixed hardware/software stack. On this dataset, RPEs are broadly similar across methods, while IEKF and IS achieve a lower ATE than MUSE. Runtime results highlight the accuracy-latency trade-offs across the three approaches. In the discussion, we outline the evaluation choices used to ensure a fair comparison and analyze factors that influence short-horizon metrics. Overall, this study provides a concise snapshot of accuracy and cost, helping readers choose an estimator that fits their application constraints, with all evaluation code and documentation released open-source at https://github.com/iit-DLSLab/state_estimation_benchmark for full reproducibility.

Many downstream decisions in complex terrain require fast wind estimates at a small number of user-specified locations and heights for a given forecast valid time, rather than another dense forecast field on a fixed grid. We present WindINR, a latent-state implicit neural representation framework for continuous high-resolution local wind query and sparse-observation correction. WindINR maps static terrain descriptors, a low-resolution background field, and continuous query coordinates to a high-resolution wind state through a latent-conditioned decoder. To enable rapid inference-time correction, WindINR separates reusable representation learning from sample-specific latent-state correction. During training, a privileged encoder infers a reference latent state from high-resolution supervision, a deployable latent predictor estimates an initial latent state from inference-time inputs alone, and their discrepancies are summarized into a dataset-adaptive Gaussian prior over latent corrections. At inference time, within the WindINR module, network weights remain fixed and only the latent state is updated by minimizing a regularized correction objective using sparse observations and their uncertainty. In controlled OSSEs over the Senja region, including a UAV-aided approach scenario and random-observation robustness tests, WindINR improves local high-resolution wind estimates by updating only a compact latent state rather than the full network. The corrected representation remains continuously queryable at arbitrary coordinates and, in our CPU benchmark, yields about a $2.6\times$ online-correction speedup over full-network fine-tuning, suggesting a practical interface between kilometer-scale background products, sparse local observations, and wind queries in complex terrain.

We show that the core components of the Transformer---attention, residual connections, and normalization---arise naturally from a single geometric state estimation problem. Modeling the latent state in polar coordinates naturally separates radial and hyperspherical dynamics, yielding a precision-weighted filtering procedure in which normalization enforces the hyperspherical constraint, attention aggregates directional evidence, and the residual connection implements an incremental state update. The standard Transformer block with rotary positional encodings is recovered by discarding the geometric correction terms of the resulting state estimator, showing that its architecture follows from the underlying estimation problem rather than from independent design choices. The proposed \textit{Polar Transformer} retains these geometric corrections.

In safety-critical scenarios, the protection level of the autonomous navigation system is crucial for enabling mobile robots to perform safe tasks. However, existing studies on probabilistic navigation systems for robots usually perform offline accuracy evaluations using limited datasets and assume that the results can be applied to unknown real-world environments. As a result, current autonomous mobile robots often lack protection levels for online safety assessment. To fill this gap, we propose a safety-critical LiDAR-inertial odometry (LIO) that provides deterministic protection levels based on on-manifold deterministic state estimation. By adopting the unknown but bounded assumption, we derive a neat closed-form relationship between point cloud noise and the uncertainty of the estimation from the iterated closest point algorithm. Using this relationship, we design an on-manifold ellipsoidal set-membership filter and implement it within the LIO system. Leveraging the properties of the set-membership filter, our system offers the feasible sets of the estimated locations as the deterministic protection levels, serving as safety references for the robots' downstream autonomous operations. The experimental results show that our system can provide effective deterministic online safety references for diverse robots in various environments.

Continuous-time state estimation is gaining in popularity due to its abilities to provide smooth solutions, handle asynchronous sensors, and interpolate between data points. While there are two main paradigms, parametric (e.g., temporal basis functions, splines) and nonparametric (Gaussian processes), the latter has seen less adoption despite its technical advantages and relative ease of implementation. In this article, we seek to rectify this situation by providing a new simplified explanation of GP continuous-time estimation rooted in the language of factor graphs, which have become the de facto estimation paradigm in much of robotics. To simplify onboarding, we also provide three working examples implemented in the popular GTSAM estimation framework.