Optimizing 5G terrestrial positioning and navigation by learning algorithms from data

About NextNav

NextNav is a leading company providing alterative Positioning, Navigation, and Timing (PNT) solution to backup and complement GPS/GNSS. Leveraging its licensed low-band 900 MHz spectrum, NextNav utilizes 5G standard to broadcast Positioning Reference Signals (PRS), enabling terrestrial geolocation services available indoors, outdoors, and in urban canyons.

Project Overview

Mobile devices receive PRS signals from multiple base stations and measure their time of arrivals (TOAs) to determine their positions via trilateration. This trilateration problem is typically solved using nonlinear least squares (LS) or weighted LS (WLS) methods. For navigation or tracking applications, extended Kalman filter (EKF) or its variants are commonly employed o recursively refine the position estimates.

However, the WLS and Kalman approaches implicitly assume Gaussian measurement noise, an assumption that does not hold under real-world propagation conditions. Specifically, TOA measurements are often non-Gaussian and asymmetric due to multipath propagation and non-line-of-sight (NLOS) conditions. Intuitively, reflected signals traverse longer propagation paths, resulting in positively skewed ranging errors. Prior field studies on 4G Cell Reference Signals (CRS), which employ similar OFDM waveforms, have confirmed that the noise is better characterized by Laplacian, Cauchy, or Student’s t distributions rather than a Gaussian model. Moreover, the measurement errors are heteroscedastic, with their variance and shape depending on signal-related metrics. For instance, under low- to medium-SNR conditions, the error distribution is typically skewed toward positive values, whereas at high SNR levels, commonly associated with line-of-sight (LOS) scenarios, the noise becomes more symmetric, as illustrated in Fig. 1. Beyond SNR, additional features influence the noise distribution, including signal acquisition and tracking quality metrics (e.g., reference signal received power (RSRP), the prominence of the first detected peak), base station height, and so on. To improve estimation performance, the L2 loss function underlying WLS and EKF is replaced by data-driven robust loss functions, learned from field measurements, thereby enabling maximum likelihood (ML) estimation under non-Gaussian noise.

The objective is to train a model to predict the noise distribution of TOA measurements conditioned to signal quality metrics and other relevant features, in order to optimize maximum-likelihood (ML)-based positioning performance. A commonly used but suboptimal heuristic in GPS-based WLS is to define measurement weights as functions of carrier-to-noise ratio (C/N₀) and satellite elevation, which often leads to biased estimates and degraded performance, even under favorable conditions. Field measurements collected from NextNav’s 5G trial network in California, USA, combined with high-precision ground-truth data (including base station almanacs, receiver locations, and timing information), will enable the construction of a large-scale dataset for feature engineering and model training. Positioning solvers required to evaluate the newly learned loss functions are already available.

A key aspect of this work is to infer the full noise distribution rather than only its expectation (mean), as is typical in standard regression-based approaches. Modeling the full distribution provides richer information that can be exploited to improve positioning accuracy, including:

• Mode: corrects systematic positive biases in the raw measurements;
• Scale: enables adaptive weighting or ranking of measurements, reflecting their relative reliability and predictability;
• Skewness: captures the higher likelihood of positive errors, accounting for NLOS and multipath effects;
• Distribution shape: allows optimal weighting beyond simple Gaussian assumptions.

The intern is encouraged to study and implement one or more of the following modeling approaches:

• Conditional density estimation, using linear models, neural networks, or related methods;
• Quantile-based approaches, including quantile regression, decision trees/forests, or binned classification;
• Flow-based generative models.

The expected outputs include a reproducible benchmarking pipeline, comparative results across different model architectures, and a concise recommendation identifying the most promising models for further investigation.

Requirements:

• Final-year engineering student or Master’s (M2) student
• Strong background in statistics, signal processing, and AI/machine learning
• Hands-on experience with deep learning training and optimization; familiarity with modern architectures (transformers, state-space models, and generative models such as GANs, diffusion models, normalizing flows, and autoencoders) is a plus.
• Proficiency in Python, including experience with machine-learning libraries such as scikit-learn, PyTorch, or JAX, and MATLAB
• Internship duration: 6 months
• Fluency in English is required
• Start date: from March 2026
• Location: NextNav France, 76 Rue de la Demi-Lune, 92800 Puteaux
• Contact: Minh Hoang – [email protected], Mickael Thomas – [email protected]