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Annotation-Free Indoor Radio Mapping via Physics-Informed Trajectory Inference

This paper proposes an annotation-free indoor radio mapping framework that leverages Channel State Information (CSI) and a physics-informed trajectory inference model to recover user locations and construct beam maps without requiring location labels or IMU sensors, achieving high accuracy by exploiting the local spatial continuity of multipath propagation.

Original authors: Zheng Xing, Mengru Wu, Yi Zhang, Guanghui Zhang, Jun Gao, Weibing Zhao, Xuhui Zhang, Jinke Ren, Shuguang Cui

Published 2026-05-13

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CC BY 4.0

Original authors: Zheng Xing, Mengru Wu, Yi Zhang, Guanghui Zhang, Jun Gao, Weibing Zhao, Xuhui Zhang, Jinke Ren, Shuguang Cui

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 trying to draw a detailed map of a large, empty warehouse. Usually, to do this with Wi-Fi signals, you would need a team of people to walk around with clipboards, stopping every few feet to write down exactly where they are and what the Wi-Fi signal looks like at that spot. This is slow, expensive, and annoying.

Other methods try to speed this up by asking people to wear smartwatches (IMUs) that track their steps. But smartwatches can be glitchy, batteries die, and sometimes the software doesn't let you access the data. Plus, over time, the watch might think you walked a mile when you only walked a few steps (sensor drift).

This paper introduces a clever new way to build that Wi-Fi map without needing anyone to write down their location and without needing a smartwatch.

The Core Idea: "Listening to the Echoes"

Think of the Wi-Fi signal (specifically something called Channel State Information, or CSI) like a complex echo in a cave. When you move just a tiny bit, the way the sound bounces off the walls changes in a very specific, predictable pattern.

The authors realized that even though the signal is messy, if you move a small distance, the "shape" of the echo changes smoothly. They created a special mathematical ruler called a PADP (Power-Angle-Delay Profile).

The Analogy: Imagine you are walking through a forest. If you take one step, the sound of the wind in the leaves changes slightly. If you take two steps, it changes a bit more. The authors built a tool that measures how much the "wind sound" (the Wi-Fi signal) changed between two steps. They proved that if the change in the sound is small, the physical distance you walked must also be small.

How It Works: The Detective Story

The system works like a detective solving a mystery with a few clues:

The Knowns: We know where the Wi-Fi routers (Access Points) are hanging on the ceiling, and we have a floor plan of the room (we know where the walls and walkable areas are).
The Unknown: We have a recording of Wi-Fi signals as someone walked through the room, but we have no idea where they were at any given second.
The Clues:
- Volume (RSS): How loud the signal is tells us roughly how far away the router is (like shouting in a canyon).
- Direction: The signal tells us which way the router is relative to the person.
- The "Echo" Ruler (PADP): This is the secret sauce. It checks if the signal changes smoothly. If the signal suddenly jumps as if the person teleported, the system knows that's impossible and corrects the path.

The Solution: A "Physics-Informed" Guess

The computer uses a method called Bayesian Inference. Think of this as a game of "Guess the Path" where the computer makes a guess, checks it against the laws of physics (like "you can't walk through walls" and "you can't teleport"), and then refines the guess.

Step 1: It makes a rough guess of the path based on signal volume and direction.
Step 2: It checks the "Echo Ruler" (PADP). Did the signal change smoothly as the person moved? If the guess says the person jumped 10 meters but the signal only changed a tiny bit, the system knows the guess is wrong.
Step 3: It adjusts the path to make it fit the signal changes better.
Step 4: It repeats this until the path makes perfect sense with both the signal data and the rules of physics.

The Results

The team tested this in a real industrial warehouse.

Accuracy: They were able to figure out where the person was walking with an average error of less than 1 meter (about 3 feet).
The Map: Once they figured out the path, they used it to draw a high-quality "heat map" of the Wi-Fi signals in the room. The map was accurate to within 6.7% of the real signal strength.
Comparison: This was better than other methods that relied on smartwatches or required people to manually label their locations.

In Summary

This paper presents a way to map Wi-Fi signals in a building by letting the computer "listen" to how the signals naturally change as a person walks. By using the physics of how radio waves bounce off walls, the computer can reconstruct the person's path and draw the map without needing a single GPS coordinate or a smartwatch. It's like solving a puzzle where the pieces (the signals) naturally fit together if you just look at them the right way.

Technical Summary: Annotation-Free Indoor Radio Mapping via Physics-Informed Trajectory Inference

Problem Statement

Constructing indoor radio maps traditionally relies on labor-intensive site surveys requiring precise user-location labels, making the process costly and difficult to scale. Existing methods attempting to reduce calibration costs often depend on partial location annotations or utilize Inertial Measurement Units (IMUs) for relative motion cues. However, IMU-based solutions face limitations regarding hardware availability, operating system permissions, privacy policies, and accumulated sensor drift.

This paper addresses the problem of indoor radio mapping without user-location labels and without IMU measurements. The problem is formulated under a practical deployment setting where:

Access Point (AP) locations, array orientations, and the valid walkable spatial domain are known (derived from installation records or floor plans).
No Channel State Information (CSI) sample is annotated with the user's physical coordinate.
The goal is to infer the latent trajectory associated with a temporal CSI sequence and use this recovered trajectory to construct a radio map.

The challenge lies in the complex indoor environment where severe multipath propagation, asynchronous measurements, and non-line-of-sight (NLoS) components obscure the relationship between CSI variations and physical displacement.

Methodology

The authors propose a Physics-Informed Trajectory Inference Framework based on a spatially regularized Bayesian model. The core approach involves three main components:

1. Physics-Informed Spatial Continuity (PADP Feature)

The framework exploits the local spatial continuity of multipath propagation. The authors observe that small physical displacements in a quasi-static environment induce structured changes in the phase, delay, and angular responses of dominant multipath components.

PADP Construction: A Power-Angle-Delay Profile (PADP) feature distance is constructed from MIMO-OFDM CSI. This involves normalizing the CSI, projecting it onto an angular dictionary and a normalized DFT matrix, and computing the magnitude.
Continuity Proposition: It is shown that within a local neighborhood, the PADP distance between two CSI observations serves as a physically meaningful proxy for the Euclidean distance between the corresponding user locations. This relationship is modeled as a linear surrogate with additive noise, providing a pairwise regularization term for trajectory inference.

2. Bayesian Trajectory Inference Model

The problem is formulated as a joint optimization of the latent trajectory ( $X_T$ ) and propagation parameters ( $\Theta_p$ ). The objective function maximizes a spatially regularized log-likelihood:

Emission Terms: Incorporates Received Signal Strength (RSS) modeled via a log-distance path-loss model and directional information derived from a MUSIC-type search on the spatial covariance matrix.
Transition Terms: Uses a first-order Markov mobility model over a discretized spatial graph derived from the known walkable domain, constraining movement based on plausible walking speeds.
Regularization: A pairwise energy term penalizes transitions where the physical displacement is inconsistent with the observed PADP variation. This term is weighted by a parameter $\eta$ .

3. Alternating Optimization Algorithm

Since the trajectory and parameters are coupled, the authors employ an alternating optimization strategy:

Initialization: A coarse trajectory is estimated using only RSS, directional likelihoods, and mobility constraints (setting the regularization weight $\eta = 0$ ).
Parameter Estimation: Given the current trajectory, propagation parameters (path-loss coefficients, noise variances, and PADP continuity parameters) are updated using closed-form solutions or least-squares estimation.
Trajectory Refinement: With updated parameters, the trajectory is refined by maximizing the regularized objective over the spatial graph using a Viterbi-type recursion.
Radio Map Construction: Once the latent trajectory is recovered, CSI observations are associated with inferred coordinates to construct RSS, PADP, channel, and beam-domain radio maps using kernel-weighted averaging.

Key Contributions

The paper highlights four primary contributions:

Location-Label-Free Formulation: A novel problem setting for indoor radio mapping that requires no user-location labels or IMU data, relying solely on known AP geometry and walkable domains.
PADP Continuity Cue: The construction of a PADP-based CSI distance that captures local angular-delay variations, serving as a physics-informed proxy for small spatial displacements.
Regularized Bayesian Inference: A framework that integrates RSS, angle information, mobility constraints, and PADP continuity to jointly recover the latent trajectory and estimate propagation parameters.
Real-World Validation: Experimental demonstration on a real-world industrial dataset showing the method's effectiveness compared to existing baselines.

Experimental Results

The proposed framework was evaluated on the dichasus-cf0x dataset, collected in a real industrial hall (approx. 14m $\times$ 14m) with 4 distributed Uniform Planar Arrays (UPAs). Ground-truth positions were used exclusively for evaluation, not for training or inference.

Performance Metrics:

Localization Error: The proposed method achieved an average localization error of 0.88 m. This outperformed representative baselines, including channel-embedding methods (e.g., Bilateration at 0.98 m, Siamese at 1.21 m) and IMU-assisted methods (e.g., RITA at 7.58 m, GraphIPS at 2.11 m).
Radio Map Construction: The method achieved a relative beam map construction error of 6.68% and a channel reconstruction RMSE of 6.93%.
Ablation Study: Removing the PADP regularization (Proposed w/o) increased the localization error to 1.32 m, demonstrating the value of the physics-informed continuity cue.

Comparative Analysis:

IMU-assisted methods showed degraded performance, likely due to drift accumulation and domain mismatch in the industrial setting.
Clustering-based unsupervised methods (ENAP, VRLoc) also underperformed, suggesting that discrete cluster structures alone are insufficient for preserving fine-grained trajectory continuity.
The proposed method's trajectory recovery better preserved the global shape of the measured path compared to other methods, as visualized in the experimental results.

Significance and Claims

The paper claims that indoor radio maps can be constructed from CSI sequences without relying on user-location labels or auxiliary IMU measurements, provided that AP geometry and the walkable domain are known. The significance lies in:

Reducing Calibration Costs: Eliminating the need for labor-intensive site surveys and precise labeling.
Hardware Independence: Removing reliance on IMUs, thereby avoiding issues related to hardware heterogeneity, privacy, and sensor drift.
Physics-Informed Learning: Demonstrating that local angular-delay variations in CSI retain useful geometric information even in severe multipath environments, allowing for the construction of a "physics-informed" spatial continuity prior.

The authors conclude that the recovered trajectory serves as a valid spatial anchor for constructing high-fidelity radio maps (RSS, PADP, channel, and beam domains), validating the effectiveness of the proposed PADP regularization in real-world industrial scenarios.