Extended Kalman Filter

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

This paper proposes a cooperative target circumnavigation framework for multiple unmanned surface vehicles (USVs) operating without external localization. The objective is to maintain a uniform circular formation of a specified radius around a target using only limited onboard sensing. The framework adopts a heterogeneous perception strategy that distinguishes between the asymmetric sensing relationships with the target and among the USVs. Specifically, the USVs obtain relative range and displacement measurements through active perception and inter-vehicle communication, while bearing measurements to a non-cooperative target are acquired via passive sensors. To estimate relative positions--both among USVs and between each USV and the target--we employ a Maximum Correntropy Kalman Filter and a Pseudo-Linear Kalman Filter, respectively. A coupled oscillator-based formation controller is designed to ensure system observability while achieving circumnavigation. Theoretical analysis demonstrates that the controller ensures the relative motions between the USVs, as well as that between each USV and the target, satisfy the persistent excitation condition, thereby guaranteeing observability of the Kalman-based filters. The effectiveness of the proposed approach is validated through numerical simulations.

Kalman filter (KF)-based multi-object tracking (MOT) remains a strong baseline for autonomous driving due to its strong performance, computational efficiency and interpretability. In most practical systems, the process noise and measurement noise covariances are defined globally and shared across object classes, presuming identical uncertainty characteristics across heterogeneous traffic participants. This work revisits this assumption and proposes CANMOT, a class-aware and object-aligned noise modeling framework for KF-based 3D MOT. Class-specific diagonal process and measurement covariance matrices are introduced and optionally expressed in the object coordinate frame to preserve longitudinal-lateral anisotropy. Systematic experiments on the nuScenes benchmark show that class-aware and object-aligned noise modeling improves tracking performance and substantially reduces identity switches compared to state-of-the-art (SotA). In addition, the consistency of the estimated uncertainty is analyzed using the Average Normalized Estimation Error Squared (ANEES) and $χ^2$-based violation tests. The results reveal severe overconfidence in standard KF-based MOT baselines. While the proposed formulation improves calibration without modifying the underlying filtering framework, it still exhibits substantial inconsistency, highlighting the need for further research in this area. Code is available at https://github.com/rst-tu-dortmund/learned-3d-nms.

Kalman filtering performance is highly sensitive to model mismatch and noise covariance tuning. Learning-based approaches address these limitations but typically rely on supervised training with large datasets and do not produce consistent uncertainty estimates. In this paper, we propose a self-supervised Hybrid Adaptive Kalman Filter that learns structured corrections to system dynamics and process noise covariance from measurements alone while preserving the probabilistic structure of the filter. This allows the innovation likelihood to be computed and subsequently used for model classification via generalized Bayesian inference. Experimental results on real-world and simulated datasets demonstrate improved estimation accuracy and statistical consistency as well as robust classification performance across both low-data and large-data scenarios.

Robust state estimation is central to robotic autonomy, yet classical Kalman filters struggle with frequency-dependent disturbances and model mismatch such as sensor vibrations, electromagnetic interference, and periodic noise. Although Deep Kalman Filter (DKF) variants extend the Extended Kalman Filtering (EKF) framework by learning latent transitions, they lack explicit mechanisms to suppress band-limited noise components that typically corrupt sensor measurements in real-world scenarios. We introduce the Frequency-Weighted Neural Kalman Filter (FW-NKF), a unified hybrid approach that embeds a causal spectral-shaping operator into the Kalman measurement residual and jointly learns observation, and transition networks. By adapting both the filter spectrum and the latent state representation, FW-NKF attenuates the noise-dominated frequency bands while capturing complex residual structures. We conduct extensive experiments on four heterogeneous benchmarks, including chaotic systems such as multi-dimensional Lorenz systems and full-body inertial pose estimation, and find a reduction in localization error of up to 10% as well as marked improvements in orientation accuracy. Our ablation studies confirm that frequency weighting and deep latent-state modeling contribute to overall performance.

This paper introduces an estimation and control framework for dynamic landing of multi-rotor uncrewed aerial vehicles on moving platforms. The proposed method integrates nonlinear model predictive control with a real-time minimum-jerk trajectory planner that enforces a prescribed touchdown time, enabling consistent timing during the terminal descent. To enhance robustness in the presence of time-varying sensing quality, we utilize an adaptive unscented kalman filter that updates the process and measurement noise statistics online. In addition, we provide a reference feasibility analysis showing that minimum-jerk references induce bounded thrust and torque commands under standard tracking hypotheses. The proposed framework is evaluated in simulation and hardware experiments, and it is shown to achieve repeatable landings and improved platform velocity prediction accuracy relative to EKF/UKF-based methods.