Kalman Filtering

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Overview

Kalman filtering studies how to track a system’s changing, hidden state from noisy observations, using uncertainty to decide how much to trust each prediction and measurement. Linear Kalman filters and nonlinear variants such as the extended, unscented, and error-state filters are widely used in robot navigation, visual-inertial odometry, multi-object tracking, and data assimilation; evaluations often use settings such as KITTI, EuRoC, and nuScenes. Current approaches adapt noise covariances, handle delayed or distributed measurements, or combine recursive filters with neural networks and generative methods to cope with nonlinear dynamics and imperfect sensors. A central challenge is improving accuracy under model mismatch without sacrificing calibrated uncertainty, consistency, interpretability, or real-time efficiency.

Latest papers

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73 papers5 papers in the last four weeks, down 37% on the four weeks before. 0.0% of all new papers.

Mar 17, 2026

Neural Aided Adaptive Innovation-Based Invariant Kalman Filter

Autonomous platforms require accurate positioning to complete their tasks. To this end, a Kalman filter-based algorithms, such as the extended Kalman filter or invariant Kalman filter, utilizing inertial and external sensor fusion are applied. To cope with real-world scenarios, adaptive noise estimation methods have been developed primarily for classical Euclidean formulations. However, these methods remain largely unexplored in the tangent Lie space, despite it provides a principled geometric framework with favorable error dynamics on Lie groups. To fill this gap, we combine invariant filtering theory with neural-aided adaptive noise estimation in real-world settings. To this end, we derive a novel theoretical extension of classical innovation-based process noise adaptation formulated directly within the Lie-group framework. We further propose a lightweight neural network that estimates the process noise covariance parameters directly from raw inertial data. Trained entirely in a sim2real framework via domain adaptation, the network captures motion-dependent and sensor-dependent noise characteristics without requiring labeled real-world data. To examine our proposed neural-aided adaptive invariant Kalman filter, we focus on the challenging real-world scenario of autonomous underwater navigation. Experimental results demonstrate superior performance compared to existing methods in terms of position root mean square error. These results validate our sim2real pipeline and further confirm that geometric invariance significantly enhances learning-based adaptation and that adaptive noise estimation in the tangent Lie space offers a powerful mechanism for improving navigation accuracy in nonlinear autonomous platforms.

Barak Diker, Itzik Klein

Kalman FilteringInvariant EKFAutonomous Underwater Navigation
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Mar 13, 2026

Robust Automatic Differentiation of Square-Root Kalman Filters via Gramian Differentials

Square-root Kalman filters propagate state covariances in Cholesky-factor form for numerical stability, and are a natural target for gradient-based parameter learning in state-space models. Their core operation, triangularization of a matrix M∈Rn×mM \in \mathbb{R}^{n \times m}, is computed via a QR decomposition in practice, but naively differentiating through it causes two problems: the semi-orthogonal factor is non-unique when m>nm > n, yielding undefined gradients; and the standard Jacobian formula involves inverses, which diverges when MM is rank-deficient. Both are resolved by the observation that all filter outputs relevant to learning depend on the input matrix only through the Gramian MM⊤MM^\top, so the composite loss is smooth in MM even where the triangularization is not. We derive a closed-form chain-rule directly from the differential of this Gramian identity, prove it exact for the Kalman log-marginal likelihood and filtered moments, and extend it to rank-deficient inputs via a two-component decomposition: a column-space term based on the Moore--Penrose pseudoinverse, and a null-space correction for perturbations outside the column space of MM.

Adrien Corenflos

Department of Statistics, University of Warwick, Coventry, UK

Automatic DifferentiationKalman FilteringState Space Models
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Mar 13, 2026

Consistent and Efficient MSCKF-based LiDAR-Inertial Odometry with Inferred Cluster-to-Plane Constraints for UAVs

Robust and accurate navigation is critical for Unmanned Aerial Vehicles (UAVs) especially for those with stringent Size, Weight, and Power (SWaP) constraints. However, most state-of-the-art (SOTA) LiDAR-Inertial Odometry (LIO) systems still suffer from estimation inconsistency and computational bottlenecks when deployed on such platforms. To address these issues, this paper proposes a consistent and efficient tightly-coupled LIO framework tailored for UAVs. Within the efficient Multi-State Constraint Kalman Filter (MSCKF) framework, we build coplanar constraints inferred from planar features observed across a sliding window. By applying null-space projection to sliding-window coplanar constraints, we eliminate the direct dependency on feature parameters in the state vector, thereby mitigating overconfidence and improving consistency. More importantly, to further boost the efficiency, we introduce a parallel voxel-based data association and a novel compact cluster-to-plane measurement model. This compact measurement model losslessly reduces observation dimensionality and significantly accelerating the update process. Extensive evaluations demonstrate that our method outperforms most state-of-the-art (SOTA) approaches by providing a superior balance of consistency and efficiency. It exhibits improved robustness in degenerate scenarios, achieves the lowest memory usage via its map-free nature, and runs in real-time on resource-constrained embedded platforms (e.g., NVIDIA Jetson TX2).

Jinwen Zhu, Xudong Zhao, Fangcheng Zhu +4

Meituan UAV, Beijing, China · Dept. of Mechanical Engineering, Computer and Information Sciences, University of Delaware, Newark, DE

LiDAR OdometryRobot State EstimationUAV NavigationKalman Filtering
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Mar 13, 2026

From Gradients to Riccati Geometry: Kalman World Models for Single-Pass Learning

Backpropagation dominates modern machine learning, yet it is not the only principled method for optimizing dynamical systems. We propose Kalman World Models (KWM), a class of learned state-space models trained via recursive Bayesian filtering rather than reverse-mode automatic differentiation. Instead of gradient descent updates, we replace parameter learning with Kalman-style gain adaptation. Training becomes online filtering; error signals become innovations. We further extend this framework to transformer-based large language models (LLMs), where internal activations are treated as latent dynamical states corrected via innovation terms. This yields a gradient-free training and adaptation paradigm grounded in control theory. We derive stability conditions, analyze computational complexity, and provide empirical results on sequence modeling tasks demonstrating competitive performance with improved robustness and continual adaptation properties.

Andrew Kiruluta

UC Berkeley School of Information

Gradient-Free OptimizationState Space ModelsWorld Model LearningKalman FilteringContinual Learning for LLMs
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Mar 11, 2026

Distributed Kalman--Consensus Filtering with Adaptive Uncertainty Weighting for Multi-Object Tracking in Mobile Robot Networks

This paper presents an implementation and evaluation of a Distributed Kalman--Consensus Filter (DKCF) for Multi-Object Tracking (MOT) in mobile robot networks operating under partial observability and heterogeneous localization uncertainty. A key challenge in such systems is the fusion of information from agents with differing localization quality, where frame misalignment can lead to inconsistent estimates, track duplication, and ghost tracks. To address this issue, we build upon the MOTLEE framework and retain its frame-alignment methodology, which uses consistently tracked dynamic objects as transient landmarks to improve relative pose estimates between robots. On top of this framework, we propose an uncertainty-aware adaptive consensus weighting mechanism that dynamically adjusts the influence of neighbor information based on the covariance of the transmitted estimates, thereby reducing the impact of unreliable data during distributed fusion. Local tracking is performed using a Kalman Filter (KF) with a Constant Velocity Model (CVM) and Global Nearest Neighbor (GNN) data association. simulation results demonstrate that adaptive weighting effectively protects local estimates from inconsistent data, yielding a MOTA improvement of 0.09 for agents suffering from localization drift, although system performance remains constrained by communication latency.

Niusha Khosravi, Rodrigo Ventura, Meysam Basiri

Instituto Superior Técnico University of Lisbon Lisbon, Portugal

Multi-Object TrackingMulti-Robot SystemsKalman FilteringMulti-Agent Consensus
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Mar 9, 2026

Outlier-robust Autocovariance Least Square Estimation via Iteratively Reweighted Least Square

The autocovariance least squares (ALS) method is a computationally efficient approach for estimating noise covariances in Kalman filters without requiring specific noise models. However, conventional ALS and its variants rely on the classic least mean squares (LMS) criterion, making them highly sensitive to measurement outliers and prone to severe performance degradation. To overcome this limitation, this paper proposes a novel outlier-robust ALS algorithm, termed ALS-IRLS, based on the iteratively reweighted least squares (IRLS) framework. Specifically, the proposed approach introduces a two-tier robustification strategy. First, an innovation-level adaptive thresholding mechanism is employed to filter out heavily contaminated data. Second, the outlier-contaminated autocovariance is formulated using an εε-contamination model, where the standard LMS criterion is replaced by the Huber cost function. The IRLS method is then utilized to iteratively adjust data weights based on estimation deviations, effectively mitigating the influence of residual outliers. Comparative simulations demonstrate that ALS-IRLS reduces the root-mean-square error (RMSE) of noise covariance estimates by over two orders of magnitude compared to standard ALS. Furthermore, it significantly enhances downstream state estimation accuracy, outperforming existing outlier-robust Kalman filters and achieving performance nearly equivalent to the ideal Oracle lower bound in the presence of noisy and anomalous data.

Jiahong Li, Fang Deng

College of Robotics, Beijing Union University, Beijing 100101, China · Key Laboratory of Intelligent Control and Decision of Complex Systems, and also with the School of Automation, Beijing Institute of Technology, Beijing 100081, China

Covariance EstimationRobust EstimationKalman Filtering
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Mar 3, 2026

Robust Tightly-Coupled Filter-Based Monocular Visual-Inertial State Estimation and Graph-Based Evaluation for Autonomous Drone Racing

Autonomous drone racing (ADR) demands state estimation that is simultaneously computationally efficient and resilient to the perceptual degradation experienced during extreme velocity and maneuvers. Traditional frameworks typically rely on conventional visual-inertial pipelines with loosely-coupled gate-based Perspective-n-Points (PnP) corrections that suffer from a rigid requirement for four visible features and information loss in intermediate steps. Furthermore, the absence of GNSS and Motion Capture systems in uninstrumented, competitive racing environments makes the objective evaluation of such systems remarkably difficult. To address these limitations, we propose ADR-VINS, a robust, monocular visual-inertial state estimation framework based on an Error-State Kalman Filter (ESKF) tailored for autonomous drone racing. Our approach integrates direct pixel reprojection errors from gate corners features as innovation terms within the filter. By bypassing intermediate PnP solvers, ADR-VINS maintains valid state updates with as few as two visible corners and utilizes robust reweighting instead of RANSAC-based schemes to handle outliers, enhancing computational efficiency. Furthermore, we introduce ADR-FGO, an offline Factor-Graph Optimization framework to generate high-fidelity reference trajectories that facilitate post-flight performance evaluation and analysis on uninstrumented, GNSS-denied environments. The proposed system is validated using TII-RATM dataset, where ADR-VINS achieves an average RMS translation error of 0.143 m, while ADR-FGO yields 0.060 m as a smoothing-based reference. Finally, ADR-VINS was successfully deployed in the A2RL Drone Championship Season 2, maintaining stable and robust estimation despite noisy detections during high-agility flight at top speeds of 20.9 m/s. We further utilize ADR-FGO for post-flight evaluation in uninstrumented racing environments.

Maulana Bisyir Azhari, Donghun Han, Sung Jun Park +1

Unmanned Systems Research Group (USRG), School of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, South Korea.

Autonomous Drone RacingError-State Kalman FilteringVisual-Inertial OdometryAerial RoboticsKalman FilteringFactor Graph Optimization
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Mar 2, 2026

Event-Only Drone Trajectory Forecasting with RPM-Modulated Kalman Filtering

Event cameras provide high-temporal-resolution visual sensing that is well suited for observing fast-moving aerial objects; however, their use for drone trajectory prediction remains limited. This work introduces an event-only drone forecasting method that exploits propeller-induced motion cues. Propeller rotational speed are extracted directly from raw event data and fused within an RPM-aware Kalman filtering framework. Evaluations on the FRED dataset show that the proposed method outperforms learning-based approaches and vanilla kalman filter in terms of average distance error and final distance error at 0.4s and 0.8s forecasting horizons. The results demonstrate robust and accurate short- and medium-horizon trajectory forecasting without reliance on RGB imagery or training data.

Hari Prasanth S. M., Pejman Habibiroudkenar, Eerik Alamikkotervo +2

Department of Energy and Mechanical Engineering, Aalto University, 02150 Espoo, Finland

Trajectory PredictionKalman FilteringEvent-Based Vision
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Feb 17, 2026

A Comparison of Bayesian Prediction Techniques for Mobile Robot Trajectory Tracking

This paper presents a performance comparison of different estimation and prediction techniques applied to the problem of tracking multiple robots. The main performance criteria are the magnitude of the estimation or prediction error, the computational effort and the robustness of each method to non-Gaussian noise. Among the different techniques compared are the well known Kalman filters and their different variants (e.g. extended and unscented), and the more recent techniques relying on Sequential Monte Carlo Sampling methods, such as particle filters and Gaussian Mixture Sigma Point Particle Filter.

Jose Luis Peralta-Cabezas, Miguel Torres-Torriti, Marcelo Guarini-Hermann

Dept. of Electrical Engineering, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Casilla 306-22, Santiago, Chile

Robot Trajectory TrackingRobot State EstimationBayesian FilteringParticle FilteringKalman FilteringMulti-Robot Systems
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Feb 16, 2026

Kalman Filtering Based Flight Management System Modeling for AAM Aircraft

Advanced Air Mobility (AAM) operations are planned to utilize strategic flight planning services that predict temporal uncertainties to validate flight plans against hazards such as weather cells, restricted airspaces, and CNS disruption areas. This paper presents a Kalman Filter-based uncertainty propagation method that models Flight Management System (FMS) correction behavior through a sigmoid-blended measurement noise covariance. The sigmoid formulation generalizes existing discrete FMS activation thresholds into a continuous, tunable function that smoothly transitions the filter's measurement noise based on progress toward each waypoint. When the measurement noise is high, due to an inverse relationship, the Kalman gain is small and thus uncertainty grows; as the aircraft nears a waypoint, measurement noise decreases as a function of progress, the Kalman gain increases, and state covariance contracts which models the FMS progressively correcting toward the planned trajectory. The approach is computationally efficient (up to two orders of magnitude faster than Monte Carlo methods), scales with control inputs, and is parametrically tunable for different classes of aircraft. The measurement noise covariance is calibrated using real Automatic Dependent Surveillance-Broadcast (ADS-B) data from commercial Instrument Flight Rules (IFR) flights serving as surrogates for future AAM operations, achieving coverage probability conservative relative to theoretical Gaussian predictions at the 1-sigma confidence level on a hold out verification dataset (N = 36). Parameter sensitivity analysis across multiple flight routes demonstrates robust behavior, and comparative evaluation against Monte Carlo and Linear Propagation methods contextualizes the method's computational and accuracy trade-offs.

Balram Kandoria, Aryaman Singh Samyal

SkyGrid, Austin, TX, 78727

Kalman FilteringUncertainty QuantificationUncertainty Propagation
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Oct 29, 2025

Kalman-Bucy Filtering with Randomized Sensing: Fundamental Limits and Sensor Network Design for Field Estimation

Stability analysis of the Kalman filter under randomly lost measurements has been widely studied. We revisit this problem in a general continuous-time framework, where both the measurement matrix and noise covariance evolve as random processes, capturing variability in sensing locations. Within this setting, we derive a closed-form upper bound on the expected estimation covariance for continuous-time Kalman filtering. We then apply this framework to spatiotemporal field estimation, where the field is modeled as a Gaussian process observed by randomly located, noisy sensors. Using clarity, introduced in our earlier work as a rescaled form of the differential entropy of a random variable, we establish a lower bound on the expected spatially averaged clarity and show that its steady-state value converges to a grid-independent limit as the grid is refined. This result exposes fundamental performance limits through a composite sensing parameter that jointly captures the effects of the number of sensors, noise level, and measurement frequency. Simulations show close agreement between the continuous-time analytical solution and the discrete-time covariance, with the agreement improving as the sampling interval decreases. The analytical solution also avoids the recursive computations required in the discrete-time formulation. Most importantly, the derived limits provide principled and efficient guidelines for sensor network design prior to deployment.

Xinyi Wang, Devansh R. Agrawal, Dimitra Panagou

Department of Robotics, University of Michigan, Ann Arbor, MI 48109, USA · Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109, USA · Departments of Robotics and Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109, USA

Kalman Filtering
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Aug 18, 2025

Flow Matching for Efficient and Scalable Data Assimilation

Data assimilation (DA) estimates a dynamical system's state from noisy observations. Recent generative models like the ensemble score filter (EnSF) improve DA in high-dimensional nonlinear settings but are computationally expensive. We introduce the ensemble flow filter (EnFF), a training-free, flow matching (FM)-based framework that accelerates sampling and offers flexibility in flow design. EnFF uses Monte Carlo estimators for the marginal flow field, localized guidance for observation assimilation, and utilizes a novel flow path that exploits the Bayesian DA formulation. It generalizes classical filters such as the bootstrap particle filter and ensemble Kalman filter. Experiments on high-dimensional benchmarks demonstrate EnFF's improved cost-accuracy tradeoffs and scalability, highlighting FM's potential for efficient, scalable DA. Code is available at https://github.com/Utah-Math-Data-Science/Data-Assimilation-Flow-Matching.

Taos Transue, Bohan Chen, So Takao +1

Department of Mathematics and Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT, 84112 · The Computing and Mathematical Sciences Department, California Institute of Technology, 1200 E California Blvd, Pasadena, CA 91125

Flow MatchingKalman FilteringBayesian FilteringData AssimilationEnsemble Kalman Filtering
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May 12, 2025

Towards Accurate State Estimation: Motion Dynamics Kalman Filter for 3D Multi-Object Tracking

Robust 3D state estimation in multi-object tracking is crucial for object localization in self-driving vehicles. Misalignment between the Kalman filter (KF) motion model and an object's motion can cause state drift, particularly in distant and occlusion cases. The static motion model assumption in the conventional KF is widely used in 3D MOT due to its low latency; however, its estimation accuracy degrades as the object's motion disaligns with the chosen model due to traffic. Although recent work introduces a multimodel KF that runs multiple motion models simultaneously to improve state robustness, it incurs significant computational overhead, so many studies still favor the constant-motion KF to maintain efficiency. This work addresses this trade-off by introducing a motion dynamics Kalman filter (MD-KF) that accounts for motion variation through temporal modeling of object motion and adaptively scales the contribution of the motion components in the motion model to correct state-prediction drift caused by this variation, while maintaining computational efficiency by retaining a single-model structure. Evaluations on KITTI and the Waymo Open Dataset, complemented by vehicle experiments, show that MD-KF achieves tracking performance comparable to multimodel KF with an average 1.72x speedup, while outperforming it in handling highly distant and prolonged occluded objects.

Mohamed Nagy, Naoufel Werghi, Bilal Hassan +2

Khalifa University, Abu Dhabi, UAE · New York University of Abu Dhabi

Kalman Filtering3D MOTMulti-Object Tracking
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