Technical Summary: Learning Displacement-Aware WiFi Representations for Weakly Supervised Relative Localization

Problem Formulation

The paper addresses the challenge of indoor relative localization using WiFi fingerprints. Unlike conventional approaches that map WiFi fingerprints to absolute coordinates (requiring dense, costly location annotations), this work focuses on estimating the displacement vector ($\Delta_{AB}$) between two WiFi fingerprint traces ($F_A$ and $F_B$) without predicting their absolute positions.

The core difficulty lies in the nature of the data: WiFi fingerprints are ambiguous and noisy, whereas physical motion is additive. The authors aim to learn a model that can directly infer relative displacement from fingerprint traces using weak supervision. Instead of dense coordinate labels, the system utilizes stepwise motion vectors (displacement traces, $D$) obtained from inertial sensors (e.g., on robots or IoT devices) as weak labels. This formulation targets scenarios like robot following and warehouse coordination where relative spatial relationships are more actionable than global coordinates.

Methodology: Intersection Pathway (IP)

The proposed solution is a cross-modal learning framework called Intersection Pathway (IP). The architecture employs two autoencoders that share a common latent space to align fingerprint traces (f-traces) and displacement traces (d-traces).

1. Architecture Components

• f-trace Autoencoder: Uses a Transformer-based encoder to process sequences of WiFi fingerprints. This handles the ambiguity of fingerprints by capturing sequential context (upstream and downstream signals). The decoder reconstructs the input f-trace.
• d-trace Autoencoder: Uses a linear encoder and decoder to process stepwise displacement vectors. The linearity is a critical design choice to preserve the additive structure of physical motion in the latent space.
• Shared Latent Space: Both modalities are mapped to latent codes of matching dimensionality, allowing direct interaction.

2. Training Pathways

The model is trained using four specific pathways to enforce consistency between the modalities:

• Fingerprint-Direct (FD): Reconstructs the input f-trace to stabilize context-aware embeddings.
• Displacement-Direct (DD): Reconstructs the input d-trace to ensure accurate mapping of physical displacements.
• Fingerprint-Displacement-Add (FDA): Enforces that adding a latent displacement code ($e_i$) to a previous fingerprint latent code ($l_{i-1}$) yields the latent code of the next fingerprint ($l_i$). This teaches the model that latent addition corresponds to physical motion.
• Fingerprint-Fingerprint-Subtract (FFS): Enforces that subtracting adjacent fingerprint latent codes ($l_i - l_{i-1}$) yields the latent code of the displacement ($e_i$). This allows the model to infer displacement from fingerprint differences.

Training proceeds in three stages, gradually introducing these constraints to first learn robust fingerprint representations, then inject motion information, and finally align the two modalities.

3. Inference

During inference, the model takes two f-traces ($F_A, F_B$) as input. It encodes them into latent codes, computes the difference between their endpoint latent codes ($l_B - l_A$), and passes this difference through the linear d-trace decoder to output the predicted displacement vector.

Key Contributions

1. Problem Formulation: The authors formulate WiFi-based relative localization as a weakly supervised problem, enabling direct displacement estimation without dense coordinate labels.
2. Intersection Pathway Framework: They propose a cross-modal framework that aligns fingerprint and displacement traces in a shared latent space. Crucially, they enforce an additive structure where latent addition/subtraction corresponds to physical motion composition.
3. Displacement-Aware Representations: The learned representations support both relative localization and a lightweight extension to few-shot absolute localization using sparse anchors, demonstrating the utility of the learned latent space.

Experimental Results

The method was evaluated on a synthesized dataset derived from real WiFi measurements and human walking trajectories in a 20x25m indoor environment.

• Relative Localization Performance: The proposed method achieved a Displacement Error (DE) of 0.719m for displacements up to 10m and 1.751m for all ranges. It outperformed baselines using LSTM and DNN backbones, particularly in longer-range scenarios.
• Ablation Studies:
  • Removing the d-trace encoder or f-trace decoder significantly degraded performance, confirming the necessity of cross-modal interaction and reconstruction pathways.
  • Replacing the linear d-trace branch with a nonlinear one caused the largest performance drop, validating that linearity is essential for preserving displacement composition.
• Robustness: The model remained stable under moderate noise levels ($\lambda \le 2.0$) but degraded sharply with excessive perturbation.
• Few-Shot Extension: When extended to absolute localization with sparse anchors, the model achieved sub-meter accuracy, though it was more sensitive to noise than fully supervised baselines.

Significance and Claims

The paper claims that the Intersection Pathway framework successfully learns displacement-aware WiFi representations by leveraging weak supervision. Its significance lies in:

• Reducing Annotation Costs: Eliminating the need for dense coordinate labels, which are expensive to obtain at scale.
• Hardware Agnosticism: Unlike UWB or BLE systems, this approach relies on commodity WiFi and standard inertial sensors, making it broadly applicable.
• Actionable Output: By directly estimating relative displacement, the method aligns better with applications where relative positioning (e.g., robot following) is more critical than global coordinates.
• Scalability: The ability to extend the model to few-shot absolute localization suggests a pathway for practical deployment where only a few anchor points are available.

The authors conclude that the explicit cross-modal interaction and the preservation of additive structure in the latent space are the key factors enabling accurate relative localization under weak supervision.