GLocFM: A Geometry-Aware Foundation Model for 3D Indoor Wireless Localization

The paper proposes GLocFM, a Geometry-aware Localization Foundation Model for 3D indoor wireless localization that jointly exploits WiFi measurements and scene geometry represented as a 3D point cloud. The authors note that Learning-based wireless localizers often fail to utilize geometric information about the propagation environment, limiting their ability to exploit non-line-of-sight (NLoS) propagation and generalize across scenes.

The authors formulate localization as a maximum-likelihood (ML) estimation problem, where the goal is to find a transmitter position that maximizes the likelihood of the wireless observations conditioned on the scene geometry. The ML estimate is expressed as:

x̂ ML = arg max log p(Y r r∈[1,N R] x, S), x∈Ω free

where N R denotes the number of receivers, Y r is the CFR at receiver r, and Ω free is the free space volume not occupied by any object mesh.

The likelihood of a candidate transmitter position is calculated by a learned scoring function that matches the observed delay–angle-of-arrival (AoA) spectrum against the spectrum predicted for that candidate. Key components include:

1. Geometric priors: A hierarchical scene encoder extracts propagation-relevant features to produce geometric priors for LoS and one-bounce reflection paths. The scene is represented as a 3D point cloud with features including coordinates, normals, and EM attributes (relative permittivity, electrical conductivity, diffuse-scattering coefficient, cross-polarization coefficient).

2. Path modeling: The model considers LOS paths and one-bounce reflection paths, computing delays, AoAs, and attenuations. For obstruction modeling, the authors construct the opacity field following the principle of convolutional occupancy networks and introduce soft visibility to quantify obstruction levels.

3. Candidate scoring: The model computes cosine similarity between observed and predicted delay–angular spectra, then uses a learned scoring function with Transformer layers to enhance the scoring. An off-grid component prediction network ensures continuous localization output rather than discrete grid selection.

4. ToF-robust variant: For scenarios with imperfect synchronization, we further introduce a time-of-flight (ToF)-robust GLocFM model to handle unknown ToF offsets. This is achieved by drawing random ToF offsets during training (b i ∼ N(0, σ b2)) to expose the model to different offsets.

The authors "construct a multimodal dataset of 221 diverse geometric layouts, using Infinigen Indoors to produce furnished 3D indoor environments represented as 3D meshes, and use the widely adopted Sionna RT to generate wireless signals within each indoor scenario. The scenes cover offices, bedrooms, bathrooms, and kitchens, occupying areas from 3.25 m2 to 63.51 m2 with a mean of 22.37 m2. The channel simulation uses a carrier frequency of 3.5 GHz, 80 MHz bandwidth, and 1,024 OFDM subcarriers." The dataset is split into 177 training, 22 validation, and 22 test scenes.

On the synthetic GLocFM dataset, GLocFM achieves a mean localization error of 0.1429 m and 0.1746 m, which are 49.5% and 56.0% lower than that achieved by the strongest LocGPT delay-AoA baseline for NR = 4 and NR = 3, respectively. The model achieves an accuracy of 82.2% at the 0.2 m threshold for NR = 4.

On the NeRF2 dataset based on real measurements, the modified GLocFM model achieves a lower localization error than the baselines, with mean error of 0.0637 m when fine-tuned with 100% of training data, representing a 48.8% reduction compared to the strongest baseline (LocGPT with 0.1244 m mean error).

• Grid size: Reducing from N=12 to N=3 increases mean error from 0.1429 m to 0.4494 m; increasing to N=16 yields only 0.7 cm additional gain but nearly doubles computational complexity.

• Learned scoring function: Removing it substantially worsens error statistics, showing cosine similarity alone cannot resolve ambiguous candidates.

• Path model: Using LoS-only paths degrades performance by 7.5 cm compared to including one-bounce reflections.

• System configurations: Reducing UPA from 4×4 to 2×2 increases error from 0.1429 m to 0.2332 m; reducing bandwidth from 80 to 20 MHz increases error by roughly 7 cm.

• ToF robustness: The original model's mean error increases dramatically from 0.1429 to 0.7141 m under ToF offsets up to 4 ns, while the ToF-robust variant maintains error between 0.2044 and 0.2270 m, reducing error at 4 ns by 68.2%.

The authors list four main contributions: (1) proposing GLocFM as a geometry-aware foundation model grounded in maximum-likelihood principles; (2) constructing a multimodal wireless localization dataset with 221 scenes; (3) utilizing geometry priors for delay-AoA spectrum generation with a learned scoring function and ToF-robust variant; (4) demonstrating mean-error reductions of 49.5–56% on unseen synthetic scenes and 48.8% on the NeRF2 dataset with real measurements.

Improvements to AI systems:

1. Physics-grounded geometric priors for wireless signal prediction: The AI system can now explicitly model LOS and one-bounce reflection paths using 3D scene geometry (point clouds with EM attributes like permittivity and conductivity). This enables the system to predict delay–AoA spectra for any candidate transmitter position, even under NLoS conditions, by simulating path delays, angles, and attenuations from the scene structure.

2. Maximum-likelihood localization with learned scoring: Instead of direct regression or classification, the system formulates localization as an ML estimation problem. A learned scoring function (with Transformer layers) compares observed vs. predicted delay–angular spectra via cosine similarity, then refines the score to resolve ambiguities. This yields continuous, off-grid position estimates via an off-grid component prediction network, avoiding discrete grid quantization errors.

3. Soft visibility and opacity field for obstruction modeling: The system introduces a convolutional occupancy network–based opacity field to quantify partial obstructions along propagation paths. This allows the AI to handle complex indoor clutter (furniture, walls) by softly weighting path contributions, improving robustness in realistic furnished scenes.

4. ToF-robust training for imperfect synchronization: By injecting random time-of-flight offsets (sampled from a Gaussian) during training, the system learns to be invariant to unknown clock offsets. This makes the AI usable in real-world deployments without precise synchronization, maintaining low error (0.20–0.23 m) even with offsets up to 4 ns, whereas non-robust models degrade to 0.71 m.

5. Hierarchical scene encoding for cross-scene generalization: The system extracts propagation-relevant features hierarchically from 3D point clouds, enabling it to generalize to unseen room layouts (offices, bedrooms, bathrooms, kitchens) without retraining. This is validated by a 49.5–56% error reduction on unseen synthetic scenes and a 48.8% reduction on real-measurement data (NeRF2).

6. Multimodal dataset generation for training and benchmarking: The system can now generate large-scale, diverse, physically accurate wireless localization datasets (221 scenes with meshes, EM properties, and ray-traced channels). This enables training foundation models that require extensive geometry–signal paired data, and provides a standardized benchmark for future research.

What the improved AI system can do:

• Accurately localize a transmitter in 3D indoors (mean error 0.14 m with 4 receivers, 0.17 m with 3 receivers) using only WiFi CSI and a 3D point cloud of the environment, even in NLoS conditions.

• Operate in real-world, unsynchronized deployments by tolerating unknown ToF offsets, maintaining sub-0.23 m accuracy without clock calibration.

• Generalize to new rooms and layouts it has never seen, leveraging geometric priors rather than memorizing scene-specific patterns.

• Provide continuous, sub-grid position estimates (not just discrete grid cells) via the off-grid prediction network, enabling centimeter-level precision.

• Adapt to different hardware configurations (e.g., fewer antennas, lower bandwidth) with graceful performance degradation, as shown in ablations (e.g., 2×2 UPA still achieves 0.23 m error).

• Serve as a foundation model that can be fine-tuned on real measurements (e.g., NeRF2) with a 48.8% error reduction over prior state-of-the-art, making it practical for deployment in smart homes, warehouses, or IoT localization services.

Learning-based wireless localizers often fail to utilize geometric information about the propagation environment, limiting their ability to exploit non-line-of-sight (NLoS) propagation and generalize across scenes. To bridge this gap, we propose GLocFM, a Geometry-aware Localization Foundation Model, which jointly exploits WiFi measurements and scene geometry represented as a 3D point cloud. We formulate localization as a maximum-likelihood (ML) estimation problem, where the goal is to find a transmitter position that maximizes the likelihood of the wireless observations conditioned on the scene geometry. The likelihood of a candidate transmitter position is calculated by a learned scoring function that matches the observed delay--angle-of-arrival (AoA) spectrum against the spectrum predicted for that candidate. A hierarchical scene encoder extracts propagation-relevant features to produce geometric priors for LoS and one-bounce reflection paths. For scenarios with imperfect synchronization, we further introduce a time-of-flight (ToF)-robust GLocFM model to handle unknown ToF offsets. GLocFM is trained on a multi-modal synthetic indoor localization dataset comprising 221 diverse scenes whose associated wireless signals are generated using Sionna RT. On both synthetic and the NeRF squared dataset based on real measurements, GLocFM reduces mean 3D localization error relative to one of the state-of-the-art localization baselines by 49.5% and 48.8%, respectively. Ablations across different number of receiver, bandwidths, and array sizes further demonstrate the effectiveness and robustness of the proposed framework.