Enabling Motion-Induced WiFi-CSI Sensing in Multi-Robot Systems: A Simulation Framework

1 Introduction

• Existing relative-sensing approaches can require dedicated hardware, careful deployment, or favorable conditions, while WiFi offers an already widely deployed indoor sensing foundation.CSI captures fine-grained amplitude and phase across subcarriers, whereas RSSI is susceptible to indoor noise and multipath.Source: §1 · p. 2
• WSR showed that robot-motion CSI measurements combined with odometry can synthesize a virtual antenna array for inter-robot bearing estimation, but its deprecated hardware and integration demands limit deployment and reproducibility.The original implementation relies on Intel 5300 hardware and modified low-level drivers.Source: §1 · p. 2
• The paper identifies a lack of accessible simulation that combines the WSR pipeline with multi-robot operation, CSI generation, bearing estimation, and downstream localization.MATLAB WLAN Toolbox does not model continuous robot motion or environmental dynamics, while NVIDIA Aerial Omniverse is resource-intensive and tailored to large-scale 5G/6G networks.Source: §1 · pp. 2–3
• The framework reproduces the WSR pipeline in simulation, integrating MATLAB signal processing with Gazebo-based robot simulation and supporting evaluation of sensing, motion, and multi-robot configurations.Its stages include CSI and odometry generation, phase computation, virtual-array construction, Bartlett bearing estimation, and downstream localization.Source: §1 · p. 3, Figure 1 · p. 3
• The framework is experimentally validated using both simulated data and real-world measurements.It is presented as an open-source simulation framework for motion-induced WiFi-CSI sensing in multi-robot systems.Source: §1 · p. 3

2 The WSR Toolbox

• WSR uses a moving single antenna to synthesize a virtual array, with odometry reconstructing spatial sampling positions across multiple transmissions.Figure 2 depicts a circular array of 30 cm radius and a transmitter 4 m away for the far-field assumption [18].Source: §2 · pp. 3–4, Figure 2 · p. 4
• The toolbox extracts signal phase from CSI and constructs an AoA profile that maps incoming signal power by direction, with its peak usable as the estimated bearing.The peak magnitude can provide a likelihood score for estimate confidence.Source: §2 · p. 4
• Deployment is limited by obsolete Intel WL5300 hardware, end-of-life software, and the integration effort needed for a working multi-robot setup.The toolbox also coordinates packet exchange and captures CSI from 30 of the 48 WiFi subcarriers available under 802.11n.Source: §2 · pp. 3–4

3 Proposed simulation framework

• The framework captures raw CSI and odometry, computes signal phase and virtual-array geometry, and estimates relative bearing using Bartlett’s estimator.An application study uses the Levenberg–Marquardt algorithm for absolute position estimation.Source: §3 · p. 5
• The framework has compatibility layers for Ubuntu 20.04 with MATLAB 2022a, ROS1, and Gazebo Classic, and for Ubuntu 24.04 with MATLAB 2025b, ROS2, and GZ Gazebo.The latter configuration is used for the paper’s results.Source: §3 · p. 5
• MATLAB interfaces with Gazebo through ROS to control trajectories, collect data, and process CSI for bearing estimation and localization.Simulated and physical robots use the same ROS interfaces, and simulated data are saved in the same format as real datasets for direct interchange.Source: §3 · p. 5

3.1 Signal Model

• Under the ideal-channel assumption, the central carrier is modeled as a monochromatic wave whose amplitude attenuates with distance and whose phase encodes spatial separation.The model uses Euclidean distance between nodes and signal wavelength.Source: §3.1 · p. 5
• The model uses a single distance subscript because distance between nodes i and j is symmetric.The text states d_ij = d_ji.Source: §3.1 · p. 5
• The signal wavelength and inter-node distance are the defined quantities in the signal model.Distance is the Euclidean distance between nodes at time t.Source: §3.1 · p. 5

3.2 Simulating CSI Data

• Simulated CSI phase and robot odometry are the primary modeled components because they are crucial to constructing the AoA profile.The simulation incorporates four elements.Source: §3.2 · p. 5

Carrier Frequency Offset (CFO)

• Under channel reciprocity, multiplying forward and backward signals cancels equal-magnitude, opposite-sign CFO phase offsets.Each virtual antenna uses a unique fixed CFO to replicate a real hardware offset.Source: Carrier Frequency Offset (CFO) · p. 6

3.2.1 Additive Phase Noise

• Residual phase noise from antenna variance, multipath, and interference is approximated as AWGN, with variance set by average signal power and SNR.Different SNR levels can be set for each connected node pair.Source: §3.2.1 · p. 6

3.2.2 Odometry Drift

• Platform-specific odometry drift is modeled by using true robot positions to simulate CSI and odometry to calculate bearing, matching real conditions.Source: §3.2.2 · p. 6

3.2.3 Randomization in Repeated Experiments

• Moving robots’ starting positions are randomized within ±20 cm in any direction to represent offsets from manually repeated real-hardware experiments.Source: §3.2.3 · p. 7

• Under the far-field assumption, incoming wavefronts are treated as planar over robot displacement, and steering vectors encode phase shifts for discretized arrival directions.Source: §3.3 · p. 7
• Projecting the CSI signal onto all steering directions produces the AoA profile, whose peaks indicate directions of strongest received signal energy.Source: §3.3 · p. 7
• Azimuth and elevation are discretized at 1° resolution over −180° to 180° and −90° to 90°, respectively.The profile uses Bartlett’s estimator.Source: §3.3 · p. 7

• The receiver position is estimated by minimizing squared perpendicular distances from the candidate position to AoA_max bearing lines from static and mobile transmitters.Each line is defined by a transmitter’s 2D position and a direction vector derived from its bearing.Source: §3.4 · p. 8
• The perpendicular distance from a candidate receiver position to a bearing line is specified in Equation (8), and the optimization is formulated in Equation (9).Source: §3.4 · p. 8
• The nonlinear least-squares problem is solved with Levenberg–Marquardt, initialized at the centroid of active transmitters.Source: §3.4 · p. 8

4 Experiments & Results

• Across three scenarios, 100 Monte Carlo simulations per scenario test accuracy, scalability, and generalization against real-world benchmark data.The scenarios progress from 2D circular motion to elevated multi-agent motion and unstructured random walks.Source: §4 · p. 8

4.1 Benchmark Experiment: 2D Circular Motion

• The baseline scenario replicates, using four ground-level robots—three static and one mobile—with the mobile robot following a 20 cm-diameter circular trajectory at 0.04 m/s; all node pairs have SNR 30.Source: §4.1 · pp. 8–9

Benchmark Scenario Results

• With odometry, the benchmark median positioning error is 0.42 m, close to the 0.50 m reported in real experiments.Using true robot positions instead yields a 0.05 m median error and 0.02 m standard deviation under ideal conditions.Source: Benchmark Scenario Results · p. 9

4.2 Expanded Experiment: Elevated and Multiple Mobile Agents

• The expanded scenario adds one mobile and one static robot at different elevations, with selected links assigned SNR 3 to mimic NLOS conditions.Its 2D trajectories create elevation ambiguity because they lack an elevated 3D component.Source: §4.2 · p. 10

Expanded Scenario Results

• In the expanded scenario, localization improves to 0.37 m with an additional static beacon despite similar AoA performance; planar motion also leaves elevation estimates mirrored.With true pose, median position error is 0.04 m (standard deviation 0.02 m); AoA median and standard deviation are both around 1.5°.Source: Expanded Scenario Results · p. 10, Figure 5 · p. 11
• With perfect motion capture, AWGN phase noise lowers AoA confidence but does not shift the main peak or create additional peaks; lower SNR increases AoA covariance.The simulated profile variance is less severe than in real NLOS experiments because additional multipath peaks are absent.Source: Expanded Scenario Results · p. 10

4.3 Generalization Experiment: Random Walk Motion

• Random-walk runs replace circular paths with randomized linear and rotational segments while retaining the comparable 3D setup and signal conditions.Each run spans three seconds of simulation time.Source: §4.3 · p. 11

Generalization Scenario Results

• Random-walk AoA error standard deviations reach 18.72° at high noise and 3.48° at low noise; drift plus high phase noise produces effects comparable to NLOS multipath.The framework approximates NLOS conditions without the computational overhead of full 3D multipath modeling.Source: Generalization Scenario Results · p. 11

5 Discussion & Conclusion

• The MATLAB–Gazebo framework replicates the WSR toolbox to evaluate WiFi-CSI localization under realistic motion and free-form trajectories in dynamic environments.It supports nodes at different locations and heights, including configurations mimicking ceiling- or wall-mounted access points and multi-floor buildings.Source: §5 · p. 12
• 0.42 m simulated median positioning error closely aligns with the 0.50 m error reported in identical real-world experiments.Simulated AoA profiles also closely resemble real data in main-lobe direction, structure, and patterning; randomized trajectories mirrored physical AoA error magnitudes, and tunable phase noise approximated LOS and NLOS conditions.Source: §5 · p. 12
• Increasing static beacons improves localization, while node elevation does not diminish bearing estimation accuracy.Mirrored bearing estimates predicted by antenna-array geometry further demonstrate simulation fidelity; future work can address multipath-induced sidelobe variations not captured by additive noise.Source: §5 · p. 12
• Heavy algorithms can be compiled into C/C++ executables or distributed across machines via ROS to address MATLAB’s computational overhead.The paper presents the framework as a scalable, reproducible means to prototype and evaluate WiFi-CSI-based localization algorithms.Source: §5 · p. 12