Extended Kalman Filter

We study Model Predictive Path Integral (MPPI) control for nonlinear systems with additive process disturbances whose covariance is unknown, spatially varying, and slowly time-varying. A mismatched disturbance covariance produces a persistent penalty in closed-loop stability certificates, while online estimation can reduce this penalty as data are collected. We propose a cell-wise recursive covariance estimator with spatial diffusion and prove a finite-horizon error bound that separates stochastic-approximation error, spatial-smoothing bias, and temporal-drift effects. The diffusion kernel is chosen to be reversible with respect to the stationary visitation measure, making the diffusion operator dissipative in the weighted Lyapunov analysis. We then substitute the resulting covariance estimate into the MPPI sampling distribution and derive an adaptive stability certificate with an explicit learning penalty. The main result is a payoff theorem: after a computable crossover time, the adaptive controller achieves a strictly tighter certified stability bound than any fixed covariance choice whose mismatch exceeds the residual smoothing and drift allowance. Numerical experiments illustrate the estimator convergence and the resulting stability-tightening effect.

A central challenge in building intelligent systems is enabling agents to jointly perceive complex inputs, form hypotheses about hidden patterns, and design informative experiments to test them. To study this problem, we propose ZendoWorld, a controlled interactive environment in which agents must infer a logical rule about visual game observations, acquire information by proposing new scenes, and refine their hypotheses based on feedback from the game environment. We evaluate several agents spanning pure VLM reasoning, Bayesian particle filtering, dynamic concept discovery, and neuro-symbolic methods. Our main findings are: (1) high accuracy in predicting labels for observed examples does not imply recovery of the underlying rule; (2) perception and induction are distinct bottlenecks for different agent classes; and (3) VLM-based agents propose near-uninformative experiments, failing to actively reduce hypothesis uncertainty. To compare these results, we collect human data on the task, which reveals a gap in inductive reasoning, particularly for more complex rules. Overall, ZENDOWORLD takes an important step toward evaluating intelligent agents and identifies concrete avenues for improvement, particularly in domains like scientific discovery.

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.

Accurate and robust localization is essential for autonomous mobility systems in real-world environments. While fusing Inertial Measurement Unit (IMU) data with satellite-based correction signals provides precise vehicle pose estimates, performance degrades substantially during outages. Recent studies indicate that Machine Learning (ML) can improve IMU-based proprioceptive localization, highlighting untapped potential for onboard sensors readily available in production vehicles. This paper introduces Physics-Regularized Machine Learning for Localization (PRML2), a hybrid framework that combines the complementary strengths of Kalman filtering and data-driven learning to estimate vehicle pose directly from onboard sensors. A key aspect of PRML2 is its physics-regularized learning, enabled by end-to-end training of an ML model through a differentiable Kalman filter. This improves consistency with vehicle motion models, thereby enhancing both localization accuracy and generalization across driving conditions. We evaluate the performance limits of ML-enhanced onboard odometry on a publicly available dataset and show that PRML2 achieves superior localization accuracy and demonstrates real-time capability. This work also introduces a novel dataset to support vehicle localization research under low-friction conditions. The proposed framework provides a robust and cost-effective solution for vehicle localization under degraded sensing conditions by integrating learning with physics-based priors.

Federated Learning (FL) is fundamentally challenged by statistical heterogeneity, where non-identically distributed (non-IID) data induces client drift that severely hampers global convergence. While existing approaches attempt to mitigate this drift through spatial-domain gradient correction or regularization, they overlook the intrinsic spectral structure of optimization signals. In this work, we revisit client drift from a novel frequency-domain perspective and uncover a critical Spectral Bias of Drift: inter-client gradient divergence is predominantly concentrated in low-frequency components which encode client-specific distributional shifts, while high-frequency components representing fine-grained features remain relatively consistent. Motivated by this, we propose SpecGradFilter, a unified Spectral Gradient Filtering Framework that tames heterogeneity by suppressing discordant low-frequency signals. Crucially, we demonstrate that SpecGradFilter is a generalizable principle, effective not only via precise FFT-based truncation but also through spatial approximations like Gaussian detrending. Extensive experiments on benchmarks such as CIFAR-10/100 and Tiny-ImageNet demonstrate that SpecGradFilter significantly performs better performance in highly Non-IID settings with negligible communication overhead, establishing a new paradigm for robust federated optimization.

Physical sensing and actuation noise floors should inform how much belief resolution a decision-making system can reliably use. We introduce Finite Reliability Representations (FRR), a framework for covering belief spaces by reliability cells: regions within which the optimal action-value function Q*(b,u) varies by at most a tolerance epsilon, uniformly over actions. The framework is formulated on beliefs rather than states and uses a cover rather than an equivalence quotient, because approximate decision-closeness is not transitive in general. A central technical point is that noisy Bayesian updates should not be treated as globally contractive on arbitrary beliefs. We therefore separate three objects: the fixed-observation filter map, the predictive observation law, and the controlled belief-transition kernel. For nonlinear continuous-state systems, FRR is obtained under a reachable-set Lipschitz modulus for the belief-transition kernel. For finite-state POMDPs, the same construction becomes exact on the belief simplex: prediction is linear, Bayesian correction is a normalized positive linear map, sensor noise enters through observation-distribution distinguishability, and actuation uncertainty enters through an action-execution channel. Under the corresponding action-value Lipschitz condition, an FRR cover supports a cell-constant policy whose suboptimality is bounded by 2 epsilon/(1 - gamma). We also introduce reliability entropy, the logarithm of the minimal number of reliability cells, as a measure of certified decision-relevant belief complexity. The framework distinguishes representation sufficiency from fundamental performance floors imposed by sensing, process, and actuation noise. It applies to finite POMDPs, linear-Gaussian filters, locally linearized nonlinear filters, and particle-filter implementations through analytic or empirical certification of reliability cells.

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).

Closed-loop (or feedback) error-state Kalman filters with their relatives and offspring are the state-of-the-art in modern aided inertial navigation research. Estimated inertial navigation system (INS) errors are continually fed back to the INS to correct the nominal system state before subsequent predictions. Conversely, in safety-critical aeronautical applications, open-loop (or feedforward) systems are an undisputed standard, where the inertial mechanization is strictly decoupled to allow for operational independence and fault isolation of computing units. We assess the performance impacts of this architectural choice beyond qualitative system-safety justifications using a standard inertial mechanization in geodetic coordinates and direct position aiding. Simulations using a variety of inertial sensor error characteristics, ranging from consumer to navigation grade systems, showcase the trade-off between smooth information fusion for high-end IMUs using an open-loop filter and the inherent long-term stability of the closed-loop architecture.

Global navigation systems require state estimation algorithms that handle Earth's curvature, Earth's rotation, and gravitational variations. These factors can typically be neglected in local navigation algorithms for robots, drones, etc. In classical error-state Kalman Filtering (ESKF) the error state dynamics are trajectory-dependent. Invariant ESKFs utilize Lie Group symmetries to represent the error, which can render error propagation trajectory-independent for group-affine systems. Choosing between a standard filter (where position and velocity errors are defined additively in the navigation frame), a left-invariant filter (where errors are represented in the body frame) and a right-invariant filter (where errors are represented in the navigation/world frame) depends on system dynamics and sensor configuration. This note presents the mathematical formulas for four classical and invariant ESKFs for globally applicable aided inertial navigation systems. It is intended to serve as a systematic reference for comparison and implementation.

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.

Data assimilation models state dynamics conditioned on sequential observations, and has wide-ranging scientific applications. In the filtering setting, the goal is to model the posterior over the current state given all observations so far. Classical solutions typically make simplifying distributional or functional assumptions, e.g., linear-Gaussian systems, which can be inaccurate in many scenarios. In principle, particle filters (PFs) remove these assumptions, yet often collapse in high dimensions. Recent generative approaches learn conditional state transitions, but without principled Bayesian updates they do not recover the correct filtering posterior and can accumulate error over long horizons. In this work, we introduce Flow Proposal Particle Filters (FPPF), which learn a conditional generative model based proposal approximating the variance-minimizing optimal proposal for particle propagation. Conditioning on observations steers particles toward high-likelihood regions before weighting, reducing weight variance and delaying degeneracy. Since our proposal admits tractable likelihood evaluation, FPPF computes accurate importance weights and retains a Bayesian update step. We further extend FPPF to high-dimensional problems through localization strategies, adressing another standard PF failure mode. Extensive experiments on a variety of dynamical systems show that FPPF outperforms statistical baselines and other generative methods in non-linear, non-Gaussian, and high-dimensional regimes.

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.

Inertial navigation systems aided by three-dimensional landmark measurements constitute a fundamental problem in robotic perception and state estimation. Classical SO(3)-based Extended Kalman Filter (SO(3)-EKF) approaches provide practical solutions, but suffer from the false observability problem, in which the filter becomes overconfident in unobservable directions, leading to degraded estimation performance. The Invariant EKF (IEKF) addresses this limitation by reformulating the system dynamics as a group-affine system on a Lie group, although its measurement update does not fully satisfy certain state compatibility properties. More recently, the Iterated Invariant EKF (IterIEKF) was proposed to further improve the IEKF by ensuring, in the low-noise regime, that the estimated state remains on the observed state manifold while the uncertainty is confined to its tangent space. In this work, we formulate and apply the IterIEKF to landmark-based inertial 3D localization for the first time. Through numerical simulations, we show that the proposed approach outperforms the classical SO(3)-EKF, the Iterated SO(3)-EKF, and the IEKF in terms of both estimation accuracy and consistency.

This paper proposes a Bayesian filtering-based approach for learning the dynamics of a physical system from partial, noisy measurements. We model the system dynamics using a Lagrangian mechanics formulation. As in Lagrangian neural networks (LNNs), we parameterize the kinetic and potential energies with neural networks. The unknown external forces in the Lagrangian formulation are modeled as white Gaussian noise. The corresponding Euler--Lagrange equations then yield a continuous-time stochastic state-space model (SSM) that describes the system dynamics. The neural network parameters and system states are then jointly learned via a maximum-likelihood method using Gaussian-approximation-based Bayesian filters. The effectiveness of the proposed method is demonstrated on pendulum and Duffing oscillator examples, and its performance is compared with conventional LNNs and with approximate Bayesian filters using known system models.

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.

In environmental monitoring as well as emergency response applications such as wildfires, wind velocity measurement is essential. Quadrotor UAVs have become popular platforms for wind velocity estimation due to their maneuverability, compact size, and cost-effectiveness. Numerous studies use the Extended Kalman Filter (EKF) to estimate the wind velocity based on the quadrotor dynamic model. However, most of them use hovering quadrotors only for wind estimation, others use a near-linear trajectory to estimate near-constant velocities. Furthermore, EKF performance is constrained by its reliance on linearized approximations of the nonlinear quadrotor dynamics around current states, limiting accuracy in highly nonlinear scenarios, including windy conditions. This study proposes the use of an Unscented Kalman Filter (UKF), a nonlinear estimator to provide accurate wind estimations while maintaining the trajectory of the quadrotor UAV. The quadrotor is modeled on the Special Euclidean group SE(3) and the approach is evaluated through numerical simulations using a geometric controller to maintain quadrotor flight paths. The results indicate that as the nonlinearity of the simulation increases, the UKF consistently outperforms the EKF. This demonstrates the potential of the UKF as a reliable estimator for highly nonlinear scenarios, capable of maintaining the trajectory with minimal deviation while providing accurate wind velocity estimations.

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

Extensive context has become the norm as Large Language Models (LLMs) are increasingly deployed in long-horizon tasks. The concern that increasing context length degrades model capabilities, known as context rot, has become a central issue for these applications. In this paper, we focus on deep search scenarios, aiming to investigate the rot phenomenon and its mitigation strategies. By evaluating four flagship open-source models across three benchmarks, we reveal a prevalent but unnoticed rot phenomenon: extensive context causes models to directly give up or prematurely provide uncertain answers, and this issue is exacerbated as the context grows. Through pruning experiments, we demonstrate the relationship between the accumulated context and the rot phenomenon. Furthermore, we investigate mitigating this issue through context management and post-hoc rejection sampling. For context management, we systematically evaluate seven different methods across three categories, based on performance, cost, and impact on context rot, providing clear guidance for strategy selection and usage. For rejection sampling, we develop a rot-aware filtering strategy and demonstrate its effectiveness across three aggregation methods. Finally, we show that these two approaches can be combined for further performance improvements.

We propose a robust Extended Kalman Filter (EKF) architecture for land navigation using an array of hundreds of low-cost micro-electromechanical systems (MEMS) inertial sensors. The main challenges in this setting are bursty sensor-specific bias errors, bias drift, and the need to aggregate many inertial measurements without increasing the computational burden of the navigation filter. To address these challenges, we introduce Robust Inertial Sensor Array Fusion (RISAF), a pre-filtering framework that combines dynamic percentile gating with real-time bias tracking before the EKF prediction step. The proposed aggregation suppresses anomalous sensor readings and compensates for individual sensor drift while preserving the vehicle-level kinematic signal. Because the resulting fused inertial measurements are passed to a standard EKF, the navigation filter retains a minimal state vector and supports real-time execution. We evaluate RISAF through extensive simulations and real-world field tests in GNSS-denied environments, with the data provided as supplementary material. Compared with a baseline that averages the sensor readings, RISAF achieves substantially improved azimuth accuracy and reduced drift accumulation. These results demonstrate that robust fusion of large MEMS inertial arrays can bridge a substantial part of the gap between cost-effective hardware and tactical-grade inertial navigation performance.

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.

Nowadays mobile robots have wide engineering applications. Simultaneous localization and mapping (SLAM) is an important task of these robots. The major and common algorithms used for this task are based on extended Kalman filter (EKF). One of the main problems in EKF-based SLAM is its divergence. The nonlinearity of motion and observation models and linearization error are the main reasons for the divergence. There have been some efforts to address this problem with limited success. In this paper, by applying a simple compass and using an effective transformation, we transform the non-linear state space model into a linear model. Then, by applying the original KF to this model, we reach a new method, which is called LMKF SLAM. We show that the LMKF SLAM is significantly superior to the state-of-the-art methods, especially EKF-based SLAMs, both in accuracy, convergence, and computational complexity. The proposed method is also more stable with respect to the uncertainty of sensors values and changes in system parameters. Experimental results verify these points.

Online latent state estimation constitutes a fundamental challenge within the artificial intelligence field, serving as a foundational tool for diverse applications, including sequential decision making, anomaly and change-point detection. In this paper, a novel online distributed sensing framework, where agents collaborate and exchange information to perform latent state estimation, is presented. The proposed estimator combines available partial domain knowledge with the representation capabilities of deep neural networks. In particular, the designed sensing framework incorporates prior estimates, optimized consensus weights, and Kalman-like recursive updates to perform decentralized inference, without relying on knowledge of noise statistics. Extensive experiments on linear, chaotic (Lorenz), and practical wireless tracking environments reveal that the proposed Covariance-Agnostic Neural Kalman Consensus Filter (CA-NKCF) outperforms traditional distributed Kalman and particle filters as well as purely model-free deep neural networks, exhibiting robustness even when the underlying motion and observation models are misspecified. It is also demonstrated that CA-NKCF's performance advantage remains stable across varying noise levels, random communication topologies, latent state dimensions, and observation clutter densities induced by scattering objects in wireless systems.

Combined-cycle gas turbines (CCGTs) play a key role in modern power generation, offering both high efficiency and reduced environmental impact. However, their complex thermo-fluid and mechanical interactions complicate fault detection, particularly when labeled fault data are scarce. In this paper, we introduce the Kalman Prototypical Network (KPN), a metric-based few-shot learning (FSL) framework specifically tailored for CCGT fault diagnosis. We model the evolution of class prototypes as latent stochastic states in a dynamic system to reduce episodic variance and improve robustness in embedding representation. Synthetic data sets generated with a high-fidelity Modelica-based dynamic simulation of an offshore CCGT system were used, simulating both normal operation and progressive leak faults under transient conditions. Application of the proposed framework on simulated leak fault detection tasks demonstrate that KPN outperforms conventional FSL methods such as Matching Networks, Relation Networks, and MAML in both accuracy and stability under varying support and query configurations. The proposed framework significantly improves training convergence and generalization by stabilizing class representations, making it well-suited for real-world CCGT fault detection where labeled data is limited.

Bayesian filtering of partially and noisily observed dynamical systems seeks to infer the evolving conditional distribution of the state of a dynamical system, given observations, in an online fashion. This Bayesian filtering distribution is the natural object for uncertainty quantification, but it is rarely available as a supervised learning target. However, one can often use the forecast model to generate synthetic system trajectories, along with synthetic observations. We introduce the proper scoring ensemble filter (PSEF), an ensemble data assimilation method based on training an analysis map to approximate the filtering distribution using only synthetic state--observation trajectories. The analysis step is represented as a permutation-invariant, transformer-based map that takes as input a forecast ensemble and observations, producing an analysis ensemble. Training is based on strictly proper scoring rules -- with the energy score used in our implementation -- so that probabilistic accuracy is rewarded over the whole probability distribution. We prove that, under a realizability assumption, the population objective is minimized by the true Bayesian filtering distribution. We also derive the finite-ensemble empirical objective used in training and relate its single state--observation trajectory form to the population objective, using a mean-field consistency argument. Numerical experiments show that the learned filter accurately approximates challenging filtering distributions, including nonlinear, non-Gaussian, and multi-modal posteriors, and achieves stronger performance in data assimilation tasks than classical methods or learning-based methods with mean-squared-error objectives. For close-to-Gaussian problems, learning a correction to the EnKF is the best approach, while for highly non-Gaussian problems an end-to-end approach that discards this inductive bias is superior.

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.

Accurate extended pose estimation (orientation, velocity, and position) for IMU-instrumented articulated rigid-body systems is a key challenge in robotics and human motion analysis. The invariant extended Kalman filter (IEKF) addresses this problem for a single rigid body with convergence guarantees and consistency under unobservability, but extending these properties to articulated systems is nontrivial: inter-body pose coupling prevents a direct application, and incorporating joint kinematic constraints within the invariant framework remains an open problem. To address this gap, we introduce the relative L-extended pose, a Lie group representation for kinematic-tree systems. With one IMU per body, it yields group-affine dynamics and allows joint constraints to be expressed in invariant form. We incorporate these constraints as noise-free pseudo-measurements within an iterated IEKF (IterIEKF), thereby preserving the convergence and consistency guarantees of invariant filtering. Validated on both a UR5e robot and a human leg, the proposed IterIEKF outperforms all EKF, IterEKF, and absolute-pose IterIEKF baselines. It converges faster, exhibits lower run-to-run variability, and consistently achieves the lowest RMSE, with reductions of at least 50% compared to the second-best filter across all scenarios considered in this work.

Predicting temporal Quality of Service (QoS) data is critical for optimizing network services and rationalizing resource allocation in cloud computing and service-oriented systems. Existing mainstream methods have achieved promising predictive performance. However, their purely data-driven manner limits their ability to capture non-stationary temporal patterns, thereby leading to accuracy degradation when temporal QoS data exhibits fluctuations. To tackle this limitation, we propose a novel Extended Kalman Filter-Enhanced Latent Feature Analysis (EKL) model to perform efficient and accurate temporal QoS prediction from the perspective of bidirectional model-data-driven learning. Its main idea is three-fold: a) designing a model-driven feature producer to obtain the temporal latent features to capture the intricate temporal pattern following the principle of an Extended Kalman Filter; b) building a data-driven feature producer based on the alternating least squares algorithm to identify time-invariant latent features describing intrinsic user-service characteristics; c) exploiting a density-oriented parallel strategy that achieves workload balancing by sorting users in accordance with their service invocation density, which effectively elevates computational efficiency. In addition, we provide a rigorous theoretical analysis to formally prove the convergence of the proposed EKL. Experimental evaluations conducted on real-world temporal QoS datasets reveal that our proposed EKL surpasses existing state-of-the-art models with respect to both computational efficiency and prediction accuracy for missing temporal QoS data.

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.

Robust locomotion and navigation for legged robots relies heavily on dependable odometry. Traditional multi-sensor fusion for such state estimation requires meticulous sensor calibration and platform-specific kinematic modeling, which complicates deployment. Industrially packaged exteroceptive sensors can provide accurate motion tracking but remain vulnerable to perceptually degraded conditions. We thus develop a plug-and-play, robust legged odometry system that eliminates the need for explicit exteroceptive-to-proprioceptive calibration or system kinematic modeling. Our approach leverages established exteroceptive motion pipelines as a continuous supervisory signal to train an online learned velocity neural network directly from proprioceptive data. An Invariant EKF (InEKF) is then used to fuse the learned proprioceptive or exteroceptive velocity (if any) and IMU data. When exteroception fails due to environmental degradation, the system seamlessly falls back to using the learned proprioceptive model, yielding a resilient legged odometry that readily adapts to new hardware. We demonstrate the platform-agnostic, easily deployable nature of our approach on different quadruped platforms, showcasing promising results in maintaining robust motion estimation across challenging scenarios.

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.

Characterizing non-Gaussian posterior distributions in partially observed high-dimensional nonlinear systems remains a fundamental challenge in data assimilation. Ensemble Kalman filters rely on Gaussian approximations that can be inaccurate for strongly non-Gaussian posteriors, whereas particle filters suffer from severe scalability limitations. Recent score-based generative approaches improve posterior characterization but typically require supervised training with ground-truth posterior samples, which are unavailable in most practical applications. We introduce $Ω$ (Operator-based Mixture Ensemble for Generative Assimilation), a scalable framework that integrates conditional Gaussian surrogate modeling, unsupervised score learning, and generative sampling. The conditional Gaussian surrogate provides a nonlinear non-Gaussian baseline approximation while admitting closed-form conditional posterior distributions for the unresolved variables. First, $Ω$ exploits these closed-form conditional distributions to analytically recover the high-dimensional unobserved component, reducing computational cost and mitigating the curse of dimensionality. Second, $Ω$ learns only the residual discrepancy beyond an analytical baseline through denoising score matching using ensemble trajectories alone, eliminating the need for ground-truth posterior samples and substantially reducing the learning burden. Third, $Ω$ reconstructs the full non-Gaussian posterior distribution of both observed and unobserved variables via a Gaussian mixture representation, capturing multimodal, skewed, and heavy-tailed statistics. Finally, $Ω$ employs annealed Langevin sampling to iteratively refine ensemble members from the baseline toward the target posterior. $Ω$ is validated on several turbulent models with intermittency and extreme events, consistently improving posterior accuracy.

We study the problem of system identification in heterogeneous settings, where different systems may follow distinct underlying dynamics. Existing clustered system identification approaches often rely on iterative training-based cluster assignment, which can be sensitive to learning uncertainty and model initialization. In contrast, we propose a one-shot, training-free clustering method that identifies similar systems using the structure of their locally observed data. Specifically, each system estimates a local state covariance matrix, and cluster identities are inferred by measuring the alignment between the leading covariance eigenspaces of different systems. We provide a mathematical interpretation of the proposed similarity score and develop a finite-sample analysis that characterizes how covariance estimation error induces eigenspace perturbations in terms of the underlying system dynamics. We then derive a probability bound for pairwise false merges and a global clustering success guarantee. Numerical experiments demonstrate that the proposed eigenspace-based clustering method effectively identifies systems with shared dynamics, leading to lower personalized model-estimation error compared with training-based clustering and non-clustered baselines.

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.

This paper presents an invariant extended Kalman filtering (InEKF) approach for real-time state estimation of humanoid robots operating on non-inertial ground using only onboard proprioceptive sensing. The proposed approach estimates the robot's base position and velocity relative to the moving ground frame without requiring direct measurements of ground motion or externally mounted sensors. By exploiting kinematic constraints at the stance foot through foot-mounted IMUs, the filter accounts for ground-induced nonlinearities in the process and measurement models while remaining fully proprioceptive. The estimator is formulated to admit a right-invariant measurement model, enabling favorable error dynamics under large initial uncertainties. Observability analysis establishes conditions under which the robot's relative base position and velocity are observable with respect to the non-inertial ground frame. Experiments with the Digit humanoid robot standing and squatting atop a swaying and pitching ground showcase a 96% speedup in convergence rate and an 80% reduction in position estimate errors over existing InEKFs. Walking experiments on a uni-axially rotating ground achieve an average estimation error of less than 9 cm for an initial error of up to 1 m.

This paper proposes a constant time-delay trajectory tracking method for vehicle convoys operating without inter-vehicle communication, a common coordinate system, or global positioning. The method integrates a probabilistic sequence-to-sequence (Seq2Seq) neural network with an invariant extended Kalman filter (IEKF) to warm-start the prediction process, allowing accurate estimation of a leader vehicle's relative trajectory on the SE(2) manifold. A geometric model predictive controller is further incorporated to fully exploit the manifold-based trajectory predictions for improved control performance. The system can handle arbitrary nonlinear trajectories with varying speeds and motion profiles while reducing the need for expert-based domain knowledge for the design of trajectory following systems, even under long trajectory delays. The effectiveness of the method is validated through comparisons with a pure IEKF baseline, learning-based methods, and the ground-truth trajectory in kinematic simulations, as well as in experiments using real robotic vehicles.

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 UAV operations on ships require reliable vision-based relative pose estimation, yet at-sea validation is costly, weather-dependent, and risky. This paper presents a hardware-validated vision-in-the-loop framework that enables fully autonomous indoor flight while emulating photorealistic maritime environments. Rendered maritime views are processed onboard by a deep transformer-based monocular pose estimator. Delayed vision measurements are fused with high-rate IMU data using a delayed Kalman filter to provide consistent state estimates for geometric control. The system captures critical embedded effects, including perception latency, asynchronous updates, and computational constraints, that are absent in pure simulation. Autonomous takeoff, trajectory tracking, and landing experiments demonstrate stable closed-loop flight. The results establish a safe and hardware-realistic intermediate stage for developing maritime UAV autonomy prior to shipboard deployment.

Joint prediction sets for multivariate time series should control a single event while adapting to cross-coordinate dependence. We study filtered conformal ellipsoids: a frozen state-space filter emits a one-step predictive mean and covariance, and split-conformal calibration is applied to the resulting Mahalanobis scores. The filter is used to choose the ellipsoid shape; conformal calibration chooses the scalar radius, so the construction benefits from a learned predictive covariance without relying on Gaussian tail probabilities for coverage. The main difficulty is that filtered scores are dependent and learned recurrent filters need not contract in their raw hidden state; we therefore analyse contraction in an observable predictive-law quotient that identifies hidden states producing the same future sequence of emitted Gaussian laws. Under a stable Bayes Gaussian-projection filter, covariance bounds, and a finite-horizon observability Fisher condition, small excess Gaussian negative log-likelihood implies contraction of the learned emitted laws. Combined with a threshold-autocovariance envelope this yields a Chebyshev-type approximate coverage bound for filtered split-conformal prediction under dependence; a sharper Bernstein-type bound requires an additional geometric-mixing concentration assumption. Under Gaussian oracle realisability we also obtain a near-oracle log-volume comparison within the class of conditionally valid Gaussian ellipsoid rules. We instantiate the framework with a GCN-GRU filter with diagonal-plus-low-rank covariance. On moderate-size graph-native traffic benchmarks (METRLA-$20$ and PEMSBAY-$50$), the learned filter gives sharper at-target ellipsoids than static-covariance and non-filter baselines; at full-graph scale and on non-graph-native datasets, factor and copula baselines can be stronger.

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.

We establish sufficient conditions for robust positive invariance under state- and input-dependent disturbances with anisotropic covariance structure. The proposed ansatz maps a fixed ellipsoidal template through a GP-derived positive-definite matrix field, subsuming scalar homothetic scaling while retaining finite graph-based verification. The resulting LMI conditions couple the learned field to Schur-stable dynamics; an isotropic fallback with inflation factor $r=1/(1-γ_{\mathrm{cl}})$ proves admissibility. During each learning epoch the field is frozen, so online tube evaluation is one GP covariance query and a small matrix square root, with no online set iteration or LMI solve. Quadrotor simulations show a $195\times$ reduction in 3D velocity-tube volume and a $2.1{\times}10^5$ reduction in the joint 7D velocity-control subspace relative to a non-adaptive homothetic baseline. This extended version adds full proofs, a separated offline/online complexity analysis, and controller-sweep, contraction, and projection-area studies.

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.

Auto-regressive models have emerged as powerful tools for sequential data, from language to video. Understanding how and why these models learn latent representations remains an open theoretical question. In this work, we demonstrate that when trained by empirical risk minimization on data from partially observed linear dynamical systems, two-layer linear auto-regressive models naturally learn to approximate Kalman filtering. In particular, we show that the learned hidden representation coincides, up to a similarity transformation, with the state estimates produced by the optimal (Kalman) filter, even though the model has no explicit knowledge of the underlying dynamics or state. The result follows from three main insights. First, we establish that the Kalman filter is well approximated by an auto-regressive model with bounded truncation error. Second, we show that despite non-convexity, the two-layer optimization landscape is benign, i.e., all stationary points are either strict saddles or global minima. Finally, as our main contributions, we provide finite-sample guarantees on prediction error, parameter estimation error, and latent state recovery. Numerical simulations support the theoretical results and demonstrate that the latent representations of auto-regressive models recover state estimates.

The ensemble Kalman filter (EnKF) is widely adopted for sequential data assimilation, but fails for solutions with discontinuities, such as shocks in compressible flows. Uncertainty in shock location induces multimodal ensemble statistics that violate the Gaussian assumptions underlying the EnKF, producing large-scale spurious oscillations in the analysis state. We introduce a feature-preserving latent-EnKF that performs the ensemble update in a learned low-dimensional latent space, where shock and flow features admit a smooth manifold representation, thereby preserving sharp features during EnKF analysis. The updated latent state is mapped back to physical state through a shared decoder for all ensemble members. The algorithm eliminates the member-specific ordered training and positivity flooring used in prior approaches. Numerical experiments on a Sod shock tube and Mach 2 shock interaction with a 2D cylinder, using sparse and noisy observations, show accurate feature recovery of shocks and contact discontinuities without spurious oscillations.

Visual localization in complex indoor environments remains a critical challenge for robotics and AR applications. Sequential localization, where pose estimates are refined over time, is important for autonomous agents. However, traditional methods often require storing extensive image databases or point clouds, leading to significant overhead. This paper introduces a novel, lightweight approach to sequential visual localization using 3D scene graphs. Our method represents the environment with a compact scene graph, where nodes represent objects (with coarse meshes) and edges encode spatial relationships. For each image in the localization phase, we extract per-patch semantic features, predicting object identities. Localization is performed within a particle filter framework. Each particle, representing a camera pose, projects the coarse object meshes from the scene graph into the image, assigning object identities to patches based on visibility. The similarity of the per-patch features, in the input image, and object features from the scene graph determines the weight of a particle. Subsequent images are incorporated sequentially, refining the pose estimate. By leveraging a compact scene graph and efficient semantic matching, our method significantly reduces storage while maintaining performance on real-world datasets. The code will be available at https://github.com/DmblnNicole/sg2loc.

Accurate position estimation is crucial for the successful implementation of future lunar landings using autonomous vehicles, especially in dangerous environments with sparse terrain features. In this paper, we propose a terrain relative navigation (TRN) algorithm combining our deep-learning crater detector, which was designed specifically for the NASA Crater Detection Challenge problem, and an Extended Kalman Filter (EKF). Our detector analyzes crater features from the monocular images acquired from orbit, and their matches with craters from a global database are identified via a Hungarian assignment approach followed by the consensus-based outliers removal method. The estimated measurements are then used to refine an EKF, where spacecraft pose estimation in the Lunar-Centered Lunar-Fixed (LCLF) frame of reference, augmented with altitude aiding information, constrains radial drift. The simulation results indicate that even if the spacecraft is off from its actual location up to 5 km, TRN could recover from this situation, achieving navigation error reduction to a few hundred meters. It should be noted that in order to maintain crater feature correspondences, it is important to match the image resolution and the scales within the scene to the detector training set distribution.

Data assimilation (DA) in subsurface flow entails calibrating model parameters to match observed data, typically at wells, while preserving geological realism. Latent diffusion models (LDMs) provide efficient mappings from high-dimensional geological model space to a low-dimensional latent variable, reducing the dimensionality of the inverse problem while maintaining plausibility in posterior geomodels. However, the high nonlinearity in the LDM mapping may degrade the performance of Kalman-gain-based ensemble updates. We present a systematic comparison of DA algorithms applied to large-scale 3D channelized geomodels with hierarchical geological uncertainty. We compare model-space and latent-space DA using the ensemble smoother with multiple data assimilation (ESMDA), and demonstrate a key trade-off: model-space updates achieve significant uncertainty reduction but produce geologically unrealistic posterior models, while latent-space updates preserve realism but exhibit limited uncertainty reduction. Motivated by this, we explore rigorous Markov chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) algorithms in the 3D-LDM latent space. To accommodate their high computational demands, we develop a fast surrogate flow model that approximates well-rate responses. MCMC and SMC are evaluated against ESMDA across three synthetic test cases, with DA performed in the LDM latent space. All models maintain geological realism due to the LDM parameterization. MCMC and SMC are consistent with one another and achieve lower data mismatch and more uncertainty reduction than latent-space ESMDA. Our overall results demonstrate that ensemble Kalman methods may provide overestimated posterior uncertainty with highly nonlinear parameterizations, while rigorous Monte Carlo sampling, enabled by fast surrogate models, can provide a more reliable alternative.

Precise state estimation for navigation of autonomous agricultural robots is often compromised by sensor outages (GNSS/LiDAR/Visual) and high-frequency vibrations inherent in off-road environments. This paper proposes a robust navigation algorithm based on a jerk-augmented Extended Kalman Filter (EKF) integrated with a Multiple Tuning Factor (MTF) adaptation method. Unlike standard EKF approaches that assume constant measurement noise, our method dynamically adjusts the measurement covariance matrix in real-time, allowing the system to cope with sudden disturbances and sensor outliers. We evaluate the algorithm using real-world data from a Salin247 autonomous robot. Results demonstrate that jerk-augmentation combined with MTF adaptation significantly reduces 3D position Root Mean Square Error (RMSE) compared to baseline EKF models, providing superior dead-reckoning capabilities.

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.

Reliable navigation in GPS-denied environments remains a fundamental challenge in robotics, aerospace, and autonomous vehicle applications. This paper presents a Dual Quaternion-Based Unscented Kalman Filter (DQUKF) equipped with a Visual Inertial Odometry (VIO) algorithm for accurate state estimation enabling navigation in GPS denied locations. The proposed framework formulates the DQUKF in an error state manner, where the nominal pose is represented by a unit dual quaternion and the local pose error is represented by a 6-dimensional twistor parameterization used for sigma point generation, covariance propagation, and measurement correction. In parallel, the VIO algorithm tracks features across image frames, synchronizes measurements between the IMU and camera, and provides visual constraints that complement inertial propagation. Simulation results on the EuRoC MAV dataset show that the proposed DQUKF converges under high initialization uncertainty and achieves a position RMSE of 0.2584~m in the difficult flight sequence, outperforming the benchmark filters.

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 work introduces a hybrid deep learning approach integrated with an Unscented Kalman Filter (UKF) to enhance pose estimation accuracy in Visual-Inertial Odometry (VIO) for autonomous navigation. The proposed model employs a Vision Transformer (ViT) network to effectively capture temporal dependencies from inertial measurement unit (IMU) data and utilizes a Multiscale Convolutional Neural Network (MCNN) to learn optical flow-based motion cues from visual data. An adaptive sensor fusion module dynamically weights IMU and visual features by leveraging estimated uncertainty, thus improving robustness in diverse and challenging environmental conditions. Additionally, a novel uncertainty-aware loss function is proposed to explicitly incorporate prediction uncertainty into the learning process, enabling robust and accurate navigation under noisy, incomplete, or unreliable sensor inputs. Comprehensive evaluations of the KITTI dataset demonstrate that the proposed method significantly outperforms baseline approaches, achieving superior performance in terms of Absolute Trajectory Error (ATE) and Relative Pose Error (RPE). The lightweight and computationally efficient model processes data at 155 FPS on an NVIDIA A100 GPU, making it highly suitable for deployment in resource-constrained autonomous systems.