GNSS Denied Navigation Techniques

• GNSS Denied Navigation is the study of methods and sensor fusion architectures designed to maintain localization and tracking without satellite signals, crucial for challenging environments like subterranean, underwater, and urban canyons.
• Key techniques include dead-reckoning, acoustic beacon multilateration, map-matched magnetometry, and visual-inertial systems, each addressing specific error propagation challenges.
• Advanced sensor fusion methods using EKF/UKF and cooperative positioning frameworks ensure bounded error and high reliability, validated through simulation frameworks and rigorous performance metrics.

GNSS-denied navigation is the set of methodologies, sensor fusion architectures, and operational protocols enabling precise localization and trajectory tracking in the absence or disruption of Global Navigation Satellite System (GNSS) signals. This challenge, critical in subterranean, underwater, urban canyon, military, and planetary environments, necessitates alternative observation modalities and robust estimation frameworks due to the inherent drift and error accumulation in dead-reckoning and inertial-only solutions.

1. Principles and Failure Modes of Dead-Reckoning

Dead-reckoning navigation solely integrates inertial measurements (accelerometer, gyroscope) and locally sensed velocities to propagate the vehicle state when external fixes are unavailable. The dominant error propagation mechanisms include bias drift and unmodeled perturbations:

• Position error: Without periodic GNSS updates, position errors accrue quadratically due to accelerometer bias $b_a$ and process noise $w_a$. For typical MEMS IMU grades (bias ∼ several $10^{-5}$ m/s²), Schuler oscillation and long-term drift result in tens of kilometers error over multi-hour missions (Wang et al., 2023).
• Attitude error: Gyro bias and magnetometer model errors lead to unbounded yaw drift and slow divergence in roll/pitch. For high-quality gyroscopes (e.g., RLG bias ≲$10^{-3}$ deg/h), orientation can remain drift-free over several hours, but MEMS units exhibit degree-scale drift (Kurda et al., 16 Dec 2025).

Mitigation of these failure modes relies on periodic absolute observations or correction from exteroceptive sensors and map references.

2. Alternative Observational Modalities

a) Acoustic and Beacon-based Navigation

Underwater vehicles (UUVs) employ acoustic beacon networks, with beacon positions optimized via constrained Lloyd’s algorithm to guarantee 3D coverage of the operational volume. Position estimation is achieved through Time-of-Flight (ToF) multilateration:

$$\hat p = \arg\min_p \sum_{i=1}^m \left(\|p - b_i\| - (c\,\Delta t_i)\right)^2$$

Acoustic detection, with 2 km radius typical for low-duty HF pulses, provides single-digit meter accuracy with appropriately distributed beacons. Hierarchical planners using HTN domains govern closed-loop waypoint navigation and re-planning (Albore et al., 22 Jan 2026).

b) Magnetometry and Geophysical Map Matching

Quantum diamond magnetometers facilitate map-matched localization by associating scalar magnetic intensity readings with high-resolution Total Magnetic Intensity (TMI) maps. Probabilistic Data Association (PDA) and batch PMHT smoothers resolve non-injective ambiguities and fuse measurements:

$$z_k = \sum_{i=1}^n w_i p_i,\qquad R_k = \sum_{i=1}^n w_i\left[(p_i-z_k)(p_i-z_k)^T + \alpha\,\sigma^2 I_3\right]$$

This methodology constrains position drift to hundreds of meters over hours with sub-nT sensitivity, but performance degrades in low-excursion regions (Wang et al., 2023).

c) Visual-Inertial and Scan-Matching Approaches

Visual odometry (VO) and visual-inertial navigation systems (VINS) employ incremental displacement estimates from ground-view cameras (Virtual Vision Sensor, VVS), fused in Lie-group EKFs:

$$\left[ R_{k+1} = R_k\,\exp([(\omega_{m,k}-b_{\omega,k})\Delta t]_\times),\quad v_{k+1} = v_k + (R_k(a_{m,k}-b_{a,k})+g)\Delta t \right]$$

Relative pose increments and metric scale from baro-aided altitude or LiDAR-derived heightmaps maintain bounded drift for extended GNSS outages (Gallo et al., 2023, Werner et al., 1 Oct 2025). For ground vehicles, BEVRender generates synthetic bird's-eye-view images, aligning them with geo-referenced aerial maps via normalized cross-correlation for frequent absolute corrections (Jin et al., 2024).

d) Cooperative and Distributed Positioning

Wireless networks of mobile agents and anchors employ distributed factor-graph estimation, with ranging measurements (TOA/AOA/RSS) and finite-sample scaled unscented transforms (SUT):

• Each agent propagates belief over its 3D coordinates using internal odometry and spatial range factors.
• Enhanced anchor-upgrading and pseudo-anchor mechanisms reduce iterations and computational cost.
• Achieves meter-level accuracy with order-of-magnitude lower complexity than SPAWN and UCL-native belief propagation (Cao et al., 2022).

3. Sensor Fusion Architectures and State Estimation

GNSS-denied state estimation universally relies on multi-sensor fusion, typically via Extended/Unscented Kalman Filters (EKF/UKF) or particle-filter schemes:

• State vector: $x = [p, v, q, b_g, b_a]$ (position, velocity, attitude, gyro/accel biases).
• Propagator: INS mechanization equations augmented with additional sensor inputs (DVL, EM logs, VO/VIO, magnetometer, LiDAR).
• Measurement update: $z = Hx + v$, $K = P H^T (H P H^T + R)^{-1}$.

Specialist approaches implement error-state propagation on SO(3), integrate virtual ground-velocity sensors from visual-inertial pipelines, and reinforce stability via attitude and altitude priors (PI-inspired cost terms) or direct scan-to-map registration via Euclidean Distance Fields for LiDAR (Martínez-Rozas et al., 29 May 2025, Gallo et al., 2022).

4. Performance Metrics and Experimental Results

Quantitative evaluations span marine, aerial, tunnel, and off-road environments:

Architecture	Platform	Drift/Error (typical)	Remark	Reference
Acoustic beacon multi-lat.	UUV	8 m mean pos. error	2 km detection radius, stealth.	(Albore et al., 22 Jan 2026)
Quantum magnetometry	UAV/UGV	250 m RMS pos. error	Batch PMHT, 10 s updates	(Wang et al., 2023)
VINS with VVS (SO(3) Manifold)	UAV (fixed-wing)	0.19% horizontal drift	90%+ drift reduction	(Gallo et al., 2023)
BEVRender (cross-view reg.)	UGV	19–22 m mean error	>50% match rate, 0.12 s/f real-time	(Jin et al., 2024)
Direct LiDAR Localization	UAV/UGV (marsupial)	0.14 m pos., <1° yaw	DLL 0.08s/scan, long-duration	(Martínez-Rozas et al., 29 May 2025)
LIO + RLG-INS (Odyssey)	Automotive	<1% drift/100m	GNSS-denied tunnels/garages	(Kurda et al., 16 Dec 2025)
Angle-robust vision net	UAV	100% SR(ideal), 67% disturbed	Point-to-point nav, no gallery	(Wang et al., 2024)

Performance degrades with sensor quality, environmental texture, and feature variability but is fundamentally bounded by aiding frequency, extrinsic calibration, and the availability of distinctive observations.

5. Simulation Frameworks and Evaluation Methodologies

Stochastic high-fidelity simulators model aircraft dynamics, sensor errors, weather/wind/turbulence, and control/guidance loops for rigorous Monte Carlo evaluation of navigation algorithms. These frameworks provide ground-truth against which GNSS-denied drift, attitude stability, and position accuracy are quantitatively compared (Gallo, 2021).

Key metrics include:

• Absolute Trajectory Error (ATE): Pointwise Euclidean error to ground-truth after alignment.
• Relative Pose Error (RPE): Drift over fixed-length windows (e.g., 100 m).
• Success Rate (SR): Fraction of runs arriving within target threshold.
• Mean/Max Error: Over Monte Carlo runs and terrains.

6. Specialized Systems and Future Directions

• Tethered marsupial UAV–UGV systems extend aerial endurance and leverage ground-platform power, with coordinated path planning and direct LiDAR localization enabling sub-meter precision for long-duration inspection (Martínez-Rozas et al., 29 May 2025).
• Gradient-guided reinforcement learning for geomagnetic navigation yields >97% SR in >400 km missions, outperforming metaheuristics in diverse GNSS-denied scenarios, but reliant on gradient quality and model fidelity (Bai et al., 2024).
• Ring Laser Gyroscope INS elevates the ground truth for GNSS-denied benchmarking, enabling sub-degree orientation stability over hours (Kurda et al., 16 Dec 2025).
• Distributed cooperative positioning via spatio-temporal factor graphs and SUT maintains meter-level multi-agent localization with low complexity and modest communication (Cao et al., 2022).

Ongoing directions include large-scale benchmarking in Odyssey and UAV_AR368 datasets, adaptive sensor fusion, learned inter-sensor weighting, extension of BEV-based cross-view matching to multi-modal and non-planar terrain, and field deployment of stealth beacon networks at sea.

7. Limitations, Challenges, and Integration Concepts

Persistent limitations involve:

• Texture and anomaly dependence: VO/VIO, magnetometry, and BEV methods require sufficient environmental distinctiveness.
• Scale and vertical ambiguity: Altitude errors remain problematic for vision-based scale estimation, necessitating barometric or LiDAR supplementation.
• Data and computational constraints: Large map databases and high-frequency sensor fusion challenge embedded platforms.
• Stealth and reliability: Underwater acoustic methods must minimize detectability and guarantee temporal coverage.

Integration of GNSS-denied stacks mandates redundancy across modalities (IMU, VO, EM/DVL, LiDAR, magnetometry, cooperative agents), robust time-synchronization, and adaptive filtering frameworks. For long-range autonomy, fusion of virtual vision sensors, map-matching aids, and tightly coupled inertial propagation are requisite for bounded-error navigation over extended GNSS-denied missions.