🔢 mathematics

A Robust 5G Terrestrial Positioning System with Sensor Fusion in GNSS-denied Scenarios

This paper proposes a robust 5G-based terrestrial positioning system for GNSS-denied environments that combines multi-carrier carrier phase ranging, deep learning for NLOS identification, and sensor fusion with an error-state Kalman filter to achieve sub-5-meter accuracy in urban scenarios.

Original authors: Hamed Talebian, Nazrul Mohamed Nazeer, Darius Chmieliauskas, Jakub Nikonowicz, Mehdi Haghshenas, Łukasz Matuszewski, Mairo Leier, Aamir Mahmood

Published 2026-04-08

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Hamed Talebian, Nazrul Mohamed Nazeer, Darius Chmieliauskas, Jakub Nikonowicz, Mehdi Haghshenas, Łukasz Matuszewski, Mairo Leier, Aamir Mahmood

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are driving a car in a dense city. Usually, your GPS (like Google Maps) tells you exactly where you are by listening to tiny whispers from satellites high above. But what if you drive into a deep canyon of skyscrapers, or a tunnel, or a jam-packed parking garage? The satellite signals get blocked, scrambled, or lost. You are suddenly "blind," and your navigation system fails.

This paper proposes a brilliant new way to navigate without satellites, using the 5G network (the same one that gives your phone fast internet) as a giant, invisible ruler.

Here is the breakdown of how they built this "5G GPS" using three clever tricks, explained with simple analogies.

1. The Problem: The "Fuzzy Ruler"

To measure distance with 5G, the system listens to the "carrier wave" of the signal. Think of a radio wave like a slinky (a coiled spring).

The Issue: If you count how many full coils (waves) fit between the cell tower and your car, you get a rough distance. But the signal is so fast that you can't see where the exact start of the wave is. It's like trying to measure a long hallway using a ruler that only has markings every 10 feet, but you don't know which "10-foot" mark you are standing on. You know you are somewhere between 10 and 20 feet, or 100 and 110 feet, but you aren't sure. This is called Integer Ambiguity.

The Solution: The "Virtual Ruler"
The authors created a "Virtual Ruler." Instead of using one frequency (one type of slinky), they use two slightly different frequencies.

The Analogy: Imagine you have two rulers. One has markings every 10 feet, and the other every 10.5 feet. If you line them up, the marks will only perfectly match up once every 210 feet. By comparing the two, the system can instantly figure out exactly where you are within that huge 210-foot gap without needing to count every single small wave.
The Result: They solved the "which number are we?" mystery instantly, allowing them to measure distance with centimeter-level precision (like measuring a car's position to within the width of a coin).

2. The Problem: The "Echo Chamber"

Even with a perfect ruler, 5G signals bounce off buildings.

The Analogy: Imagine shouting in a canyon. You hear your voice come back to you. But sometimes, the echo bounces off a side wall and takes a longer, weird path before hitting your ear. If your navigation system thinks that long, bouncy echo is the direct sound, it will calculate that you are much further away than you really are. In 5G terms, this is called NLOS (Non-Line-of-Sight).
The Consequence: If the system uses these "fake" bouncy signals, your location could be off by hundreds of meters.

The Solution: The "Smart Bouncer"
The team built a Deep Learning AI (a type of computer brain) that acts like a nightclub bouncer at the cell tower.

How it works: The AI listens to the "shape" of the signal. A direct signal (LOS) looks like a clean, sharp clap. A bouncy signal (NLOS) looks like a messy, smeared echo.
The Action: The AI instantly identifies the "messy" signals and says, "No entry!" It throws them out before they can mess up the calculation. It only lets the clean, direct signals into the math equation.

3. The Problem: The "Blackout"

Sometimes, even with the AI bouncer, there are no cell towers with a clear view of you (maybe you are in a deep underground parking lot). The 5G signal is completely gone.

The Solution: The "Blindfolded Dancer" (Sensor Fusion)
When the 5G signal disappears, the system switches to a backup plan using sensors already inside your car or phone:

The IMU (Inertial Measurement Unit): This is like your inner ear. It feels when you accelerate, turn, or tilt. It knows you moved, even if it doesn't know exactly where you are.
The Camera (Visual Odometry): This is like your eyes. It looks at the street and counts how many steps you took by watching the buildings move past.
The Fusion (The "Smart Brain"): The system uses a mathematical tool called a Kalman Filter. Think of this as a very smart coach.
- When 5G is working, the coach says, "Trust the 5G ruler! It's perfect."
- When 5G goes dark, the coach says, "Okay, trust the IMU and the Camera! They aren't perfect, but they are better than nothing."
- As soon as 5G comes back, the coach instantly corrects any small drift the camera or IMU made.

The Big Picture: The "KITTI" Test

To prove this works, the researchers didn't just guess; they tested it using a famous dataset called KITTI.

The Setup: They took a car driving through a real city (with real buildings and real signal problems).
The Simulation: They simulated what the 5G signals would have looked like in that city.
The Result: Their system kept the car's location accurate to within 5 meters (about the length of a large car), even when the "satellite" (5G) signals were blocked. This is as good as, or better than, standard commercial GPS.

Summary

This paper presents a "Swiss Army Knife" for navigation:

The Virtual Ruler: Uses math tricks to measure distance with extreme precision.
The AI Bouncer: Kicks out fake, bouncing signals that would cause errors.
The Smart Coach: Blends 5G data with camera and motion sensors so that even if the network goes down, you never lose your way.

It's a robust, "fail-safe" system designed to keep us safe and found, even when the sky is blocked by skyscrapers or the signal is jammed.

1. Problem Statement

Global Navigation Satellite Systems (GNSS) are the standard for positioning but suffer from critical vulnerabilities, including signal jamming, spoofing, and obstruction in urban canyons or indoor environments (GNSS-denied scenarios). While 5G networks offer a potential alternative, traditional 5G positioning methods (based on Time of Arrival, Angle of Arrival, or Received Signal Strength) often lack the centimeter-level accuracy required for autonomous driving and industrial automation. Furthermore, these methods degrade significantly in Non-Line-of-Sight (NLOS) conditions due to multipath effects.

The core challenges addressed in this paper are:

Integer Ambiguity (IA): Resolving the unknown integer number of carrier wavelengths between the User Equipment (UE) and Base Stations (BS) to achieve high precision.
NLOS Identification: Distinguishing between Line-of-Sight (LOS) and NLOS links, as NLOS signals introduce large ranging errors.
Continuity: Maintaining accurate positioning when LOS signals are temporarily blocked or unavailable.

2. Methodology

The authors propose a hybrid, end-to-end terrestrial positioning system that integrates three main components: Carrier Phase Positioning (CPP), Machine Learning (ML) for Link Classification, and Sensor Fusion.

A. Carrier Phase Positioning (CPP) with Virtual Wavelength

Instead of relying on external Radio Access Network (RAN) assistance or complex hybrid data fusion to resolve integer ambiguity, the system uses a multi-frequency virtual wavelength approach:

Mechanism: By measuring the phase difference between two distinct carrier frequencies ( $f_1$ and $f_2$ ), the system creates a "virtual wavelength" ( $\lambda_v = c / \Delta f$ ).
Benefit: By selecting an appropriate frequency spacing, the virtual wavelength can be made significantly larger than the physical carrier wavelength (e.g., ~416 meters). This expands the unambiguous range, allowing the system to determine the distance without explicitly resolving the integer ambiguity for typical urban link distances.
Noise Reduction: The system employs a linear averaging of phase differences across multiple subcarriers (comb-type allocation) rather than vector summation. This method includes a phase progression constraint (monotonicity) to filter out outliers caused by specular reflections, ensuring the estimate aligns with physical propagation laws.

B. ML-Based LOS/NLOS Classification

To prevent NLOS signals from corrupting the trilateration process, the system employs a Temporal Convolutional Neural Network (T-CNN):

Input: The model analyzes the Channel Impulse Response (CIR) derived from Sounding Reference Signals (SRS).
Architecture: A lightweight T-CNN uses stride operations for downsampling (reducing parameters compared to max-pooling) to detect temporal patterns in multipath structures.
Output: It provides a probabilistic score (soft decision) to classify links as LOS or NLOS. Links classified as NLOS are excluded from the positioning calculation.
Confidence: The model outputs confidence regions, allowing for "soft exclusion" of unreliable links rather than hard binary decisions.

C. Sensor Fusion (ES-EKF)

To ensure continuity when LOS conditions are lost (e.g., entering a tunnel or dense urban canyon), the system fuses data using an Error-State Extended Kalman Filter (ES-EKF):

Inputs:
- CPP: Provides absolute position updates when $\ge$ 3 LOS base stations are available.
- Visual Odometry (VO): Uses stereo cameras to estimate relative motion and trajectory.
- Inertial Measurement Unit (IMU): Provides high-frequency acceleration and angular velocity data.
Operation: The ES-EKF maintains a nominal state (position, velocity, orientation) and estimates the error state. It dynamically weights the inputs: relying on CPP when available for absolute correction, and switching to IMU/VO propagation during signal outages to prevent drift.

3. Key Contributions

Ambiguity-Free Ranging Framework: A standalone multi-frequency framework that resolves integer ambiguity via virtual wavelength processing, eliminating the need for external RAN assistance or complex hybrid search algorithms.
Confidence-Aware NLOS Filtering: A novel T-CNN architecture for real-time LOS/NLOS classification using CIR data, featuring a confidence-aware $\kappa$ score for robust link selection.
Hybrid Sensor Fusion Architecture: A unified ES-EKF framework that seamlessly integrates 5G CPP with visual and inertial sensors, ensuring continuous tracking even in GNSS-denied and NLOS environments.
Network Planning Insights: Demonstrated via ray-tracing simulations that optimizing 5G networks for positioning (prioritizing LOS visibility) requires denser Base Station deployment compared to traditional communication-focused planning.

4. Results and Evaluation

The system was evaluated using the KITTI dataset (urban driving scenario) combined with 3GPP-compliant channel simulations (Sionna ray tracing and 3GPP TR 38.901 UMi models).

Accuracy in LOS: Under LOS conditions with at least three Base Stations, the system achieves centimeter-level accuracy (e.g., 23.4 cm at the 90th percentile for 2D positioning).
Impact of NLOS Filtering: Without NLOS exclusion, positioning errors in mixed environments can exceed 60 meters. The T-CNN filtering reduces this error significantly, bringing performance close to pure LOS scenarios.
Sensor Fusion Performance:
- Visual Odometry (VO) alone: Absolute Trajectory Error (ATE) of 11.56 m.
- IMU + VO: ATE of 15.60 m (drift accumulation).
- Fused System (SRS/PRS + IMU + VO): Achieved an ATE of ~4.63–4.66 meters.
Comparison: The proposed solution outperforms state-of-the-art systems by a factor of 2 in terms of ATE, achieving performance comparable to public commercial GNSS services even in challenging urban environments.

5. Significance

This paper validates the feasibility of using 5G infrastructure as a primary, resilient alternative to GNSS. By addressing the specific technical hurdles of carrier phase ambiguity and NLOS interference, and by integrating complementary sensors, the proposed system offers a robust solution for:

GNSS-denied environments: Critical for autonomous vehicles in urban canyons, tunnels, and indoor facilities.
Mission-critical applications: Enabling centimeter-level accuracy required for industrial IoT, smart cities, and autonomous driving.
Future 5G-Advanced Networks: The methodology aligns with 3GPP Release 18 standards (Carrier Phase Positioning), providing a practical implementation roadmap for next-generation terrestrial localization.

The work highlights that while 5G positioning is theoretically capable of high precision, its practical deployment requires a holistic approach combining advanced signal processing, machine learning for channel classification, and multi-sensor fusion.