Sensor Fusion Framework Overview

• Sensor fusion frameworks are systems that integrate data from diverse sensor modalities to improve accuracy and mitigate individual sensor limitations.
• They use model-based, optimization-based, or learning-based methods to fuse asynchronous, heterogeneous measurements in real time.
• Applications span autonomous driving, robotics, SLAM, and sensor security, demonstrating enhanced robustness and adaptability.

Sensor fusion frameworks are algorithmic and software architectures designed to combine data from multiple, typically heterogeneous, sensors to produce accurate, robust, and consistent estimates of variables of interest, such as system state, environment representation, or trajectories. Fusion is essential for overcoming limitations of individual sensors—such as occlusion, noise, failure, and uncertainty—and underpins applications in autonomous vehicles, robotics, human activity recognition, assistive navigation, SLAM, and cyber-physical system security. Modern frameworks employ model-based, optimization-based, or learning-based methodologies; ensure real-time operation; support extensibility for new sensor modalities; and increasingly address robustness to sensor degradation and adversarial attacks.

1. Fundamental Principles and Objectives

Sensor fusion exploits complementary, redundant, or synergistic information from diverse sources to yield state estimates or representations that outperform any single sensor. Frameworks are designed to handle:

• Measurement heterogeneity: Diverse sensor modalities (e.g., GNSS, IMU, radar, vision, LiDAR) differ in dimensionality, sampling frequency, physical model, and noise statistics. Fusion frameworks must convert raw sensor outputs to unified residual forms with appropriately modeled covariances (Liu et al., 19 Sep 2024, Ligocki et al., 2020).
• Uncertainty and error: Fusing heterogeneous streams requires systematic estimation or modeling of time-varying measurement uncertainties—often achieved via data-driven approaches (e.g., Gaussian Mixture Models, online EM) or robust outlier rejection (Liu et al., 19 Sep 2024, Wei et al., 2018).
• Time synchronization and alignment: Asynchronous data streams are aligned either by interpolation, continuous-time splines, or time-indexed packaging to ensure consistency in multi-sensor state representation (Li et al., 2023, Sani et al., 6 Nov 2024).
• Plug-and-play modularity: Modern fusion systems decouple core estimation from sensor-specific front-ends, allowing arbitrary addition and removal of modalities with minimal reengineering; factor nodes or plugin APIs are typical mechanisms (Liu et al., 19 Sep 2024, Sandy et al., 2018, Ligocki et al., 2020).

2. Mathematical Formulations and Algorithms

Sensor fusion frameworks are commonly grounded in three mathematical paradigms:

• Factor graph optimization: States are represented as nodes over a sliding window, with measurement factors encoding sensor-model residuals and covariances. Joint MAP estimation is solved as sparse nonlinear least squares, often via Levenberg–Marquardt, with principled marginalization for scalability (Liu et al., 19 Sep 2024, Sandy et al., 2018, Jia et al., 2021, Zhang et al., 11 Jul 2025):

$$\chi^* = \arg\min_{\chi} \Bigg\{ \|r_P(\chi)\|^2 + \sum_{\text{factors}} \|r(\cdot)\|^2_{\Sigma^{-1}} \Bigg\}$$

• Moving Horizon Estimators (MHE): Frameworks such as ConFusion manage a batch of $N$ states, fusing both measurement updates and process dynamics factors, with automatic marginalization for long-term consistency (Sandy et al., 2018).
• Kalman-based and observer-based methods: Fusion is achieved as a sequence of predict and update steps, extended to accommodate nonlinear manifolds, multi-modal graphs, or error-state models (EKF, ES-EKF, graph-aware Kalman filters) (Oliva et al., 1 Oct 2025, Sani et al., 6 Nov 2024, Silva et al., 27 Jan 2025).
• Continuous-time fusion: Spline-based methods parameterize the trajectory via cubically cumulative B-splines in both Euclidean and quaternion domains, enabling asynchronous data incorporation and analytic kinematic interpolation. Optimization is performed over the current spline window (Li et al., 2023).

Frameworks increasingly incorporate adaptive weighting, either via data-driven EM algorithms (for noise estimation, e.g., GMM), RL-based actor-critic modules (dynamic sensor weighting, (Jia et al., 2021)), or learned reliability masks (SelectFusion’s soft/hard gating (Chen et al., 2019)).

3. Handling Heterogeneity, Outlier Rejection, and Uncertainty

Robust sensor fusion hinges on actively addressing:

• Measurement heterogeneity: Each modality undergoes tailored preprocessing—IMU pre-integration for inertial sequences, GNSS pseudorange and TDCP modeling, 4D radar ego-velocity extraction, vision-based feature encoding, LiDAR voxelization, and semantic segmentation for cameras. All are converted to residual forms suited for fusion (Liu et al., 19 Sep 2024, Sandy et al., 2018, Ming et al., 3 Mar 2024).
• Outlier detection: Outlier rejection is realized via rule-based checks (e.g., Doppler-aided cycle-slip detection on TDCP (Liu et al., 19 Sep 2024)), thresholding of residuals (e.g., deviation between predicted and observed shifts (Dasgupta et al., 2021)), or reliability estimation (soft/hard mask selection (Chen et al., 2019)).
• Online uncertainty modeling: GNSS pseudorange noise is modeled as data-driven GMMs optimized by EM; the resulting parameterization feeds into dynamically updated measurement covariances (Liu et al., 19 Sep 2024). Continuous uncertainty propagation is reinforced by sliding-window batch strategies (Sandy et al., 2018).
• Conflict measurement: Several frameworks assign sensor weights via explicit conflict scores, quantifying the degree of overlap of interval-valued evidence over all sensor combinations. Fusion weights are inversely proportional to cumulative conflict, diminishing the influence of unreliable sensors (Wei et al., 2018).

4. Modularity, Extensibility, and Plug-and-Play Design

Sensor fusion frameworks are increasingly architected to allow seamless reconfiguration:

Framework	Modularity Principle	Sensor Addition/Removal Mechanism
UniMSF (Liu et al., 19 Sep 2024)	Factor graph, residual front-end per sensor	Add/remove factors, unchanged state vector
ConFusion (Sandy et al., 2018)	Plugin APIs, sliding window MHE	Register sensor plugin, build residual factor
Atlas Fusion (Ligocki et al., 2020)	Data loader/algorithm plugin system	Define DataModel/Loader, integrate pipeline branch

This modularity is essential for scaling from minimal to sensor-rich platforms, supporting evolving sensor suites in robotics and ITS, and providing a basis for benchmarking under systematic degradation (Zhang et al., 11 Jul 2025).

5. Experimental Evaluation and Performance Analysis

Rigorous validation is a hallmark of advanced fusion frameworks:

• ITS Localization (UniMSF): Real-world deployments fusing GNSS, IMU, and 4D-radar demonstrate decimeter-level trajectory accuracy even under GNSS occlusion, with robust outlier rejection and online noise estimation yielding up to 19.4% lower RMSE compared to classic IMU/pr/TDCP baselines (Liu et al., 19 Sep 2024).
• Robotic Manipulation (ConFusion): Whole-body sensor fusion using batch optimization yields up to 50% lower RMS error than extended Kalman filters and supports complex multi-sensor configurations (Sandy et al., 2018).
• GNSS Spoofing Attack Detection: LSTM-based location-shift prediction, turn classification via k-NN/DTW, and motion-state comparison yield 100% detection of sophisticated attacks with negligible latency, validated over tens of real-world driving scenarios (Dasgupta et al., 2021, Dasgupta et al., 2 Jan 2024).
• SLAM Robustness (Ground-Fusion++): Fusing GNSS, RGB-D, LiDAR, IMU, and wheel odometry, and adaptively switching between subsystems, achieves state-of-the-art RMSE across stringent visual, LiDAR, and GNSS-degraded benchmarks (Zhang et al., 11 Jul 2025).
• Lightweight Observer Design: TBOD observer design matches or significantly surpasses EKF orientation accuracy, and remains computationally competitive (Oliva et al., 1 Oct 2025).

6. Applications Across Domains

Sensor fusion frameworks underpin a broad range of technical domains:

• Autonomous driving and ITS: Global localization (UniMSF), 3D occupancy prediction (OccFusion), robust multi-object tracking via graph-based filters (SAGA-KF) (Liu et al., 19 Sep 2024, Ming et al., 3 Mar 2024, Sani et al., 6 Nov 2024).
• SLAM and state estimation: Factor graph and continuous-time optimization for robust trajectory estimation under challenging and degraded environments (Zhang et al., 11 Jul 2025, Li et al., 2023).
• Cyber-physical system security: Attack detection and isolation using multi-sensor redundancy and fusion algorithms with provable error bounds, combined with $H_\infty$ control for string-stability in vehicle platoons (Yang et al., 2021).
• Human activity recognition and healthcare: Multimodal fusion (audio, video, RFID)—with quantified interpretability—substantially improves classification accuracy across activity stages (Yang et al., 25 Oct 2025).
• Assistive navigation: Complementary fusion of ultrasonic, vision, IMU, and GPS sensors delivers integrated feedback and navigation for blind and visually impaired persons (Silva et al., 27 Jan 2025).
• Human pose estimation: Unified kinematic fusion of IMU and vision in parametric skeleton space achieves state-of-the-art pose accuracy, with systematic evaluation under varied occlusion and sensor configurations (Bao et al., 2022).

7. Limitations, Challenges, and Future Directions

While sensor fusion frameworks now deliver robust, flexible, and modular fusion, open challenges persist:

• GNSS outages and unobservability: Performance necessarily degrades under prolonged GNSS loss or insufficient satellite visibility; internal drift can be masked until reacquisition (Liu et al., 19 Sep 2024, Zhang et al., 11 Jul 2025).
• Degradation handling and adaptive weighting: Matching dynamic environments, sensor malfunctions, or adversarial attacks requires further development of online adaptation strategies and degeneracy-aware switching (Zhang et al., 11 Jul 2025, Jia et al., 2021).
• Latency in noise estimation and large-scale optimization: Real-time requirements tax frameworks employing online EM/GMM or complex continuous-time splines, especially under low-frequency sensors or sparse samples (Liu et al., 19 Sep 2024, Li et al., 2023).
• Scaling interpretability and reliability: While explicit reliability masks (soft/hard fusion) and conflict measures are effective in two-sensor scenarios, extending these methods to larger, more heterogeneous sensor configurations and providing transparent interpretability is an open direction (Chen et al., 2019, Wei et al., 2018).
• Extensibility to new modalities: Future frameworks will increasingly incorporate learned quality estimators, semantic scene understanding, low-dimensional Gaussian intermediates, and task-adaptive multi-modal graphs (Sani et al., 6 Nov 2024, Liu et al., 27 May 2025).

This suggests that sensor fusion frameworks will continue to evolve toward higher modularity, greater adaptivity to environmental and sensor conditions, increased computational efficiency, and richer support for interpretability and reliability estimation—driven by diverse application demands and expanding sensor suites across autonomous systems, robotics, and healthcare.