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IMU-Aided Motion Compensation of RSS Measurements for Dynamic Visible Light-Inertial Localization

Xiao Sun, Zhenqi Zheng, Jianzhu Huai, Xingxing Li, Wanwei Zhang, Yuan Zhuang

arXiv:2610.23188v1eess.SP

TL;DR

Rapid PD motion makes DFT-derived RSS window-averaged rather than instantaneous, challenging VLP positioning. The paper uses high-rate IMU motion estimates to correct RSS before tightly or simply coupled VLP/INS fusion. Across eight held-out dynamic trials, correction reduced pooled position and inclination RMSE against the LiDAR/IMU reference.

  • Problem

    During rapid PD motion, DFT processing produces window-averaged RSS while positioning estimators use it as instantaneous, creating a discrepancy that degrades positioning accuracy.

    Source: §I · p. 2

  • Method

    The correction uses high-rate IMU-derived motion to estimate the difference between averaged DFT RSS and instantaneous RSS before VLP/INS fusion.

    Source: §I · p. 2, §III · p. 4

  • Results

    56.0% reduction in pooled 3D position RMSE and 71.9% reduction in PD-normal inclination RMSE across eight held-out dynamic trials relative to the LiDAR/IMU reference.

    Source: §V · p. 10

  • Takeaways & Limitations

    The correction operates before fusion in both tightly and simply coupled VLP/INS frameworks, and the reported experiments validate it for highly dynamic receiver motion.

    Source: §V · p. 10

Abstract

from arXiv · show

Visible Light Positioning (VLP) offers high-precision indoor positioning using existing LED infrastructure. However, in VLP systems using Photodiodes (PDs) as receivers, rapid movement of the PD causes measurement inaccuracies as the Discrete Fourier Transform (DFT) processing yields averaged rather than instantaneous Received Signal Strength (RSS) values. To address this challenge, we propose an RSS correction algorithm that integrates Inertial Measurement Unit (IMU) data with VLP observations to compensate for motion-induced distortions. Our approach leverages IMU-derived motion parameters to model the temporal variation of optical signals during the DFT window, enabling instantaneous RSS estimation. The algorithm is embedded within both tightly and simply coupled VLP/INS integration frameworks that estimate the pose of the moving receiver. This work targets highly dynamic indoor navigation. Simulations validate the correction model, and total-station-tracked experiments confirm reduced RSS discrepancies against model references. Across eight held-out high-dynamic handheld trials with peak translational and angular speeds of 2.25 m/s and 284 deg/s, correction reduces the pooled 3D position and PD-normal inclination root mean square errors relative to the LiDAR/IMU reference with a shared IMU by 56.0% and 71.9%, respectively. Both datasets and source code are publicly available.

I. INTRODUCTION

PD-based VLP uses RSS from DFT processing, but during rapid receiver motion the resulting window-averaged signal differs from the instantaneous RSS assumed by positioning estimators. This work models that discrepancy and uses high-rate IMU motion estimates to correct RSS before fusion.

I. INTRODUCTION

  • Prior high-dynamic VLP studies focused mainly on image sensors, while this work targets motion-induced bias in windowed RSS from a single moving PD.The cited image-sensor work addressed blur, latency, or decoding, without proposing adaptation to PD systems.Source: §I · p. 1
  • DFT processing over a time window yields averaged rather than instantaneous RSS during rapid PD motion, creating a systematic discrepancy that degrades positioning accuracy.The signal varies within the window as receiver position and orientation change.Source: §I · p. 2
  • The proposed correction maps IMU-derived translation and rotation within the Fourier window to the difference between averaged and midpoint RSS before VLP/INS fusion.It can be inserted into tightly coupled or simple integration without adding states or graph factors.Source: §I · p. 2
  • The work releases high-dynamic VLP datasets with synchronized PD and IMU measurements and VLP/INS fusion code for reproducible evaluation.The stated coverage includes rapid attitude changes and fast running.Source: §I · p. 2

II. VISIBLE LIGHT POSITIONING AIDED WITH INS

The section presents the VLP/INS processing pipeline and the optical model used to relate LED signals to receiver pose. The Lambertian RSS model depends on position and the PD normal derived from receiver attitude.

A. System Overview

  • DFT separates known LED modulation frequencies to extract each LED’s RSS, while IMU integration supplies motion estimates for correction before either VLP/INS scheme estimates pose.The pipeline supports tightly coupled and simple integration.Source: A. System Overview · p. 2

B. Quaternion-based Lambertian Model

  • The received optical power follows a Lambertian model parameterized by irradiance and incidence angles, LED transmit power and Lambertian order, PD area, and LED-to-PD geometry.The PD normal and LED emission direction are defined upward in the stated ceiling-mounted configuration.Source: B. Quaternion-based Lambertian Model · p. 3
  • Receiver attitude determines the PD normal through a rotation matrix or Hamilton quaternion, providing the orientation representation used by the optical model.The quaternion is converted to the same rotation through the standard quaternion-to-DCM conversion.Source: B. Quaternion-based Lambertian Model · p. 3

C. Simple Integration of VLP and INS

Simple VLP/INS integration uses the INS-derived PD normal to solve for position, whereas the tightly coupled framework jointly estimates pose from RSS and IMU pre-integration. The correction is applied before residual construction without changing the backend state vector or graph structure.

C. Simple Integration of VLP and INS

  • Simple integration substitutes the INS-derived PD normal into the Lambertian model and solves for three position unknowns, provided LED geometry is adequate.At fixed position, rotation about the PD normal leaves instantaneous RSS unchanged, so RSS alone cannot recover all six pose degrees of freedom.Source: C. Simple Integration of VLP and INS · p. 3
  • Errors in the INS-derived PD normal propagate through the Lambertian model into the simple-integration position solution.This scheme therefore relies on the accuracy of that normal.Source: C. Simple Integration of VLP and INS · p. 3

D. Tightly Coupled VLP/INS Positioning

  • The tightly coupled backend jointly estimates position and attitude from epoch-wise RSS and IMU pre-integration, while the original formulation treats DFT-derived RSS as instantaneous.The sliding-window optimization combines IMU, RSS, and constraint residuals; the RSS correction precedes residual construction and leaves the state vector and graph structure unchanged.Source: D. Tightly Coupled VLP/INS Positioning · p. 3

III. RSS MEASUREMENT CORRECTION IN VLP

The section introduces an IMU-aided RSS correction that estimates the difference between DFT-window averages and instantaneous RSS. It builds on a Lambertian differential model, with a sign-convention adjustment relative to.

III. RSS MEASUREMENT CORRECTION IN VLP

  • High-frequency IMU measurements estimate the difference between DFT-averaged RSS and instantaneous RSS to correct motion-induced distortions.The corrected measurements are intended to address temporal averaging that degrades positioning accuracy in dynamic scenarios.Source: §III · pp. 3–4

A. Differential Form of Lambertian Model

  • The correction uses the Lambertian model’s differential response to position and angle disturbances as its starting point.The differential form is reused from with a sign-convention adjustment for the attitude perturbation.Source: A. Differential Form of Lambertian Model · p. 4

B. Mathematical Foundation of DFT Averaging Effect

The DFT amplitude is treated as an approximation to the optical envelope’s window average under stated signal conditions. The correction then estimates the average-to-midpoint RSS difference using motion propagated across the DFT window from IMU samples.

B. Mathematical Foundation of DFT Averaging Effect

  • The normalized DFT amplitude approximates the window-averaged envelope for a nonnegative, bin-aligned signal when its twice-modulation-frequency envelope projection is negligible.For tapered windows, the corresponding average is window-weighted.Source: B. Mathematical Foundation of DFT… · p. 4
  • Controlled single-tone tests show close agreement between DFT-derived amplitudes and window averages, with errors bounded by the neglected projection term.The reported support applies within the tested settings; parameter sweeps and projection-bound verification are in the supplementary material.Source: B. Mathematical Foundation of DFT… · p. 4

C. RSS Correction

  • The correction computes the difference between average RSS and midpoint RSS by integrating RSS variation over the DFT window.The discrete form uses IMU angular rate and integrated velocity to represent changing attitude and position; the uncorrected RSS is the DFT-derived average.Source: C. RSS Correction · pp. 4–5
  • Position and attitude are propagated within the Fourier window, while local RSS sensitivities and related quantities are updated at IMU timestamps.The PD trajectory is integrated from velocity and attitude from angular rate; the correction uses these sample-wise updates to account for changing optical geometry.Source: C. RSS Correction · p. 5
  • With a 1.0 s symmetric DFT window, assigning RSS to its midpoint requires a 0.5 s wait for the remaining samples before correction and fusion.The corrected observations are then held fixed during the subsequent solve.Source: C. RSS Correction · p. 5
  • The correction costs O(NM) operations without adding graph states, residual blocks, or Jacobian terms.Using fixed coefficients within the window can introduce approximately 80% correction error at 2 m/s and approximately 90% at 45°/s in the reported simulations.Source: C. RSS Correction · pp. 5–6

IV. RESULTS AND ANALYSIS

The evaluation examines whether RSS correction adds benefits beyond the VLP/INS backend, using pose, RSS, motion-intensity, window-selection, extraction-method, and physical-reference comparisons. The paper defines highly dynamic motion by a translational or angular-speed threshold, and notes that correction discrepancy depends on motion and optical geometry.

IV. RESULTS AND ANALYSIS

  • The evaluation spans pose errors, RSS correction accuracy, motion intensity, DFT window selection, alternative extraction methods, and physical validation.Physical references include LiDAR/IMU and independent total-station position measurements.Source: §IV · p. 6
  • Motion is classified as highly dynamic at translational speed of at least 1 m/s or angular speed above 30°/s, with either condition sufficient.The definition applies to simulations and physical experiments and includes rapid inclination changes at a fixed receiver position.Source: §IV · p. 6
  • The averaged-to-midpoint RSS discrepancy depends on receiver motion, PD-normal changes, LED geometry, and DFT window length.Source: §IV · p. 6

1) Simulation setup:

The simulation setup models a PD-and-IMU-equipped vehicle under optical and measurement effects, then tests correction across translational and rotational motion patterns. RSS is derived from simulated sampled photocurrent using DFT.

1) Simulation setup:

  • The simulations assume equal LED optical power and Lambertian order 1, and include reflections, PD measurement noise, and ADC quantization noise.The simulated 12-bit ADC generates 12,000 Hz PD-current samples with integer values from 0 to 4095.Source: 1) Simulation setup · p. 6
  • The simulated photocurrent is processed by DFT to obtain RSS, which is then corrected; RSS is reported in microcontroller-sampling LSB.Photoelectric signal conversion is not modeled.Source: 1) Simulation setup · p. 6
  • Two complementary scenarios test translational averaging during UAV motion and RSS averaging from rapid PD-normal changes at a fixed handheld-device position.The UAV follows circular motion at constant speed while ascending; the handheld device changes inclination rapidly in a 5 m × 5 m × 5 m scenario.Source: 1) Simulation setup · p. 6

2) RSS correction model validation:

The simulations validate RSS correction against instantaneous LOS references and examine its sensitivity to window length, IMU quality, and motion intensity. Correction improves positioning and inclination estimates in the tested translational and rapid-inclination scenarios, with its benefit and accuracy depending on motion and measurement conditions.

2) RSS correction model validation:

  • Pooled over five LEDs and 19 epochs, corrected RSS RMSE was 0.4762 LSB with the perturbation model and 0.4870 LSB with numerical correction, versus 0.9671 LSB uncorrected.The two correction predictions had a mutual RMSE of 0.0246 LSB; residual differences from the required correction reflect reflection, noise, and quantization in DFT observations.Source: 2) RSS correction model validation · p. 6, Figure 6 · p. 7

3) DFT window and IMU sensitivity:

  • A 1.0 s DFT window was selected to balance spectral separation and motion variation; corrected mean positioning error rose from 0.0425 m for IMU1 to 0.0789 m for noisier IMU5.Short 0.1 s windows were noisy, while 2.0 s windows reduced local-linearization accuracy; correction remained better than the uncorrected baseline across five IMU grades.Source: 3) DFT window and IMU sensitivity · pp. 6–7, Figure 7 · p. 7, Table I · p. 7

4) Translation and inclination tests:

  • Mean 3D position-error reduction increased from 30.8% at 1 m/s to 78.4% at 2.5 m/s, then was 76.9% at 3 m/s.These simulated circular-ascending-motion inputs used the same tightly coupled backend.Source: 4) Translation and inclination tests · p. 7, Figure 8 · p. 7
  • In Scenario 2’s rapid inclination changes at a fixed receiver position initialized at its true starting position, RSS correction reduced mean absolute pitch error from 4.703° to 0.498° and roll error from 4.323° to 0.875°.Source: 4) Translation and inclination tests · p. 7

5) RSS extraction methods and offline runtime:

The section compares corrected FFT RSS extraction with alternative methods, reports offline batch runtimes, and describes the real-world evaluation setup. The experiments use independent references and include eight held-out high-dynamic trials, with figures showing position and inclination errors relative to LiDAR/IMU tracking.

B. Real-world experiments

  • Figures report RSS correction across five extraction methods and eight held-out trials, including 3D position and PD-normal inclination errors relative to LiDAR/IMU; fast-running trajectories and errors share scales across trials.The held-out trials comprise attitude-variation trials A1–A3 and fast-running trials R1–R5.Source: Figure 9 · p. 8, Figure 11 · p. 8, Figure 12 · p. 9

5) RSS extraction methods and offline runtime:

  • Corrected FFT achieved the lowest pooled RSS RMSE at 0.5228 LSB, compared with 0.5440 LSB for BPF, 1.3536 LSB for STFT, and 2.2735 LSB for both short-window DFT and Goertzel.The comparison pooled 95 errors across five LEDs and 19 valid epochs against instantaneous LOS RSS.Source: 5) RSS extraction methods and offline… · p. 8, Figure 9 · p. 8
  • Corrected FFT processed the 20 s input in a median offline 0.0377 s, while BPF, short-window DFT, STFT, and Goertzel took 0.5637, 0.0046, 0.0368, and 0.0034 s, respectively.These batch times exclude per-update computation, end-to-end latency, acquisition waiting, and fusion optimization.Source: 5) RSS extraction methods and offline… · p. 8

B. Real-world experiments

  • The real-world evaluation uses synchronized PD and IMU datasets, total-station position and Lambertian RSS references, and LiDAR/IMU tracking for faster-motion pose evaluation.The campaigns used the same six-LED frequency configuration, 200 Hz IMU, and 1 s DFT windows, despite changes in room furnishings.Source: B. Real-world experiments · p. 8

1) Pose estimation under rapid motion:

Across held-out dynamic trials, RSS correction reduced position and PD-normal inclination errors relative to the LiDAR/IMU reference. Total-station-tracked trials also showed reduced RSS discrepancies and lower pooled positioning error with simple VLP/INS integration.

1) Pose estimation under rapid motion:

  • The eight held-out trials comprised three attitude-variation trials and five fast-running trials, with peak speeds of 2.25 m/s and 284°/s.The reference shares the IMU stream with VLP/INS, so errors measure reference agreement rather than independent absolute accuracy.Source: 1) Pose estimation under rapid motion · p. 9
  • Across 2,487 common epochs, 3D RMSE fell from 0.329 to 0.145 m (56.0% reduction) and inclination RMSE from 9.24° to 2.60° (71.9% reduction).The 95th-percentile 3D error decreased from 0.634 to 0.255 m.Source: 1) Pose estimation under rapid motion · p. 9

2) Total-station validation of RSS and positioning:

V. CONCLUSION

  • The correction addresses the difference between window-averaged DFT measurements and instantaneous RSS, and simulations and total-station measurements support its use during rapid motion.The conclusion reports reductions of 56.0% and 71.9% in position and inclination RMSE relative to the LiDAR/IMU reference.Source: §V · p. 10

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