Graph-based Multi-sensor Fusion

• Graph-based multi-sensor fusion is a framework that uses graph structures to integrate heterogeneous sensor data for consistent, robust state estimation.
• It leverages Bayesian models, deep feature fusion, and optimization techniques like factor graphs to adaptively handle sensor uncertainties.
• The approach enables plug-and-play sensor integration and fault-tolerance, improving decision-making in dynamic and challenging environments.

A generic sensor fusion algorithm is a computational framework that combines data from multiple heterogeneous or homogeneous sensors to produce an estimate or inference that is more accurate, reliable, or robust than could be obtained from any single sensor in isolation. Such algorithms are designed to be modular, application- and sensor-agnostic, and often able to accommodate unknown or changing error statistics, varying sensor modalities (e.g., vision, LiDAR, IMU, GPS, sonar), and flexible state representations including manifold-valued quantities. The principal objective is to achieve consistent, high-quality estimation or decision making, even in the presence of outlier, faulty, or missing sensor data. Modern research emphasizes not only statistical consistency and optimality, but also computational efficiency, modularity, interpretability, and dataset/sensor-agnostic adaptability.

1. Fundamental Principles and Architectures

Generic sensor fusion involves constructing an estimation or inference pipeline abstracted from any specific sensor physics, assumptions about the environment, or fixed measurement types. Core principles include:

• Modality and dataset agnosticism: Algorithms must absorb diverse sensor inputs (e.g., point clouds, images, depth maps), without requiring hand-tuning for sensor placement, noise profile, or scene geometry. For example, PointFusion processes both images and 3D point clouds via independent branches before fusion, with no quantization or bird’s-eye projections (Xu et al., 2017).
• Early versus late fusion: Early fusion architectures combine sensor features before output-level decision making, thereby leveraging cross-modal context (e.g., see PointFusion’s joint feature fusion; factor-graph-based solutions in Holistic Fusion (Nubert et al., 8 Apr 2025)).
• Reliability/uncertainty modeling: Modern algorithms adaptively estimate per-sensor (and per-feature, per-voxel, or per-anchor) reliability, either through analytical models (e.g., Mahalanobis-distance in Bayesian fusion (Echeverri et al., 2017)), learned confidence networks (Rozumnyi et al., 2019), or dynamic gating in deep networks (Chen et al., 2019).
• Generic integration with sound state representations: Fusion frameworks generalize beyond vector state spaces to arbitrary manifolds (e.g., orientations in SO(3)) through abstract boxplus/boxminus (⊕,⊖) operators, enabling reuse of estimation code on non-Euclidean spaces (Hertzberg et al., 2011).

2. Statistical Fusion Methods

A variety of statistical fusion schemes underlie generic algorithmic frameworks:

• Bayesian and Kalman-based fusion: Hierarchical structures where each sensor stream is handled by a local Bayesian estimator (frequently a Kalman filter), with outputs fused at a global level (e.g., through convex combinations of local posteriors weighted by Mahalanobis-based reliability and majority-voting consistency) (Echeverri et al., 2017).
• Generalized likelihood-ratio fusion: For joint detection problems, fusion can be posed as a generalized likelihood-ratio test, aggregating sensor evidence using a product (weighted geometric mean) of single-sensor GLR statistics, yielding analytic false-alarm/detection guarantees and facilitating easy addition of further modalities (Oreshkin et al., 2013).
• Interval and conflict-based fusion: For disparate or non-Gaussian evidence, conflict measures quantify lack of agreement (interval overlap) between sensor outputs, producing weights that downscale nonconforming sensors. These methods tolerate faults and unknown error distributions, with established algorithms (Marzullo, Brooks–Iyengar) offering formal fault-tolerance (Alonso et al., 2022, Wei et al., 2018).

3. Deep and Learned Fusion Frameworks

Deep learning has led to generic sensor fusion algorithms with powerful feature abstraction capabilities:

• Feature-level fusion with attention/gating: Approaches such as SelectFusion (Chen et al., 2019) and attention-based recurrent filters (Guo, 2019) process each modality via neural “expert” networks, then adaptively learn soft (continuous) or hard (stochastic, discrete) fusion masks for latent features, dynamically attending to the most reliable information streams based on context.
• Learned confidence and weighting: For volumetric data (e.g., multi-sensor depth maps), networks can learn voxel-wise, per-sensor confidences based on local image/patch statistics, feeding these into fusion as weights over truncated signed distance functions (TSDFs) to enable robust, semantic 3D reconstructions (Rozumnyi et al., 2019).
• Generic nonlinear aggregators: Fuzzy integrals—particularly the Choquet and its bi-capacity extension (Bi-MIChI)—serve as universal nonlinear fusers. Bi-MIChI integrates sensor scores according to learned bi-capacities, modeling both synergistic and antagonistic interactions, and is trainable under uncertain bag-level labels (Vakharia et al., 2024).

Fusion Family	Weighting Mechanism	Robustness Guarantee
Bayesian/Kalman	Data/adaptive reliability	Probabilistic, covariance-adaptive
Deep feature fusion	Learned soft/hard masks	Empirical, interpretable, adaptive
Conflict/interval	Overlap-based conflict	Analytical, fault-tolerant (to τ)
Fuzzy integrals	Learned fuzzy/bi-capacity	Nonlinear complementarity, explain.

4. Optimization-Based Fusion: Factor Graphs and Moving Horizon Estimation

Recent frameworks treat sensor fusion as a modular optimization over a factor graph or moving horizon estimator (MHE):

• Sliding-window/batch optimization: Highly generic approaches, such as those used in ConFusion (Sandy et al., 2018) and Holistic Fusion (Nubert et al., 8 Apr 2025), assemble arbitrary process and measurement “factors” into a windowed nonlinear least-squares problem. Each factor encodes a constraint (e.g., IMU preintegration, visual reprojection, landmark observation), and state evolution is handled on arbitrary manifolds via ⊕/⊖ operators (Hertzberg et al., 2011).
• Plugin/modularized factors: Measurements from new sensors are integrated at runtime by defining their residual and Jacobians, with the framework automatically organizing state and static parameters, scheduling marginalizations, and handling asynchronous measurement arrival (Nubert et al., 8 Apr 2025).
• Reference-frame handling and context: Explicit modeling of reference-frame drift/alignment (as random walks in SE(3)), time-varying extrinsics, and dynamic environmental context enables seamless multimodal, setup-agnostic fusion for robotics, navigation, and mapping (Nubert et al., 8 Apr 2025).

5. Handling Faults, Outliers, and Missing Data

Generic sensor fusion algorithms incorporate mechanisms to ensure resilience in the presence of faulty sensors, outliers, and missing data:

• Reliability-adaptive weighting: Adaptive weights computed from Mahalanobis distance, fusion deviation, or learned per-feature gates serve to reduce reliance on unreliable sensors in real time (Echeverri et al., 2017, Nemec et al., 2017, Chen et al., 2019).
• Conflict, coverage, and interval-based methods: (Marzullo, Brooks–Iyengar) Fault-tolerant rules offer MSE-optimality up to τ faulty sensors and guarantee consensus via coverage criteria. For highly non-Gaussian error statistics, coverage-based strategies significantly outperform linear fusion (Alonso et al., 2022).
• Robust batch/bayesian methods: By representing sensor model uncertainty in the factor graph or fusion weights, and integrating inference over all plausible configurations, global robustness is obtained without hard threshold-based outlier rejection (Sandy et al., 2018, Rozumnyi et al., 2019).

6. Practical Implementations, Performance, and Trade-offs

Extensive experimental validation demonstrates the efficacy and breadth of generic sensor fusion algorithms:

• Cross-domain performance: PointFusion achieves state-of-the-art or competitive 3D object-detection across radically different datasets (KITTI: lidar+camera, SUN-RGBD: indoor RGB-D) with identical architecture and hyperparameters (Xu et al., 2017).
• Robustness under degradation: SelectFusion’s hard fusion remains stable under severe sensor dropouts, noise, misalignment, and occlusions, outperforming naive concatenation and even vision/inertial-only deep networks (Chen et al., 2019).
• Batch vs filter trade-off: Moving-horizon or factor-graph-based fusion achieves lower error, better consistency, and smoother estimates compared to classic (iterated) EKF at the expense of controllable, linear-in-window computational cost (Sandy et al., 2018, Nubert et al., 8 Apr 2025).
• Computational efficiency: Adaptive MSE-based fusion methods operate at similar computational cost to fixed-gain filters but attain faster dynamic response than EKF, and are more stable under dynamic state changes (Nemec et al., 2017).

7. Extensions, Generality, and Software Integration

Generic fusion frameworks are designed for extensibility and long-term maintainability:

• State-space abstraction: Encapsulation of non-Euclidean state via ⊕/⊖ enables “write-once, run everywhere” estimation code, with automatic support for orientation, pose, and compound states (Hertzberg et al., 2011).
• Plug-and-play measurement models: Adding new modalities or measurement types requires only defining new factor-residuals, with the global optimizer and marginalization machinery handling the rest (Nubert et al., 8 Apr 2025, Sandy et al., 2018).
• Fusion algorithm hierarchy: Layered architectures (e.g., local “expert” filters, global Bayesian fusion) facilitate both high-frequency filtering and robust global integration of asynchronous, multi-timescale streams (Echeverri et al., 2017).
• Real-time online calibration: Some adaptive fusion methods exploit fusion deviation as a calibration signal for online compensation of sensor drifts and temperature effects via stochastic optimization (Nemec et al., 2017).

In conclusion, generic sensor fusion algorithms represent a mature and evolving field combining statistical estimation, optimization, modular design, and deep learning. They enable robust, scalable, sensor- and scenario-agnostic integration of multimodal data for state estimation, perception, and control across domains including robotics, autonomous vehicles, assistive devices, and sensor networks (Xu et al., 2017, Rozumnyi et al., 2019, Chen et al., 2019, Echeverri et al., 2017, Nubert et al., 8 Apr 2025).