Bayesian Filtering

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Bayesian filtering studies how to update beliefs about hidden states as new observations arrive, which supports reliable prediction and decision-making when measurements are noisy or incomplete. Kalman and Gaussian filters offer efficient updates for roughly unimodal beliefs, while particle, ensemble, and variational methods handle nonlinear or non-Gaussian systems; newer approaches also use learned proposals, score models, and generative flows. These methods are used in robotics, target tracking, navigation, and large-scale data assimilation, where both accurate state estimates and calibrated uncertainty matter. A central challenge is balancing computational cost and scalability against the ability to represent complex posterior distributions, especially in high-dimensional systems with sparse observations or changing dynamics.

Latest papers

58 papers7 papers in the last four weeks, down 22% on the four weeks before. 0.0% of all new papers.

May 20, 2026

A Semantic and Occlusion-Aware GM-PHD Filter

This paper proposes a new birth model including semantic information derived from deep learning to create an occlusion-aware Gaussian Mixture Probability Hypothesis Density (GM-PHD) filter. Unlike prior approaches that rely on simplistic or uniform assumptions, the proposed Semantic-Occlusion Aware (S-OA) birth model defines initialization terms by explicitly considering regions of occlusion and by leveraging semantic information about the environment. This enables the filter to accurately represent where new objects are more likely to appear, thereby improving tracking performance in complex and high-density driving scenarios. The method is evaluated through Monte Carlo simulations and experiments on the KITTI dataset. Performance is assessed by measuring the latency between first detection and track initiation, along with the mean absolute cardinality error and the Optimal Subpattern Assignment (OSPA) metric. Results demonstrate that the S-OA birth model reduces initialization delay in occlusion-heavy settings, matching or outperforming the strongest baseline in approximately 70% of cases. A sensitivity analysis of birth model weights is also provided. Overall, the findings underscore the benefits of integrating occlusion reasoning and semantic priors into Bayesian tracking frameworks for autonomous driving.

Jovan Menezes, Mark Campbell

Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA

Bayesian Filtering Autonomous Driving Perception Multi-Object Tracking

May 19, 2026

Training-Free Bayesian Filtering with Generative Emulators

Bayesian filtering is a well-known problem that aims to estimate plausible states of a dynamical system from observations. Among existing approaches to solve this problem, particle filters are theoretically exact for non-linear dynamics and observations, but suffer from poor scalability in high dimensions. In this work, we show that diffusion-based emulators of dynamical systems can be used to implement, without additional training, an optimal variant of particle filters that has remained largely unexplored due to implementation challenges with classical numerical solvers. Experiments on nonlinear chaotic systems, including atmospheric dynamics, demonstrate that the proposed approach successfully scales particle filtering to high-dimensional settings.

Thomas Savary, François Rozet, Gilles Louppe

SAIL, Montefiore institute, University of Liège, Belgium.

Particle Filtering Bayesian Filtering Data Assimilation

May 18, 2026

SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogate

Data assimilation (DA) addresses the problem of sequentially estimating the state of a dynamical system from noisy and incomplete observations. In this work, we employ a diffusion model as a world model to simulate and predict the system's dynamics. Recently, score-based diffusion models have learned global diffusion priors that effectively model (stochastic) dynamics, revealing strong potential for data assimilation. In this paper, we investigate how information from noisy observations can be incorporated to enable continuous correction and refinement of the predicted system state when using a diffusion prior. Motivated by particle filtering methods, we represent the posterior distribution using a set of particles. After receiving noisy observations, the diffusion model is guided using the observation likelihood to steer the generation process toward observation-consistent states. Nevertheless, such guidance does not guarantee sampling from the true posterior. We therefore employ a Sequential Monte Carlo approach over the diffusion trajectory, viewed as a path measure, to reweight and resample particles, thereby correcting the generation process and ensuring convergence toward the desired posterior distribution. This leads to an unbiased particle filtering method that rigorously fuses observational data with diffusion model simulations.

Lifu Wei, Yinuo Ren, Naichen Shi +1

Department of Mechanical Engineering, Northwestern University, Evanston, IL, United States · Institute for Computational & Mathematical Engineering, Stanford University, Stanford, CA, United States · Department of Industrial Engineering & Management Sciences, Northwestern University, Evanston, IL, United States

Particle Filtering Bayesian Filtering Data Assimilation Diffusion Models

May 15, 2026

The Score Kalman Filter

A central obstacle in nonlinear Bayesian filtering is representing the belief distribution. Moment-based filters address this by propagating polynomial moments and reconstructing a density from them. Recent work completes the predict-update loop via the maximum-entropy (MaxEnt) principle, but each step requires the partition function and its gradient, both

n

-dimensional integrals whose cost scales exponentially, restricting the demonstrated MaxEnt moment filtering to

n \le 4

. We avoid the partition function entirely by combining score matching with Stein's identity. In our setting, score matching reduces the density fit to a single linear solve whose coefficients are assembled directly from the propagated moments. The same parameters then drive Stein's identity to close the moment hierarchy during prediction and to recover posterior moments after each Bayesian update, keeping the full predict-update loop free of partition function evaluation. The resulting Score Kalman Filter (SKF) reduces to the classical information-form Kalman filter as a special case and performs every step through linear algebra. On nonlinear coupled-oscillator networks, the SKF runs through

n=20

and reports lower RMSE than the EKF, UKF, EnKF, and particle-filter baselines on the tested synthetic benchmarks.

Kaito Iwasaki, Anthony Bloch, Taeyoung Lee +1

Department of Mathematics University of Michigan · Department of Mechanical and Aerospace Engineering George Washington University · Department of Naval Architecture & Marine Engineering and Department of Robotics University of Michigan

Kalman Filtering Bayesian Filtering

May 13, 2026

Coupling-Informed Transport Maps for Bayesian Filtering in Nonlinear Dynamical Systems

A likelihood-free transport filtering method is proposed based on the couplings between state and observation variables. By exploiting a block-triangular structure in the transport map, the analysis step of filtering is reformulated as the minimization of the maximum mean discrepancy (MMD) between the true joint measure and its transport-based approximation. To circumvent the non-convexity in the MMD optimization, we introduce a training-free transport filter method via gradient flows, which leads to an analytic computation for the transport map that implies the steepest descent direction of the MMD. The proposed approach accurately approximates non-Gaussian filtering posteriors and avoids particle collapse. We provide a convergence analysis for the expectation of the MMD between the approximated posterior and the truth posterior. Finally, we extend the method to high-dimensional problems through domain localization. Numerical examples demonstrate the superior performance of our approach over conventional filtering methods in nonlinear, non-Gaussian scenarios.

Dengfei Zeng, Lijian Jiang, Shuyu Sun +1

School of Mathematical Sciences, Tongji University, Shanghai, 200092 China · School of Mathematical Sciences, Tongji University, Shanghai, 200092 China, Key Laboratory of Intelligent Computing and Applications (Ministry of Education), Tongji University, Shanghai, 200092 China

Dynamical Systems Simulation-Based Inference Bayesian Filtering Optimal Transport

May 12, 2026

Precision Tracked Transformer via Kalman Filtering, Kriging and Process Noise

The Transformer is the foundational building block of modern AI, yet offers no principled handling of uncertainty, which is prevalent in real applications: cold-start tokens with sparse histories in sequential recommendation, heterogeneous signal quality in language models, and attention sinks induced by unconstrained softmax. Every token is treated with uniform confidence. We show this uniformity is a degenerate case of our Bayesian Filtering Transformer (BFT): attention becomes precision-weighted kriging, the residual connection becomes a Kalman update with adaptive gain, and the FFN becomes a dynamics model propagating precision via a Jacobian--plus--process-noise rule. Observation precision comes from a parameter-free Restricted Maximum Likelihood (REML) estimator with a conjugate Bayesian prior. BFT replaces any Transformer layer with negligible overhead. On sequential recommendation, BFT applied to three major architectures yields significant gains on six benchmarks, with the largest improvements on cold-start users and rare items where uncertainty is highest. On supervised fine-tuning of large language models with noisy data, BFT improves robustness in two regimes: noisy supervision (token-label corruption in question answering) and noisy context (retrieval-augmented QA with real RAG distractors). A single principled modification -- restoring precision -- unlocks substantial headroom across both classical sequence-modeling and modern LLM regimes.

Bo Long, Deepak Agarwal, Jelena Markovic-Voronov +2

LinkedIn Core AI

Bayesian Filtering Transformer Attention Mechanisms Language Model Robustness

May 7, 2026

Online Bayesian Calibration under Gradual and Abrupt System Changes

Bayesian model calibration is central to digital twins and computer experiments, as it aligns model outputs with field observations by estimating calibration parameters and correcting systematic model bias. Classical Bayesian calibration introduces latent parameters and a discrepancy function to model bias, but suffers from parameter--discrepancy confounding and is typically formulated as an offline procedure under a stationary data-generating assumption. These limitations are restrictive in modern digital twin applications, where systems evolve over time and may exhibit gradual drift and abrupt regime shifts. While data assimilation methods enable sequential updates, they generally do not explicitly model systematic bias and are less effective under abrupt changes. We propose Bayesian Recursive Projected Calibration (BRPC), an online Bayesian calibration framework for streaming data under simulator mismatch and nonstationarity. BRPC extends projected calibration to the online setting by separating a discrepancy-free particle update for calibration parameters from a conditional Gaussian process update for discrepancy, preserving identifiability while enabling bias-aware adaptation under gradual system evolution. To handle abrupt changes, BRPC is integrated with restart mechanisms that detect regime shifts and reset the calibration process. We establish theoretical guarantees for both components, including tracking performance under gradual evolution and false-alarm and detection behavior for restart mechanisms. Empirical studies on synthetic and plant-simulation benchmarks show that BRPC improves calibration accuracy under gradual changes, while restart-augmented BRPC further improves robustness and predictive performance under abrupt regime shifts compared to sliding-window Bayesian calibration and data assimilation baselines.

Yang Xu, Chiwoo Park

Department of Industrial and Systems Engineering University of Washington Seattle, WA 98195

Particle Filtering Bayesian Filtering Model Calibration Digital Twins

May 4, 2026

Natural Gradient Bayesian Filtering: Geometry-Aware Filter for Dynamical Systems

Bayesian filtering is a cornerstone of state estimation in complex systems such as aerospace systems, yet exact solutions are available only for linear Gaussian models. In practice,nonlinear systems are handled through tractable approximations,with Gaussian filters such as the extended and unscented Kalman filters being among the most widely used methods. This tutorial revisits Gaussian filtering from an information-geometric perspective, viewing the prediction and measurement update steps as inference procedures over state distributions. Within this framework, we introduce a geometry-aware Gaussian filtering approach that leverages natural gradient descent on the statistical manifold of Gaussian distributions. The resulting Natural Gradient Gaussian Approximation (NANO) filter iteratively refines the posterior mean and covariance while respecting the intrinsic geometry of the Gaussian family and preserving the positive definiteness of the covariance matrix. We further highlight fundamental connections to the classical Kalman filtering, showing that a single natural-gradient step exactly recovers the Kalman measurement update in the linear-Gaussian case. The practical implications of the proposed framework are illustrated through case studies in representative nonlinear estimation problems,including satellite attitude estimation, simultaneous localization and mapping, and state estimation for robotic systems including quadruped and humanoid robots.

Chang Liu, Wenhan Cao, Zeju Sun +8

School of Advanced Manufacturing and Robotics, Peking University, China. · School of Vehicle and Mobility, Tsinghua University, China. · Beijing Institute of Mathematical Sciences and Applications (BIMSA), China. +3

Bayesian Filtering Robot State Estimation

May 1, 2026

Learning Discriminators for Resampling in the Ensemble Gaussian Mixture Filter through a Normalizing Flow Approach

The ensemble Gaussian mixture filter (EnGMF) is a powerful, convergent particle filter capable of medium-to-high dimensional non-linear filtering. The EnGMF relies on a resampling step that can generate physically unrealistic posterior samples, that would subsequently produce physically meaningless forecasts. This work introduces the discriminator-informed resampling procedure, that augments the posterior resampling step with a discriminator that accepts or rejects candidate particles based on their physical plausibility. In this work these discriminators are learned through a normalizing flow approach. Numerical experiments on both the Ikeda map and the Lorenz '63 system show that discriminator informed resampling procedure consistently reduces error relative to the standard EnGMF in low-ensemble regimes.

Zain Jabbar, Andrey A. Popov

Particle Filtering Bayesian Filtering Data Assimilation

May 1, 2026

Robust volatility updates for Hierarchical Gaussian Filtering

Hierarchical Gaussian Filtering (HGF) networks allow for efficient updating of posterior distributions (beliefs) about hidden states of an agent's environment. HGF parent nodes can target the mean or variance of their children. New information entering at input nodes leads to a cascade of belief updates across the network according to one-step update equations for each node's mean and precision (inverse variance). However, the original form of the update equations for variance-targeting parents(volatility coupling) can in some regions of parameter space lead to negative posterior precision, a logical impossibility which causes the updating algorithm to terminate with an error. In this report, we introduce a modified quadratic approximation to the variational energy of volatility-coupled nodes that avoids negative posterior precision. The key idea is to interpolate between two quadratic expansions of the variational energy: one at the prior prediction and one at a second mode whose location is obtained in closed form via the Lambert W function. The resulting update equations are robust across the entire parameter space and faithfully track the variational posterior even for large prediction errors.

Christoph Mathys, Nicolas Legrand, Peter Thestrup Waade +2

Interacting Minds Centre, Aarhus University, 8000 Aarhus C, Denmark · Centre for Humanities Computing, Aarhus University, 8000 Aarhus C, Denmark · Translational Neuromodeling Unit, University of Zurich & ETH Zurich, 8032 Zurich, Switzerland +1

Bayesian Filtering Hierarchical Bayesian Modeling Variational Inference

May 1, 2026

Breaking the Communication-Accuracy Trade-off: A Sparsified Information Diffusion Framework for Multi-Agent Collaborative Perception

The growing relevance of multi-agent systems has drawn increasing focus on communication-efficient filters for collaborative perception to alleviate the system's communication burden. While the event-triggered (ET) mechanism can improve communication efficiency in collaborative state estimation, an inevitable trade-off exists between estimation accuracy and communication cost in ET filters. This paper proposes a fast and accurate ET diffusion-based filter for real-time multi-agent collaborative target tracking, aiming to reduce the system's data transmission without compromise in tracking performance. The proposed filter achieves improved tracking accuracy, reduced data transmission, and accelerated convergence using an error-minimized ET cubature information filter (CIF) for local estimation, and a correlation-aware diffusion strategy for global fusion. The experimental results confirm the scalability of the proposed EDC-CIF algorithm and demonstrate its efficacy in simultaneously reducing estimation error and computation time while significantly enhancing communication efficiency.

Jirong Zha, Chenyu Zhao, Nan Zhou +5

Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China · Shenzhen Institute of Artificial Intelligence and Robotics, Shenzhen, China, 518000 · Shenzhen Smart City Technology Development Group, Shenzhen, China, 518000

Bayesian Filtering Cooperative Perception Multi-Agent Communication

Apr 23, 2026

SNGR: Selective Non-Gaussian Refinement for Ambiguous SLAM Factor Graphs

We present Selective Non-Gaussian Refinement (SNGR), a SLAM framework that augments iSAM2 with targeted nested sampling on windows where Gaussian approximations are likely to fail. We detect such regions using the condition number of joint marginal covariances and selectively refine them using the full nonlinear factor graph likelihood, with a gating mechanism to avoid degradation in multimodal cases. Experiments on range-only SLAM with wrong data association show that SNGR achieves high-precision failure detection and consistent local likelihood improvements while reducing computational cost relative to exhaustive non-Gaussian inference. These results highlight both the promise and the limitations of selective refinement for approximate SLAM posteriors.

Anushka Kulkarni, Sarthak Dubey

Northeastern University, Boston, MA, USA

Simultaneous Localization and Mapping Factor Graph Optimization Bayesian Filtering Robot Localization

Apr 11, 2026

Natural Gradient Gaussian Approximation Filter on Lie Groups for Robot State Estimation

Accurate state estimation for robotic systems evolving on Lie group manifolds, such as legged robots, is a prerequisite for achieving agile control. However, this task is challenged by nonlinear observation models defined on curved manifolds, where existing filters rely on local linearization in the tangent space to handle such nonlinearity, leading to accumulated estimation errors. To address this limitation, we reformulate manifold filtering as a parameter optimization problem over a Gaussian-distributed increment variable, thereby avoiding linearization. Under this formulation, the increment can be mapped to the Lie group through the exponential operator, where it acts multiplicatively on the prior estimate to yield the posterior state. We further propose a natural gradient optimization scheme for solving this problem, whose iteration process leverages the Fisher information matrix of the increment variable to account for the curvature of the tangent space. This results in an iterative algorithm named the Natural Gradient Gaussian Approximation on Lie Groups (NANO-L) filter. Leveraging the perturbation model in Lie derivative, we prove that for the invariant observation model widely adopted in robotic localization tasks, the covariance update in NANO-L admits an exact closed-form solution, eliminating the need for iterative updates thus improving computational efficiency. Hardware experiments on a Unitree GO2 legged robot operating across different terrains demonstrate that NANO-L achieves approximately 40% lower estimation error than commonly used filters at a comparable computational cost.

Tianyi Zhang, Wenhan Cao, Chang Liu +2

School of Vehicle and Mobility, Tsinghua University, Beijing, China · College of Engineering, Peking University, Beijing, China · School of Vehicle and Mobility and College of Artificial Intelligence, Tsinghua University, Beijing, China

Robot State Estimation Bayesian Filtering Lie Group Methods Natural Gradient Methods

Apr 9, 2026

A Machine Learning Framework for Turbofan Health Estimation via Inverse Problem Formulation

Estimating the health state of turbofan engines is a challenging ill-posed inverse problem, hindered by sparse sensing and complex nonlinear thermodynamics. Research in this area remains fragmented, with comparisons limited by the use of unrealistic datasets and insufficient exploration of the exploitation of temporal information. This work investigates how to recover component-level health indicators from operational sensor data under realistic degradation and maintenance patterns. To support this study, we introduce a new dataset that incorporates industry-oriented complexities such as maintenance events and usage changes. Using this dataset, we establish an initial benchmark that compares steady-state and nonstationary data-driven models, and Bayesian filters, classic families of methods used to solve this problem. In addition to this benchmark, we introduce self-supervised learning (SSL) approaches that learn latent representations without access to true health labels, a scenario reflective of real-world operational constraints. By comparing the downstream estimation performance of these unsupervised representations against the direct prediction baselines, we establish a practical lower bound on the difficulty of solving this inverse problem. Our results reveal that traditional filters remain strong baselines, while SSL methods reveal the intrinsic complexity of health estimation and highlight the need for more advanced and interpretable inference strategies. For reproducibility, both the generated dataset and the implementation used in this work are made accessible.

Milad Leyli-Abadi, Lucas Thil, Sebastien Razakarivony +2

Institut de recherche technologique SystemX, Palaiseau, France · École Polytechnique, LIX, Palaiseau, France · Safran Tech, Magny-les-Hameaux, France

Predictive Maintenance Bayesian Inverse Problems Bayesian Filtering

Apr 8, 2026

Amortized Filtering and Smoothing with Conditional Normalizing Flows

Bayesian filtering and smoothing are central to data assimilation in nonlinear dynamical systems. Recent advances in deep generative models provide flexible approximations of the associated non-Gaussian posterior distributions. However, several existing approaches require the score to be re-estimated or a transport map to be constructed at each assimilation step. We propose an amortized framework for filtering and smoothing that reuses trained conditional models across observation sequences and assimilation times. The framework jointly learns a shared recurrent summary network and two conditional normalizing flows from simulated state and observation trajectories. The recurrent network represents each observation history by a fixed-dimensional summary that conditions the filtering approximation and, together with the next state, the backward transition approximation. An information-theoretic analysis shows that, under the Markov assumption, a summary sufficient for filtering is also sufficient for the backward kernel. Combining the terminal filtering approximation with the backward kernels yields an approximate joint smoothing distribution. Numerical experiments on advection-diffusion, Burgers, and Lorenz systems demonstrate the accuracy of the proposed filtering and smoothing approximations and characterize the evolution of their errors beyond the training horizon.

Tiangang Cui, Xiaodong Feng, Chenlong Pei +2

School of Mathematics and Statistics, The University of Sydney, Camperdown, NSW 2006, Australia · Institute of Advanced Study, Beijing Normal-Hong Kong Baptist University, Zhuhai 519087, China · SKLMS & Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences +1

Bayesian Filtering Data Assimilation Bayesian Inference Amortized Inference

Apr 3, 2026

Rethinking Forward Processes for Score-Based Nonlinear Data Assimilation in High Dimensions

Data assimilation is the process of estimating the state of a dynamical system over time by combining model predictions with measurements. This task becomes challenging when the system is nonlinear and high-dimensional. To address this, score-based Bayesian filters have recently emerged. However, these methods still show unsatisfactory performance in certain cases, particularly under spatially sparse measurements. Such degradation stems from heuristic approximations of the likelihood score, whose errors can accumulate over time. This limitation arises because the methods simply adopt a classical forward process for generative modeling that transforms a data distribution toward a Gaussian distribution, which is independent of the measurement equation. Here, we propose a forward process tailored for filtering that transforms the system state toward the measurement space, enabling a theoretically sound formulation of the likelihood score. Based on this, we develop the Measurement-Aware Score-based Filter (MASF). We evaluate MASF on Kolmogorov flow, a high-dimensional fluid benchmark with up to

\mathcal{O}(10^5)

dimensions, under diverse measurement operators, including nonlinear cases with a dimensional mismatch between the state and the measurements. MASF shows improved performance over existing score-based filters and ensemble-type Kalman filters. Notably, MASF achieves up to a

28.2\times

wall-clock speedup compared with the baselines when using amortized pretraining. Our implementation is available at https://github.com/tcnllab-oss/masf.

Eunbi Yoon, Won Chang, Donghan Kim +1

KAIST · Seoul National University

Data Assimilation Bayesian Filtering Score-Based Generative Modeling

Apr 2, 2026

Cross-Modal Visuo-Tactile Object Perception

Estimating physical properties is critical for safe and efficient autonomous robotic manipulation, particularly during contact-rich interactions. In such settings, vision and tactile sensing provide complementary information about object geometry, pose, inertia, stiffness, and contact dynamics, such as stick-slip behavior. However, these properties are only indirectly observable and cannot always be modeled precisely (e.g., deformation in non-rigid objects coupled with nonlinear contact friction), making the estimation problem inherently complex and requiring sustained exploitation of visuo-tactile sensory information during action. Existing visuo-tactile perception frameworks have primarily emphasized forceful sensor fusion or static cross-modal alignment, with limited consideration of how uncertainty and beliefs about object properties evolve over time. Inspired by human multi-sensory perception and active inference, we propose the Cross-Modal Latent Filter (CMLF) to learn a structured, causal latent state-space of physical object properties. CMLF supports bidirectional transfer of cross-modal priors between vision and touch and integrates sensory evidence through a Bayesian inference process that evolves over time. Real-world robotic experiments demonstrate that CMLF improves the efficiency and robustness of latent physical properties estimation under uncertainty compared to baseline approaches. Beyond performance gains, the model exhibits perceptual coupling phenomena analogous to those observed in humans, including susceptibility to cross-modal illusions and similar trajectories in learning cross-sensory associations. Together, these results constitutes a significant step toward generalizable, robust and physically consistent cross-modal integration for robotic multi-sensory perception.

Anirvan Dutta, Simone Tasciotti, Claudia Cusseddu +6

BMW Group AG, München, Germany. · Department of Bioengineering, Imperial College of Science, Technology and Medicine, London, UK. · Department of Biology, University of Crete, Heraklion, Greece. +7

Visuo-Tactile Representation Learning Uncertainty-Aware Multimodal Fusion Bayesian Filtering

Mar 26, 2026

Bayesian Learning-Enhanced Navigation with Deep Smoothing for Inertial-Aided Navigation

Accurate post-processing navigation is essential for applications such as survey and mapping, where the full measurement history can be exploited to refine past state estimates. Fixed-interval smoothing algorithms represent the theoretically optimal solution under Gaussian assumptions. However, loosely coupled INS/GNSS systems fundamentally inherit the systematic position bias of raw GNSS measurements, leaving a persistent accuracy gap that model-based smoothers cannot resolve. To address this limitation, we propose BLENDS, which integrates Bayesian learning with deep smoothing to enhance navigation performance. BLENDS is a a data-driven post-processing framework that augments the classical two-filter smoother with a transformer-based neural network. It learns to modify the filter covariance matrices and apply an additive correction to the smoothed error-state directly within the Bayesian framework. A novel Bayesian-consistent loss jointly supervises the smoothed mean and covariance, enforcing minimum-variance estimates while maintaining statistical consistency. BLENDS is evaluated on two real-world datasets spanning a mobile robot and a quadrotor. Across all unseen test trajectories, BLENDS achieves horizontal position improvements of up to 63% over the baseline forward EKF.

Nadav Cohen, Itzik Klein

N. Cohen and I. Klein are with the Hatter Department of Marine Technologies, Charney School of Marine Sciences, University of Haifa, Israel.

Inertial Navigation Bayesian Filtering Kalman Filtering

Mar 24, 2026

Autoregressive Guidance of Deep Spatially Selective Filters using Bayesian Tracking for Efficient Extraction of Moving Speakers

Deep spatially selective filters achieve high-quality enhancement with real-time capable architectures for stationary speakers of known directions. To retain this level of performance in dynamic scenarios where only the speakers' initial directions are given, accurate, yet computationally lightweight tracking algorithms become necessary. Assuming a frame-wise causal processing style, temporal feedback allows for leveraging the enhanced speech signal to improve tracking performance. In this work, we investigate strategies to incorporate the enhanced signal into lightweight tracking algorithms and autoregressively guide deep spatial filters. Our proposed Bayesian tracking algorithms are compatible with arbitrary deep spatial filters. To increase the realism of simulated trajectories during development and evaluation, we develop a synthetic data generation framework based on the social force model. Results validate that the autoregressive incorporation significantly improves the accuracy of our Bayesian trackers, resulting in superior enhancement with none or only negligibly increased computational overhead. Real-world recordings complement these findings and demonstrate the generalizability of our methods to unseen acoustic conditions.

Jakob Kienegger, Timo Gerkmann

Signal Processing Group, Department of Informatics, University of Hamburg, 22527 Hamburg, Germany

Bayesian Filtering Direction-of-Arrival Estimation Speech Enhancement Spatial Audio

Mar 16, 2026

ModTrack: Sensor-Agnostic Multi-View Tracking via Identity-Informed PHD Filtering with Covariance Propagation

Multi-View Multi-Object Tracking (MV-MOT) aims to localize and maintain consistent identities of objects observed by multiple sensors. This task is challenging, as viewpoint changes and occlusion disrupt identity consistency across views and time. Recent end-to-end approaches address this by jointly learning 2D Bird's Eye View (BEV) representations and identity associations, achieving high tracking accuracy. However, these methods offer no principled uncertainty accounting and remain tightly coupled to their training configuration, limiting generalization across sensor layouts, modalities, or datasets without retraining. We propose ModTrack, a modular MV-MOT system that matches end-to-end performance while providing cross-modal, sensor-agnostic generalization and traceable uncertainty. ModTrack confines learning methods to just the Detection and Feature Extraction stage of the MV-MOT pipeline, performing all fusion, association, and tracking with closed-form analytical methods. Our design reduces each sensor's output to calibrated position-covariance pairs

(\mathbf{z}, R)

; cross-view clustering and precision-weighted fusion then yield unified estimates

(\hat{\mathbf{z}}, \hat{R})

for identity assignment and temporal tracking. A feedback-coupled, identity-informed Gaussian Mixture Probability Hypothesis Density (GM-PHD) filter with HMM motion modes uses these fused estimates to maintain identities under missed detections and heavy occlusion. ModTrack achieves 95.5 IDF1 and 91.4 MOTA on WildTrack, surpassing all prior modular methods by over 21 points and rivaling the state-of-the-art end-to-end methods while providing deployment flexibility they cannot. Specifically, the same tracker core transfers unchanged to MultiviewX and RadarScenes, with only perception-module replacement required to extend to new domains and sensor modalities.

Aditya Iyer, Jack Roberts, Nora Ayanian

Department of Computer Science, Brown University, Providence, RI, USA · School of Engineering, Brown University, Providence, RI, USA

Multi-Object Tracking Uncertainty-Aware Multimodal Fusion Bayesian Filtering Multimodal Sensor Fusion

Mar 2, 2026

B $^2$ F-Map: Crowd-sourced Mapping with Bayesian B-spline Fusion

Crowd-sourced mapping offers a scalable alternative to creating maps using traditional survey vehicles. Yet, existing methods either rely on prior high-definition (HD) maps or neglect uncertainties in the map fusion. In this work, we present a complete pipeline for HD map generation using production vehicles equipped only with a monocular camera, consumer-grade GNSS, and IMU. Our approach includes on-cloud localization using lightweight standard-definition maps, on-vehicle mapping via an extended object trajectory (EOT) Poisson multi-Bernoulli (PMB) filter with Gibbs sampling, and on-cloud multi-drive optimization and Bayesian map fusion. We represent the lane lines using B-splines, where each B-spline is parameterized by a sequence of Gaussian distributed control points, and propose a novel Bayesian fusion framework for B-spline trajectories with differing density representation, enabling principled handling of uncertainties. We evaluate our proposed approach, B

^2

F-Map, on large-scale real-world datasets collected across diverse driving conditions and demonstrate that our method is able to produce geometrically consistent lane-level maps.

Yiping Xie, Yuxuan Xia, Erik Stenborg +5

Zenseact, Lindholmspiren 2, Gothenburg, Sweden. · Department of Electrical Engineering, Linköping University, Linköping, Sweden. · Yuxuan Xia was a Post-doc with Zenseact, and he is now with the Department of Automation and Perception, Shanghai Jiao Tong University, Shanghai, China. +1

HD Map Construction Bayesian Filtering

Feb 26, 2026

Physics-informed neural particle flow for the Bayesian update step

The Bayesian update step poses significant computational challenges in high-dimensional nonlinear estimation. While log-homotopy particle flow filters offer an alternative to stochastic sampling, existing formulations usually yield stiff differential equations. Conversely, existing deep learning approximations typically treat the update as a black-box task or rely on asymptotic relaxation, neglecting the exact geometric structure of the finite-horizon probability transport. In this work, we propose a physics-informed neural particle flow, which is an amortized inference framework. To construct the flow, we couple the log-homotopy trajectory of the prior to posterior density function with the continuity equation describing the density evolution. This derivation yields a governing partial differential equation (PDE), referred to as the master PDE. By embedding this PDE as a physical constraint into the loss function, we train a neural network to approximate the transport velocity field. This approach enables purely unsupervised training, eliminating the need for ground-truth posterior samples. We demonstrate that the neural parameterization acts as an implicit regularizer, mitigating the numerical stiffness inherent to analytic flows and reducing online computational complexity. Experimental validation on multimodal benchmarks and a challenging nonlinear scenario confirms better mode coverage and robustness compared to state-of-the-art baselines.

Domonkos Csuzdi, Tamás Bécsi, Olivér Törő

Particle Filtering Bayesian Filtering Physics-Informed ML

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 Tracking Robot State Estimation Bayesian Filtering Particle Filtering Kalman Filtering Multi-Robot Systems

Nov 19, 2025

Recursive Entropic Variational Inference for Nonlinear State-Space Models

We present a class of algorithms for state estimation in nonlinear, non-Gaussian state-space models. Our approach is based on a variational Lagrangian formulation that casts Bayesian inference as a sequence of entropic trust-region updates subject to dynamic consistency constraints. This framework gives rise to a family of forward-backward algorithms whose structure is determined by the chosen factorization of the variational posterior. By focusing on Gauss--Markov approximations, we derive recursive schemes with favorable computational complexity. For general nonlinear, non-Gaussian models, we close the recursions using generalized statistical linear regression and Fourier--Hermite moment matching.

Hany Abdulsamad, Ángel F. García-Fernández, Simo Särkkä

Amsterdam Machine Learning Lab University of Amsterdam, Netherlands · Information Processing and Telecommunications Center Universidad Politécnica de Madrid, Spain · ELLIS Institute Finland Department of Electrical Engineering and Automation Aalto University, Finland

Bayesian Filtering Variational Inference State Space Models

Oct 30, 2025

A Sliding-Window Filter for Online Continuous-Time Continuum Robot State Estimation

Stochastic state estimation methods for continuum robots (CRs) often struggle to balance accuracy and computational efficiency. While several recent works have explored sliding-window formulations for CRs, these methods are limited to simplified, discrete-time approximations and do not provide stochastic representations. In contrast, current stochastic filter methods must run at the speed of measurements, limiting their full potential. Recent works in continuous-time estimation techniques for CRs show a principled approach to addressing this runtime constraint, but are currently restricted to offline operation. In this work, we present a sliding-window filter (SWF) for continuous-time state estimation of CRs that improves upon the accuracy of a filter approach while enabling continuous-time methods to operate online, all while running at faster-than-real-time speeds. This represents the first stochastic SWF specifically designed for CRs, providing a promising direction for future research in this area.

Spencer Teetaert, Sven Lilge, Jessica Burgner-Kahrs +1

University of Toronto Robotics Institute, Toronto, ON, Canada

Robot State Estimation Bayesian Filtering

Oct 29, 2025

PyDPF: A Python Package for Differentiable Particle Filtering

State-space models (SSMs) are a widely used tool in time series analysis. In the complex systems that arise from real-world data, it is common to employ particle filtering (PF), an efficient Monte Carlo method for estimating the hidden state corresponding to a sequence of observations. Applying particle filtering requires specifying both the parametric form and the parameters of the system, which are often unknown and must be estimated. Gradient-based optimisation techniques cannot be applied directly to standard particle filters, as the filters themselves are not differentiable. However, several recently proposed methods modify the resampling step to make particle filtering differentiable. In this paper, we present an implementation of several such differentiable particle filters (DPFs) with a unified API built on the popular PyTorch framework. Our implementation makes these algorithms easily accessible to a broader research community and facilitates straightforward comparison between them. We validate our framework by reproducing experiments from several existing studies and demonstrate how DPFs can be applied to address several common challenges with state space modelling.

John-Joseph Brady, Benjamin Cox, Yunpeng Li +1

King’s College London · Max-Planck Institut für Physik · University of Edinburgh

Particle Filtering Bayesian Filtering Differentiable Programming State Space Models

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 Matching Kalman Filtering Bayesian Filtering Data Assimilation Ensemble Kalman Filtering

Dec 24, 2024

The Constitutional Filter: Bayesian Estimation of Compliant Agents

Predicting agents impacted by legal policies, physical limitations, and operational preferences is inherently difficult. In recent years, neuro-symbolic methods have emerged, integrating machine learning and symbolic reasoning models into end-to-end learnable systems. Hereby, a promising avenue for expressing high-level constraints over multi-modal input data in robotics has opened up. This work introduces an approach for Bayesian estimation of agents expected to comply with a human-interpretable neuro-symbolic model we call its Constitution. Hence, we present the Constitutional Filter (CoFi), leading to improved tracking of agents by leveraging expert knowledge, incorporating deep learning architectures, and accounting for environmental uncertainties. CoFi extends the general, recursive Bayesian estimation setting, ensuring compatibility with a vast landscape of established techniques such as Particle Filters. To underpin the advantages of CoFi, we evaluate its performance on real-world marine traffic data. Beyond improved performance, we show how CoFi can learn to trust and adapt to the level of compliance of an agent, recovering baseline performance even if the assumed Constitution clashes with reality.

Simon Kohaut, Felix Divo, Benedict Flade +3

Artificial Intelligence and Machine Learning Group, Department of Computer Science, TU Darmstadt, 64283 Darmstadt, Germany · Honda Research Institute Europe GmbH, Carl-Legien-Str. 30, 63073 Offenbach, Germany · Uncertainty in Artificial Intelligence Group, Department of Mathematics and Computer Science, TU Eindhoven, 5600 MB Eindhoven, Netherlands +3

Bayesian Filtering Neuro-Symbolic Reasoning